11.3: Enthalpy- Introduction
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- Scott Van Bramer
- Widener University
Learning Objectives
- State the first law of thermodynamics
- Define enthalpy and explain its classification as a state function
- Write and balance thermochemical equations
- Calculate enthalpy changes for various chemical reactions
- Explain Hess’s law and use it to compute reaction enthalpies
Thermochemistry is a branch of chemical thermodynamics , the science that deals with the relationships between heat, work, and other forms of energy in the context of chemical and physical processes. As we concentrate on thermochemistry in this chapter, we need to consider some widely used concepts of thermodynamics.
Substances act as reservoirs of energy, meaning that energy can be added to them or removed from them. Energy is stored in a substance when the kinetic energy of its atoms or molecules is raised. The greater kinetic energy may be in the form of increased translations (travel or straight-line motions), vibrations, or rotations of the atoms or molecules. When thermal energy is lost, the intensities of these motions decrease and the kinetic energy falls. The total of all possible kinds of energy present in a substance is called the internal energy ( U ) , sometimes symbolized as E .
As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system. Energy is transferred into a system when it absorbs heat ( q ) from the surroundings or when the surroundings do work ( w ) on the system. For example, energy is transferred into room-temperature metal wire if it is immersed in hot water (the wire absorbs heat from the water), or if you rapidly bend the wire back and forth (the wire becomes warmer because of the work done on it). Both processes increase the internal energy of the wire, which is reflected in an increase in the wire’s temperature. Conversely, energy is transferred out of a system when heat is lost from the system, or when the system does work on the surroundings.
The relationship between internal energy, heat, and work can be represented by the equation:
\[ΔU=q+w \]
as shown in Figure \(\PageIndex{1}\). This is one version of the first law of thermodynamics, and it shows that the internal energy of a system changes through heat flow into or out of the system (positive q is heat flow in; negative q is heat flow out) or work done on or by the system. The work, w , is positive if it is done on the system and negative if it is done by the system.
A type of work called expansion work (or pressure-volume work) occurs when a system pushes back the surroundings against a restraining pressure, or when the surroundings compress the system. An example of this occurs during the operation of an internal combustion engine. The reaction of gasoline and oxygen is exothermic. Some of this energy is given off as heat, and some does work pushing the piston in the cylinder. The substances involved in the reaction are the system, and the engine and the rest of the universe are the surroundings. The system loses energy by both heating and doing work on the surroundings, and its internal energy decreases. (The engine is able to keep the car moving because this process is repeated many times per second while the engine is running.) We will consider how to determine the amount of work involved in a chemical or physical change in the chapter on thermodynamics.
As discussed, the relationship between internal energy, heat, and work can be represented as Δ U = q + w . Internal energy is a type of quantity known as a state function (or state variable), whereas heat and work are not state functions. The value of a state function depends only on the state that a system is in, and not on how that state is reached. If a quantity is not a state function, then its value does depend on how the state is reached. An example of a state function is altitude or elevation. If you stand on the summit of Mt. Kilimanjaro, you are at an altitude of 5895 m, and it does not matter whether you hiked there or parachuted there. The distance you traveled to the top of Kilimanjaro, however, is not a state function. You could climb to the summit by a direct route or by a more roundabout, circuitous path (Figure \(\PageIndex{2}\)). The distances traveled would differ (distance is not a state function) but the elevation reached would be the same (altitude is a state function).
Enthalpy
Chemists ordinarily use a property known as enthalpy (\(H\)) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum of a system’s internal energy (\(U\)) and the mathematical product of its pressure (\(P\)) and volume (\(V\)):
\[H=U+PV \]
Since it is derived from three state functions (\(U\), \(P\), and \(V\)), enthalpy is also a state function. Enthalpy values for specific substances cannot be measured directly; only enthalpy changes for chemical or physical processes can be determined. For processes that take place at constant pressure (a common condition for many chemical and physical changes), the enthalpy change (\(ΔH\)) is:
\[ΔH=ΔU+PΔV \]
The mathematical product \(PΔV\) represents work (\(w\)), namely, expansion or pressure-volume work as noted. By their definitions, the arithmetic signs of ΔV and w will always be opposite:
\[PΔV=−w \]
Combining these equations yields:
\[ \begin{align} ΔH&=ΔU+PΔV \\[4pt] &=q_\ce{p}+\cancel{w}−\cancel{w} \\[4pt] &=q_\ce{p} \end{align}\]
where \(q_p\) is the heat of reaction under conditions of constant pressure.
And so, if a chemical or physical process is carried out at constant pressure with the only work done caused by expansion or contraction, then the heat flow (\(q_\ce{p}\)) and enthalpy change (\(ΔH\)) for the process are equal.
The heat given off when you operate a Bunsen burner is equal to the enthalpy change of the methane combustion reaction that takes place, since it occurs at the essentially constant pressure of the atmosphere. On the other hand, the heat produced by a reaction measured in a bomb calorimeter is not equal to \(ΔH\) because the closed, constant-volume metal container prevents expansion work from occurring. Chemists usually perform experiments under normal atmospheric conditions, at constant external pressure with \(q = ΔH\), which makes enthalpy the most convenient choice for determining heat.
Using Enthalpy
The following conventions apply when we use \(ΔH\):
- Chemists use a thermochemical equation to represent the changes in both matter and energy. In a thermochemical equation, the enthalpy change of a reaction is shown as a Δ H value following the equation for the reaction. This \(ΔH\) value indicates the amount of heat associated with the reaction involving the number of moles of reactants and products as shown in the chemical equation. For example, consider this equation: \[\ce{H2(g) + 1/2 O2(g) ⟶ H2O (l)} \;\; ΔH=\mathrm{−286\:kJ} \label{5.4.6}\] This equation indicates that when 1 mole of hydrogen gas and 12 mole of oxygen gas at some temperature and pressure change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released to the surroundings. If the coefficients of the chemical equation are multiplied by some factor, the enthalpy change must be multiplied by that same factor (ΔH is an extensive property).
\[\begin {align*} &\textrm{(two-fold increase in amounts)}\label{5.4.7}\\ &\ce{2H2}(g)+\ce{O2}(g)⟶\ce{2H2O}(l)\hspace{20px}ΔH=\mathrm{2×(−286\:kJ)=−572\:kJ}\\ &\textrm{(two-fold decrease in amounts)}\\ &\frac{1}{2}\ce{H2}(g)+\dfrac{1}{4}\ce{O2}(g)⟶\frac{1}{2}\ce{H2O}(l)\hspace{20px}ΔH=\mathrm{\frac{1}{2}×(−286\:kJ)=−143\:kJ} \end {align*} \]
- The enthalpy change of a reaction depends on the physical state of the reactants and products of the reaction (whether we have gases, liquids, solids, or aqueous solutions), so these must be shown. For example, when 1 mole of hydrogen gas and 12 mole of oxygen gas change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released. If gaseous water forms, only 242 kJ of heat are released.
\[\ce{ H2(g) + 1/2 O2(g) ⟶ H2O(g)} \;\;\; ΔH=\ce{−242\:kJ} \]
- A negative value of an enthalpy change, Δ H , indicates an exothermic reaction; a positive value of Δ H indicates an endothermic reaction. If the direction of a chemical equation is reversed, the arithmetic sign of its Δ H is changed (a process that is endothermic in one direction is exothermic in the opposite direction).
Example \(\PageIndex{1}\): Measurement of an Enthalpy Change
When 0.0500 mol of HCl( aq ) reacts with 0.0500 mol of NaOH( aq ) to form 0.0500 mol of NaCl( aq ), 2.9 kJ of heat are produced. What is ΔH, the enthalpy change, per mole of acid reacting, for the acid-base reaction run under the conditions described ?
\[\ce{HCl (aq) + NaOH(aq) \rightarrow NaCl (aq) + H2O(l)} \nonumber \]
Solution
For the reaction of 0.0500 mol acid (HCl), q = −2.9 kJ. This ratio
\[\mathrm{\dfrac{−2.9 \; kJ}{0.0500\; mol\; HCl}} \nonumber\]
can be used as a conversion factor to find the heat produced when 1 mole of HCl reacts:
\[ΔH =\mathrm{1\; \cancel{mol\; HCl} \times \dfrac{ −2.9\; kJ}{0.0500 \;\cancel{ mol\; HCl}} =−58\; kJ} \nonumber\]
The enthalpy change when 1 mole of HCl reacts is −58 kJ. Since that is the number of moles in the chemical equation, we write the thermochemical equation as:
\[\ce{HCl}_{(aq)}+\ce{NaOH}_{(aq)}⟶\ce{NaCl}_{(aq)}+\ce{H_2O}_{(l)} \;\;\; ΔH=\mathrm{−58\;kJ} \nonumber\]
Exercise \(\PageIndex{1}\)
When 1.34 g Zn(s) reacts with 60.0 mL of 0.750 M HCl(aq), 3.14 kJ of heat are produced. Determine the enthalpy change per mole of zinc reacting for the reaction:
\[ \ce{Zn}_{(s)}+\ce{2HCl}_{(aq)}⟶\ce{ZnCl}_{(aq)}+\ce{H}_{2(g)} \nonumber\]
- Answer
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ΔH = −153 kJ
\(ΔH^\circ_{combustion}\), \(ΔH^\circ_{formation}\), \(ΔH^\circ_{fusion}\), \(ΔH^\circ_{vaporization}\)
Be sure to take both stoichiometry and limiting reactants into account when determining the Δ H for a chemical reaction.
Enthalpy changes are tabulated for a variety of different processes including combustion, formation, fusion, and vaporization. For these tabulated values the reactions are under a standard set of conditions . The IUPAC standard state is for materials at a pressure of 1 bar and solutions at a concentration of 1 M. Many thermochemical tables list values at a pressure of 1 atm, which was previously used as the standard state. Fortunately Δ H values do not change much with pressure and the new standard is close to 1 atm (1 bar = 0.987 atm). The superscripted “o” in the enthalpy change symbol designates that the value is at standard conditions.
The enthalpy changes for many types of chemical and physical processes are available in the reference literature, including those for combustion reactions, phase transitions, and formation reactions. As we discuss these quantities, it is important to remember enthalpy is an extensive property - the amount of material matters. The tabulated enthalpy values are typically listed per-mole or per-gram. You must take this into account for any calculations. For enthalpy calculations with chemical reactions you must also take the stoichiometry and limiting reactants into account for Δ H calculations.
Summary
If a chemical change is carried out at constant pressure and the only work done is caused by expansion or contraction, q for the change is called the enthalpy change with the symbol Δ H , or \(ΔH^\circ \) for reactions occurring under standard state conditions. The value of Δ H for a reaction in one direction is equal in magnitude, but opposite in sign, to Δ H for the reaction in the opposite direction. And Δ H is directly proportional to the quantity of reactants and products.
Key Equations
- \(ΔU=q+w\)
- \(ΔH^\circ_\ce{reaction}=∑n×ΔH^\circ_\ce{f}\ce{(products)}−∑n×ΔH^\circ_\ce{f}\ce{(reactants)}\)
Glossary
- chemical thermodynamics
- area of science that deals with the relationships between heat, work, and all forms of energy associated with chemical and physical processes
- enthalpy ( H )
- sum of a system’s internal energy and the mathematical product of its pressure and volume
- enthalpy change (Δ H )
- heat released or absorbed by a system under constant pressure during a chemical or physical process
- expansion work (pressure-volume work)
- work done as a system expands or contracts against external pressure
- first law of thermodynamics
- internal energy of a system changes due to heat flow in or out of the system or work done on or by the system
- Hess’s law
- if a process can be represented as the sum of several steps, the enthalpy change of the process equals the sum of the enthalpy changes of the steps
- hydrocarbon
- compound composed only of hydrogen and carbon; the major component of fossil fuels
- internal energy ( U )
- total of all possible kinds of energy present in a substance or substances
- standard enthalpy of combustion (\(ΔH^\circ_\ce{c}\))
- heat released when one mole of a compound undergoes complete combustion under standard conditions
- standard enthalpy of formation (\(ΔH^\circ_\ce{f}\))
- enthalpy change of a chemical reaction in which 1 mole of a pure substance is formed from its elements in their most stable states under standard state conditions
- standard state
- set of physical conditions as accepted as common reference conditions for reporting thermodynamic properties; 1 bar of pressure, and solutions at 1 molar concentrations, usually at a temperature of 298.15 K
- state function
- property depending only on the state of a system, and not the path taken to reach that state
Contributors and Attributions
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Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


12.4: Assignment- Managerial Decisions
This assignment is available for download as a Word Document .
Read the following scenario and complete the questions and tasks below.
Marquette Manufacturing produces “invisible” electric dog fences, sold through retail locations nationwide. The selling price of the fence is $150 per unit. The cost to manufacture and market the fences is shown below. These figures represent the cost at the company’s normal volume of 3,000 units per month.
| Unit Manufacturing Costs | |
|---|---|
| Variable materials | $ 15.00 |
| Variable labor | $ 17.50 |
| Variable overhead | $ 12.50 |
| Fixed overhead | $ 16.00 |
| Total unit manufacturing costs | $ 61.00 |
| Unit Marketing Costs | |
| Variable | $ 12.00 |
| Fixed overhead | $ 17.00 |
| Total unit marketing costs | $ 29.00 |
| Total Unit Costs | $ 90.00 |
(NOTE: Unless otherwise stated, assume that no connection exists between the situation described in each question; each is independent. Also, ignore taxes or other costs not specifically mentioned in the questions.)
- The company’s marketing team estimates that sales volume could be increased to 5,000 units per month if the sales price was lowered from $150 to $125 per unit. The production manager has confirmed that they have the capacity to increase production to this level. Assume that the cost pattern will not vary at the increased level of production. If management decreases the price, what would the impact on monthly sales, income and costs be? For each figure, indicate whether the change will result in an increase, decrease or no change in the sales, income and cost. Would you recommend the reduction in sales price? Why or Why not? (Show all supporting calculations).
- At the end of the year the production manager is taking inventory and finds 600 units of an older model of invisible fencing that the company no longer manufactures. These obsolete units can be disposed of through their regular channels, thereby incurring variable marketing expenses. What is the lowest price that they should accept for these obsolete units, realizing that if they do not sell them these units will have to be thrown away. (Show all supporting calculations).
- Marquette receives a proposal from an outside contractor who offers to make and ship 1,500 fences directly to Marquette’s customers as orders arrive from Marquette’s sales force. When managers meet to discuss this proposal, Product Manager Will Hansen brings up the fact that they have the design for an electric fence that can be used for large animals that has never been produced. Will suggests that this may be the perfect time to launch this new product and at a selling price of $225 per unit it is sure to increase sales revenue. The production manager calculates that the idle time created by accepting the contractors offer would allow them to produce 1,000 of the new fence. The cost to produce the new fence would be $175 in variable manufacturing expense but fixed manufacturing and marketing costs would remain unchanged. The product mix would now be 1,000 of the new fence and 1,500 of the old fence. If Marquette wants to seriously consider taking the contractors offer, what in-house cost should be used to evaluate the outside contractor’s bid. If the payment to the outside contractor is $90 per unit, should they accept the offer? Why or why not? (Show all supporting calculations).
- On March 1, Marquette is approached by the developer of a large subdivision who wants to install an invisible fence in the yard of 1,200 homes he is constructing. The developer will contract with Marquette for the 1,200 fences on the condition that they are delivered within 30 days (March 31). This is not good timing for Marquette since they have recently signed a contract with Home Warehouse, a national home improvement chain and have been working at 100% capacity for several months. If Marquette accepts the builder’s order, it will lose 1,200 units that would normally be sold to one of its existing customers. When they tell the developer that they do not believe they can fill his order, he offers to reimburse the company for his “share” of the fixed manufacturing costs and will pay a $5,000 “bonus” on delivery. Since the sale to the developer will not incur any variable marketing costs, Marquette reconsiders accepting the developer’s order. What impact will accepting this order have on Marquette’s income in March? Should Marquette accept the order from the developer? Why or Why not? (Show all supporting calculations).
- Marquette has an opportunity to sell its product through an online retailer. To begin selling through this online platform, they are required to ship 2,000 units to the retailers’ order fulfillment warehouse. The other condition of this offer is that they pay a one-time vendor marketing fee of $5,000. To get the units to the fulfillment warehouse by the deadline Marquette will need to pay for expedited shipping at a cost of $10 per unit. What is the minimum price Marquette should charge the retailer for this initial order of 2,000 units? (Show all supporting calculations).


5.5: Concluding Futures?
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- Vicki Mayer
- University of California Press
Despite the added compensation, both material and symbolic, that Treme provided its workforce, the production demanded a lot from its eager extras. In making the series speak to the worthiness of the city’s recovery and renewal, producers sought extras who could speak to New Orleanians and for New Orleanians. Extras had to be highly invested in those vernacular details that made up Treme ’s carefully crafted mise-en-scène. The moral politics of recognition as a worker depended on whether extras could act both as referents and as bards for the place known as New Orleans. These roles could involve more labor, often for no payment, but they also raised the specter of reification when a musical number took front stage, leaving the performances of the extras in the background. In its most extreme formulation, the labor of being an extra could be framed as a gift, which perhaps unavoidably led to hurt feelings when the gift was not recognized or reciprocated.
None of these aspects of extras’ labor are registered in the quantitative analyses of jobs produced by film tax credit policies. They do, however, add nuance to the terms local and labor , which motivated these policies as well as provided fodder for both political consensus and critiques. The strategies that production companies, such as Treme ’s Fee Nah Nee, use to be more moral and just while holding the bottom line may ultimately result in other costs. If the production includes only individuals with enough free time to do the work, either paid or unpaid, then the policies cannot be said to be building toward sustainable economies. In fact, it could be that the presence of so many extras with entitlement helps drive down the day rates of those who lack the time or the proper social networks to be desirable employees in the future. At the same time, the role of production companies in promoting themselves as instruments of urban economic recovery merely furthers the notion that private companies are the best managers of the public good. In an era of endless crises—political and economic—it is worth remembering that film production companies’ reliance on cheap or free labor undermines the economic bases for public services that all workers need, such as decent public schools, health care, and wages that bring the majority above the subsistence level. Until these needs are integrated more seamlessly into the New Orleans film economy, it will be no wonder if production companies continue to put their most marginal workers at the center of their most moral employment strategies.


18.4: Beta-Adrenergic Blockers
By the end of this section, you should be able to:
- 18.4.1 Identify the characteristics of the beta-adrenergic blocker drugs used to treat hypertension.
- 18.4.2 Explain the indications, actions, adverse reactions, and interactions of the beta-adrenergic blocker drugs used to treat hypertension.
- 18.4.3 Describe nursing implications of beta-adrenergic blocker drugs used to treat hypertension.
- 18.4.4 Explain the client education related to beta-adrenergic blocker drugs used to treat hypertension.
Introduction and Use
Beta-adrenergic blockers (beta blockers) are a classification of drugs that inhibit chronotropic, inotropic, and vasoconstrictor response to catecholamine—such as epinephrine and norepinephrine—by exerting effects on adrenergic receptors beta 1, beta 2, and alpha.
Beta 1 receptors are found primarily in the heart and kidneys, and they increase the heart rate, myocardial activity, and release of renin. Beta 2 receptors are found in the smooth muscle tissue of the heart, lungs, and nervous system and increase myocardial contractility and cause muscle tremors. Alpha receptors stimulate vasoconstriction.
Beta blockers are classified as either nonselective or cardio-selective. Nonselective beta blockers affect both beta 1 and beta 2 and act on the cardiovascular and respiratory systems. Cardio-selective beta blockers, in contrast, affect beta 1, which impacts the cardiovascular system (Tucker et al., 2022).
Beta blockers decrease heart rate, decrease myocardial contractility, and decrease the rate of conduction through the atrioventricular (AV) node, thereby lowering blood pressure and heart rate. Beta blockers also cause vasodilation and decrease the release of renin and angiotensin II, promoting excretion of sodium and water from the body. Beta blockers are relatively safe for use. Beta blockers treat clients with hypertension, heart failure, arrhythmias, myocardial infarctions, migraines, glaucoma, and certain types of tremors. Beta blockers have also been used by health care providers as anxiolytics (to reduce anxiety).
Most beta blockers are taken orally. Labetalol, metoprolol, and propranolol can be administered intravenously. Extended-release beta blockers should not be crushed. Nurses should monitor blood pressure and pulse rate of clients using beta blockers. Beta blockers should not be administered if the client is hypotensive or has a heart rate of less than 60 (Farzam & Jan, 2022).
Special Considerations
Beta Blockers
Beta blockers pose an ethical dilemma for health care providers because they cause anxiolytic effects. The FDA, however, does not support this use for beta blockers. The health care provider may prescribe beta blockers off-label (against FDA-approved labeling indications for drug use) for anxiety. Therefore, the prescribed use of beta blockers for anxiolysis should be weighed against standards of practice as well as risks and benefits to the client.
(Source: Shahrokhi & Gupta, 2023)
Beta blockers may mask low blood sugar levels in clients with diabetes due to sympathetic nervous system inhibition.
(Source: Dungan et al., 2019)
Asthmatic clients and clients with chronic lung diseases should be monitored carefully while taking beta blockers because lung function can decrease due to beta 2 inhibition.
(Source: Huang et al., 2021)
Table 18.7 lists common beta blockers and typical routes and dosing for adult clients.
| Drug | Routes and Dosage Ranges |
|---|---|
|
Atenolol
( Tenormin ) |
50 mg orally daily, either alone or with diuretic therapy. If optimal response is not achieved, the dosage should increase to 100 mg orally daily. Dosage beyond 100 mg a day is unlikely to produce any further benefit. |
|
Carvedilol
( Coreq ) |
6.25–25 mg orally twice daily; maximum dose 25 mg daily. |
|
Metoprolol tartrate
( Lopressor ) |
Initial dosage:
100 mg orally daily in single or divided doses. Increase dosage at weekly (or longer) intervals until optimum blood pressure reduction is achieved.
Effective dosage: 100–450 mg daily. |
|
Nadolol
( Corgard ) |
40–320 mg orally daily. |
|
Propranolol
( Inderal LA ) |
40 mg orally twice daily; maximum dose 640 mg daily. |
Adverse Effects and Contraindications
Adverse effects of beta blockers are dizziness, fatigue, weight gain, constipation, cold hands and feet, hypercholesterolemia, shortness of breath, depression, nausea, dry mouth, and dry eyes. Serious adverse effects include bradycardia, arrhythmias, hypoglycemia, and hypotension. Rare side effects include sexual and erectile dysfunction.
Beta blockers are contraindicated in clients with moderate to severe asthma and/or chronic lung diseases due to the potential for causing an exacerbation. Beta blockers should be used cautiously in clients with AV node and sinus bradycardia because they can aggravate these conditions. Beta blockers may exacerbate symptoms of Raynaud’s phenomenon or cause this disease process in clients. People with diabetes should use beta blockers cautiously because they can mask the symptoms of hypoglycemia, causing confusion, fainting, or seizures.
Table 18.8 is a drug prototype table for beta-adrenergic blockers featuring metoprolol tartrate. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Beta-adrenergic blocker Mechanism of Action Blocks beta 1 receptors, thereby decreasing cardiac workload by slowing the heart and decreasing the systolic blood pressure |
Drug Dosage
Initial dosage: 100 mg orally daily in single or divided doses. Increased dosage at weekly (or longer) intervals until optimum blood pressure reduction is achieved. Effective dosage: 100–450 mg daily. |
|
Indications
To control hypertension In the treatment of angina, acute myocardial infarction, and heart failure Therapeutic Effects Lowers blood pressure Decreases cardiac workload |
Drug Interactions
Albuterol Clonidine Mefloquine Calcium channel blockers Ma-huang Ephedra Black cohosh Hawthorne Food Interactions Caffeine Alcohol Tobacco Licorice |
|
Adverse Effects
Fatigue/weakness Dizziness Headache Hypotension Blurred vision Dry mouth Nausea/vomiting/diarrhea Drowsiness/insomnia Tinnitus Peripheral edema Erectile dysfunction |
Contraindications
Hypersensitivity AV block Cardiogenic shock Hypotension Acute heart failure Bradycardia Sick sinus syndrome Severe peripheral arterial circulatory disorders Caution: Thyroid impairment Hepatic impairment Asthma Peripheral vascular disease Diabetes mellitus Chronic obstructive pulmonary disease (COPD) Cerebrovascular disease |
Clinical Tip
Assessing Comorbidities: Asthma, Chronic Obstructive Pulmonary Disease, and Diabetes
Nurses should always assess a client’s comorbidities—such as asthma, COPD, and diabetes—before administering beta blocker drugs. To prevent a pharmacological drug interaction, the nurse must assess whether clients are taking short-acting beta agonists (SABAs) because beta blockers can reduce their effectiveness. Additionally, nurses should be aware that beta blockers can mask the symptoms of hypoglycemia in clients with diabetes.
Nursing Implications
The nurse should do the following for clients who are taking beta-adrenergic blockers:
- Assess the client’s blood pressure and pulse on an ongoing basis with initial dosing and intermittently during drug therapy.
- Do not administer the drug if the client’s heart rate is less than 60 beats per minute and notify the health care provider.
- Assess and monitor the client for adverse effects, drug and food interactions, and contraindications.
- Provide client teaching regarding the drug and when to call the health care provider. See below for client teaching guidelines.
Client Teaching Guidelines
The client taking a beta-adrenergic blocker should:
- Take their pulse as directed before taking a beta-adrenergic blocker and do not administer the drug if the pulse is less than 60 beats/minute or as directed by their health care provider.
- Understand that beta-adrenergic blockers can induce hyperglycemia. Clients with diabetes should monitor blood glucose levels closely.
- Take this medication without regard to meals.
- Report side effects such as bradycardia, hypotension, fatigue, dizziness, constipation, or sexual dysfunction to their health care provider.
- Monitor for symptoms of worsening heart failure such as fatigue, weight gain, and peripheral edema.
The client taking a beta-adrenergic blocker should not:
- Take beta-adrenergic blockers with over-the-counter (OTC) drugs or herbal supplements such as ma-huang, ephedra, black cohosh, hawthorn, or licorice without consulting their health care provider because these supplements may interfere with the action of the beta-adrenergic blocker.
- Discontinue use without speaking with the health care provider first because this may cause exacerbation of angina and myocardial infarction.
FDA Black Box Warning
Beta-Adrenergic Blockers
Beta blocker therapy should not be abruptly stopped but gradually tapered to avoid exacerbation of angina and myocardial infarction. Seek health care provider advice before discontinuing use.


6.8: Baire Categories. More on Linear Maps
We pause to outline the theory of so-called sets of Category I or Category II, as introduced by Baire. It is one of the most powerful tools in higher analysis. Below, \((S, \rho)\) is a metric space.
A set \(A \subseteq(S, \rho)\) is said to be nowhere dense (in \(S)\) iff its closure \(\overline{A}\) has no interior points (i.e., contains no globes): \((\overline{A})^{0}=\emptyset\).
Equivalently, the set \(A\) is nowhere dense iff every open set \(G^{*} \neq \emptyset\) in \(S\) contains a globe \(\overline{G}\) disjoint from \(A.\) (Why?)
A set \(A \subseteq(S, \rho)\) is meagre, or of Category I (in \(S),\) iff
\[A=\bigcup_{n=1}^{\infty} A_{n},\]
for some sequence of nowhere dense sets \(A_{n}\).
Otherwise, \(A\) is said to be nonmeagre or of Category II.
\(A\) is residual iff \(-A\) is meagre, but \(A\) is not.
(a) \(\emptyset\) is nowhere dense.
(b) Any finite set in a normed space \(E\) is nowhere dense.
(c) The set \(N\) of all naturals in \(E^{1}\) is nowhere dense.
(d) So also is Cantor's set \(P\) (Problem 17 in Chapter 3, §14); indeed, \(P\) is closed \((P=\overline{P})\) and has no interior points (verify!), so \((\overline{P})^{0}=P^{0}=\emptyset\).
(e) The set \(R\) of all rationals in \(E^{1}\) is meagre; for it is countable (see Chapter 1, §9), hence a countable union of nowhere dense singletons {\(r_{n}\)}, \(r_{n} \in R.\) But \(R\) is not nowhere dense; it is even dense in \(E^{1},\) since \(\overline{R}=E^{1}\) (see Definition 2, in Chapter 3, §14). Thus a meagre set need not be nowhere dense. (But all nowhere dense sets are meagre why?)
Examples (c) and (d) show that a nowhere dense set may be infinite (even uncountable). Yet, sometimes nowhere dense sets are treated as "small" or "negligible," in comparison with other sets. Most important is the following theorem.
In a complete metric space \((S, \rho),\) every open set \(G^{*} \neq \emptyset\) is nonmeagre. Hence the entire space \(S\) is residual.
- Proof
-
Seeking a contradiction, suppose \(G^{*}\) is meagre, i.e.,
\[G^{*}=\bigcup_{n=1}^{\infty} A_{n}\]
for some nowhere dense sets \(A_{n}.\) Now, as \(A_{1}\) is nowhere dense, \(G^{*}\) contains a closed globe
\[\overline{G}_{1}=\overline{G_{x_{1}}\left(\delta_{1}\right)} \subseteq-A_{1}.\]
Again, as \(A_{2}\) is nowhere dense, \(G_{1}\) contains a globe
\[\overline{G}_{2}=\overline{G_{x_{2}}\left(\delta_{2}\right)} \subseteq-A_{2}, \quad \text { with } 0<\delta_{2} \leq \frac{1}{2} \delta_{1}.\]
By induction, we obtain a contracting sequence of closed globes
\[\overline{G}_{n}=\overline{G_{x_{n}}\left(\delta_{n}\right)}, \quad \text { with } 0<\delta_{n} \leq \frac{1}{2^{n}} \delta_{1} \rightarrow 0.\]
As \(S\) is complete, so are the \(\overline{G}_{n}\) (Theorem 5 in Chapter 3, §17). Thus, by Cantor's theorem (Theorem 5 of Chapter 4, §6), there is
\[p \in \bigcap_{n=1}^{\infty} \overline{G}_{n}.\]
As \(G^{*} \supseteq \overline{G}_{n},\) we have \(p \in G^{*}.\) But, as \(\overline{G}_{n} \subseteq-A_{n},\) we also have \((\forall n) p \notin A_{n}\) ; hence
\[p \notin \bigcup_{n=1}^{\infty} A_{n}=G^{*}\]
(the desired contradiction!).\(\quad \square\)
We shall need a lemma based on Problems 15 and 19 in §7. (Review them!)
Let \(f \in L\left(E^{\prime}, E\right), E^{\prime}\) complete. Let \(G=G_{0}(1)\) be the unit globe in \(E^{\prime}.\) If \(\overline{f[G]}\) (closure of \(f[G]\) in \(E\) ) contains a globe \(G_{0}=G_{0}(r) \subset E,\) then \(G_{0} \subseteq f[G].\)
Note. Recall that we "arrow" only vectors from \(E^{\prime}\) (e.g., \(\overrightarrow{0}),\) but not those from \(E\) (e.g., 0).
- Proof
-
Let \(A=f[G] \cap G_{0} \subseteq G_{0}.\) We claim that \(A\) is dense in \(G_{0};\) i.e., \(G_{0} \subseteq \overline{A}.\) Indeed, by assumption, any \(q \in G_{0}\) is in \(f[G].\) Thus by Theorem 3 in Chapter 3, §16, any \(G_{q}\) meets \(f[G] \cap G_{0}=A\) if \(q \in G_{0}.\) Hence
\[\left(\forall q \in G_{0}\right) \quad q \in \overline{A},\]
i.e., \(G_{0} \subseteq \overline{A},\) as claimed.
Now fix any \(q_{0} \in G_{0}=G_{0}(r)\) and a real \(c(0<c<1).\) As \(A\) is dense in \(G_{0}\),
\[A \cap G_{q_{0}}(c r) \neq \emptyset;\]
so let \(q_{1} \in A \cap G_{q_{0}}(c r) \subseteq f[G].\) Then
\[\left|q_{1}-q_{0}\right|<c r, \quad q_{0} \in G_{q_{1}}(c r).\]
As \(q_{1} \in f[G],\) we can fix some \(\vec{p}_{1} \in G=G_{0}(1),\) with \(f\left(\vec{p}_{1}\right)=q_{1}.\) Also, by Problems 19(iv) and 15(iii) in §7, \(c A+q_{1}\) is dense in \(c G_{0}+q_{1}=G_{q_{1}}(c r)\). But \(q_{0} \in G_{q_{1}}(cr)\). Thus
\[G_{q_{0}}\left(c^{2} r\right) \cap\left(c A+q_{1}\right) \neq \emptyset;\]
so let \(q_{2} \in G_{q_{0}}\left(c^{2} r\right) \cap\left(c A+q_{1}\right),\) so \(q_{0} \in G_{q_{2}}\left(c^{2} r\right),\) etc.
Inductively, we fix for each \(n>1\) some \(q_{n} \in G_{q_{0}}\left(c^{n} r\right),\) with
\[q_{n} \in c^{n-1} A+q_{n-1},\]
i.e.,
\[q_{n}-q_{n-1} \in c^{n-1} A.\]
As \(A \subseteq f\left[G_{0}(1)\right],\) linearity yields
\[q_{n}-q_{n-1} \in f\left[c^{n-1} G_{0}(1)\right]=f\left[G_{0}\left(c^{n-1}\right)\right], \quad n>1.\]
Thus for each \(n>1,\) there is \(\vec{p}_{n} \in G_{0}(c^{n-1})\), (i.e., \(|\vec{p}_{n}|<c^{n-1})\) such that \(f(\vec{p}_{n})=q_{n}-q_{n-1}.\) Now, as \(|\vec{p}_{n}|<c^{n-1}\) and \(0<c<1\),
\[\sum_{1}^{\infty}\left|\vec{p}_{n}\right|<+\infty;\]
so by the completeness of \(E^{\prime}, \sum \vec{p}_{n}\) converges in \(E^{\prime}\) (Theorem 1 in Chapter 4, §13). Let \(\vec{p}=\sum_{k=1}^{\infty} \vec{p}_{k};\) then
\[\begin{aligned} f(\vec{p}) &=f\left(\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \vec{p}_{k}\right)=\lim _{n \rightarrow \infty} f\left(\sum_{k=1}^{n} \vec{p}_{k}\right) \\ &=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} f\left(\vec{p}_{k}\right) \text { for } f \in L\left(E^{\prime}, E\right). \end{aligned}\]
But \(f(\vec{p}_{k})=q_{k}-q_{k-1}(k>1),\) and \(f(\vec{p}_{1})=q_{1};\) so
\[\sum_{k=1}^{n} f\left(\vec{p}_{k}\right)=q_{1}+\sum_{k=2}^{n}\left(q_{k}-q_{k-1}\right)=q_{n}.\]
Thus
\[f(\vec{p})=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} f\left(\vec{p}_{k}\right)=\lim _{n \rightarrow \infty} q_{n}=q_{0}.\]
Moreover, \(\left|\vec{p}_{k}\right|<c^{k-1}(k \geq 1).\) Thus
\[|\vec{p}| \leq \sum_{k=1}^{\infty}\left|\vec{p}_{k}\right|<\sum_{k=1}^{\infty} c^{k-1}=\frac{1}{1-c};\]
i.e.,
\[\vec{p} \in G_{\overrightarrow{0}}\left(\frac{1}{1-c}\right).\]
But \(q_{0}=f(\vec{p});\) so
\[q_{0} \in f\left[G_{\overrightarrow{0}}\left(\frac{1}{1-c}\right)\right].\]
As \(q_{0} \in G_{0}(r)\) was arbitrary, we have
\[G_{0}(r) \subseteq f\left[G_{0}\left(\frac{1}{1-c}\right)\right],\]
or by linearity,
\[G_{0}(r(1-c)) \subseteq f\left[G_{0}(1)\right]=f[G].\]
This holds for any \(c \in(0,1).\) Hence
\[f[G] \supseteq \bigcup_{0<c<1} G_{0}(r(1-c))=G_{0}(r). \quad \text {(Verify!)}\]
Thus all is proved.\(\quad \square\)
We can now establish an important result due to S. Banach.
Let \(f \in L\left(E^{\prime}, E\right),\) with \(E^{\prime}\) complete. Then \(f\left[E^{\prime}\right]\) is meagre in \(E\) or \(f\left[E^{\prime}\right]=E,\) according to whether \(f\left[G_{0}(1)\right]\) is or is not nowhere dense.
- Proof
-
If \(f\left[G_{0}(1)\right]\) is nowhere dense in \(E,\) so also is \(f\left[G_{0}(n)\right], n>0.\) (Verify by Problems 15 and 19 in §7.) But then
\[f\left[E^{\prime}\right]=f\left[\bigcup_{n=1}^{\infty} G_{0}(n)\right]=\bigcup_{n=1}^{\infty} f\left[G_{\overrightarrow{0}}(n)\right]\]
is a countable union of nowhere dense sets, hence meagre, by definition.
Now suppose \(f\left[G_{0}(1)\right]\) is not nowhere dense; so \(\overline{f\left[G_{0}(1)\right]}\) contains some \(G_{q}(r) \subseteq E.\) We may assume \(q \in f\left[G_{\overrightarrow{0}}(1)\right]\) (if not, replace \(q\) by a close point from \(f\left[G_{0}(1)\right]).\) Then \(q=f(\vec{p})\) for some \(\vec{p} \in G_{0}(1).\) The latter implies
\[|-\vec{p}|=|\vec{p}|=\rho(\vec{p}, \overrightarrow{0})<1;\]
so
\[G_{-\vec{p}}(1) \subseteq G_{\overrightarrow{0}}(2).\]
Also, as \(\overline{f\left[G_{\overline{0}}(1)\right]} \supseteq G_{q}(r),\) translation by \(-q=f(-\vec{p})\) yields
\[\overline{f\left[G_{\overline{0}}(1)\right]}+f(-\vec{p}) \supseteq G_{q}(r)-q=G_{0}(r),\]
i.e.,
\[G_{0}(r) \subseteq \overline{f\left[G_{-\vec{p}}(1)\right]} \subseteq \overline{f\left[G_{\overrightarrow{0}}(2)\right]}.\]
Hence \(\overline{f\left[G_{\overrightarrow{0}}(1)\right]} \supseteq G_{0}\left(\frac{1}{2} r\right)\) (why?); so, by the Lemma
\[f\left[G_{\overrightarrow{0}}(1)\right] \supseteq G_{0}\left(\frac{1}{2} r\right) \text { in } E.\]
This implies \(f\left[G_{\overrightarrow{0}}(2 n)\right] \supseteq G_{0}(n r),\) and so
\[f\left[E^{\prime}\right] \supseteq \bigcup_{n=1}^{\infty} G_{0}(n r)=E,\]
i.e., \(f\left[E^{\prime}\right]=E,\) as required. Thus the theorem is proved.\(\quad \square\)
Let \(f \in L\left(E^{\prime}, E\right),\) with \(E^{\prime}\) and \(E\) complete. Then the map \(f\) is open on \(E^{\prime}\) iff \(f\left[E^{\prime}\right]=E,\) i.e., iff \(f\) is onto \(E\).
- Proof
-
If \(f\left[E^{\prime}\right]=E,\) then by Theorem 1, \(f\left[E^{\prime}\right]\) is nonmeagre in \(E,\) as is \(E\) itself. Thus by Theorem 2, \(f\left[G_{\overrightarrow{0}}(1)\right]\) is not nowhere dense, and (1) follows as before. Hence by Problems 15(iii) and 19 in §7, \(f\left[G_{\vec{p}}\right] \supseteq\) some \(G_{q}\) whenever \(q=f(\vec{p})\). (Why?) Therefore, \(G_{\vec{p}} \subseteq A \subseteq E^{\prime}\) implies
\[G_{f(\vec{p})} \subseteq f\left[G_{\vec{p}}\right] \subseteq f[A];\]
i.e., \(f\) maps any interior point \(\vec{p} \in A\) into such a point of \(f[A].\) By Problem 8 in §7, \(f\) is open on \(E^{\prime}.\)
Conversely, if so, then \(f\left[E^{\prime}\right]\) is an open set \(\neq \emptyset\) in \(E,\) a complete space; so by Theorems 1 and 2, \(f\left[E^{\prime}\right]\) is nonmeagre and equals \(E.\) (See also Problem 16(ii) in §7.)\(\quad \square\)
Note 1. Theorem 3 holds even if \(f\) is not one-to-one.
Note 2. If in Theorem 3, however, \(f\) is bijective, it is open on \(E^{\prime},\) and so \(f^{-1} \in L\left(E, E^{\prime}\right)\) by Note 1 in §7. (This is the promised general proof of Corollary 2 in §6.)
Let \(E^{\prime} b e\) complete. Let \(\mathcal{N}\) be a family of maps \(f \in L\left(E^{\prime}, E\right)\) such that
\[\left(\forall x \in E^{\prime}\right)\left(\exists k \in E^{1}\right)(\forall f \in \mathcal{N}) \quad|f(\vec{x})|<k.\]
("\(\mathcal{N}\) is bounded at each \(\vec{x}\).")
Then \(\mathcal{N}\) is "norm-bounded," i.e.,
\[\left(\exists K \in E^{1}\right)(\forall f \in \mathcal{N}) \quad\|f\|<K,\]
with \(\|\quad\|\) as in §2.
- Proof
-
It suffices to show that \(\mathcal{N}\) is "uniformly" bounded on some globe,
\[\left(\exists c \in E^{1}\right)\left(\exists G=G_{\vec{p}}(r)\right)(\forall f \in \mathcal{N})(\forall \vec{x} \in G) \quad|f(\vec{x})| \leq c.\]
For then \(|\vec{x}-\vec{p}| \leq r\) implies
\[2 c>|f(\vec{x})-f(\vec{p})|=|f(\vec{x}-\vec{p})|,\]
or (setting \(\vec{x}-\vec{p}=r \vec{y} )|\vec{y}|<1\) implies
\[(\forall f \in \mathcal{N}) \quad|f(\vec{y})|<\frac{2 c}{r} \quad\text {(why?);}\]
so
\[(\forall f \in \mathcal{N}) \quad\|f\|=\sup _{|\vec{y}| \leq 1}|f(\vec{y})|<\frac{2 c}{r}.\]
Thus, seeking a contradiction, suppose (3) fails and assume its negation:
\[\left(\forall c \in E^{1}\right)\left(\forall G=G_{\vec{p}}(r)\right)(\exists f \in \mathcal{N})\left(\exists \vec{x} \in G=G_{\vec{p}}(r)\right) \quad|f(\vec{x})|>c.\]
Then for \(c=1,\) we can fix some \(f_{1} \in \mathcal{N}\) and \(G_{\vec{x}_{1}}\left(r_{1}\right)\) such that \(0<r_{1}<1\) and
\[\left|f_{1}\left(\vec{x}_{1}\right)\right|>1.\]
By the continuity of the norm \(| |\), we can choose \(r_{1}\) so small that
\[\left(\forall \vec{x} \in \overline{G_{\vec{x}_{1}}\left(r_{1}\right)}\right) \quad|f(\vec{x})|>1.\]
Again by (4), we fix \(f_{2} \in \mathcal{N}\) and \(\vec{x}_{2} \in G_{\vec{x}_{1}}\left(r_{1}\right)\) such that \(\left|f_{2}\right|>2\) on some globe
\[\overline{G_{\vec{x}_{2}}\left(r_{2}\right)} \subseteq G_{\vec{x}_{1}}\left(r_{1}\right),\]
with \(0<r_{2}<1 / 2.\) Inductively, we thus form a contracting sequence of closed globes
\[\overline{G_{\vec{x}_{n}}\left(r_{n}\right)}, \quad 0<r_{n}<\frac{1}{n},\]
and a sequence \(\left\{f_{n}\right\} \subseteq \mathcal{N},\) such that
\[(\forall n) \quad\left|f_{n}\right|>n \text { on } \overline{G_{\vec{x}_{n}}\left(r_{n}\right)} \subseteq E^{\prime}.\]
As \(E^{\prime}\) is complete, so are the closed globes \(\overline{G_{\vec{x}_{n}}\left(r_{n}\right)} \subseteq E^{\prime}.\) Also, \(0<r_{n}<\) 1\(/ n \rightarrow 0.\) Thus by Cantor's theorem (Theorem 5 of Chapter 4, §6), there is
\[\vec{x}_{0} \in \bigcap_{n=1}^{\infty} \overline{G_{\vec{x}_{n}}\left(r_{n}\right)}.\]
As \(\vec{x}_{0}\) is in each \(\overline{G_{\vec{x}_{n}}\left(r_{n}\right)},\) we have
\[(\forall n) \quad\left|f_{n}\left(\vec{x}_{0}\right)\right|>n;\]
so \(\mathcal{N}\) is not bounded at \(\vec{x}_{0},\) contrary to (2). This contradiction completes the proof.\(\quad \square\)
Note 3. Complete normed spaces are also called Banach spaces.


3: Business Writing Style
Chapter Objectives
The purpose of this chapter is to:
- Explain the concept of plain language
- Discuss strategies to improve clarity in writing
- Highlight the difference between active and passive voice
- Emphasize the importance of positive tone
- Present ways to write inclusively
Plain Language in Business Writing
Business is about people. Business writers facilitate sales of products and services, purchases of supplies and merchandise, management and operations of units and departments, and communication with clients and customers. To be in business is to be surrounded by people who interact with you, who require something from you.
Communication is the connection between people. As long as one person is sending a message and another person is understanding it, communication is happening. A successful professional builds and maintains relationships, completes tasks, directs teams, and expresses ideas by communicating effectively. To be successful, you will need to be an effective communicator: you need to be understood.
A key skill in any professional setting is the ability to use plain language . Plain language writing--and speaking--will help you to get your message across clearly and concisely. This chapter will introduce you to the principles of plain language.
Source: Photo by Daniel Fazio on Unsplash
Clarity and Conciseness
Word selection and phrasing leads to successfully transferring meaning from the sender to the receiver. Careful word selection enhances the writer’s reputation and reflects the business’s reputation. Think of the advice a home seller receives before an open house. They will often have bread baking or apple cider simmering to create an aroma that makes the house feel like a home. This small step might help a potential buyer appreciate the house more. Solid writing skills can have the same effect for the employee. The employee gains respect and appreciation because of writing skills that project credibility and confidence.
When trying to enhance your reputation, it is tempting to want to use complex words in order to sound sophisticated. Unfortunately, using complex vocabulary may obscure your ideas and potentially damage your credibility. Remember the focus of your writing should be on the reader who needs to understand your message ( the "you-attitude "). Instead of focusing on complex words, concentrate on expressing accurate content with precise, unambiguous words so that the message is transmitted clearly. Be precise while understandable.
| Avoid | Use Instead |
| The lawyer was trying to obfuscate details during his opening speech. | The lawyer was trying to confuse the details during his opening speech. |
| The remuneration the contractor receives is commensurate with the time and materials used. | The pay the contractor receives is equal to the time and materials used. |
Choose common words instead of difficult and complicated words to make your message accessible to your audience. Inappropriate word choices will get in the way of your message. For this reason, use language that is accurate and appropriate for the writing situation. Omit jargon (technical words and phrases common to a specific profession or discipline) and slang (invented words and phrases specific to a certain group of people) unless your audience and purpose call for such language. For example, sometimes using jargon is fine as long as you can safely assume your readers also know the jargon. If you are a paralegal writing to others in the legal profession, using legal jargon is perfectly fine. On the other hand, if you are writing for people outside the legal profession, using legal jargon would most likely be confusing. Although lawyers must use legal jargon in papers they prepare for customers, those papers are designed to navigate within the legal system and may not be clear to readers outside of this demographic. Therefore, when communicating with the customer, such language should be avoided.
Also avoid using outdated words and phrases, such as "dial the number" and be straightforward in your writing rather than using euphemisms (a gentler but sometimes inaccurate way of saying something). Be clear about the level of formality each piece of writing needs and adhere to that level.
At the heart of business is the idea that "time is money." This may lead you to believe that shorter message are always better; however, concise writing is not just fast or short. Your writing must always balance the clarity of the message with efficiency. In order to write straight forward sentences that are appropriate and effective in business communication, there are a few things to keep in mind.
| Rule | Example and Explanation | Revision and Explanation |
|
Be careful not to string together too many ideas in the same sentence. A sentence like this is not only confusing but can also become boring or confusing to read. |
Michael copy edited the report, and the data tables were compiled, and the graphics looked wonderful. All three of these activities are part of the completion of a report, but they don't really belong in the same sentence. |
Michael copy edited the report while the rest of the team compiled the data tables. The graphics looked wonderful. By using a connector other than "and," the sentences actually gives more information: that the copy editing and compiling happened at the same time. Note that if we replace "while" with "after which," for example, we would be telling a somewhat different story. Also, it is great that the graphics are impressive, but that idea does not belong in the same sentence. |
|
Starting a sentence with a dependent clause can sometimes bury the important news at the back of the sentence. |
Think about the emotions a reader goes through when faced with a sentence like this: While we suffered a dismal first quarter because of supply-chain issues, and our stock prices wobbled a lot thanks to fluctuations in the Japanese market that caused the company to begin targeting employees for layoffs, the executive team is happy to report that we are on track for a profitable year. |
The executive team is happy to report that we are on track for a profitable year even though we suffered a dismal first quarter because of supply chain issues... Notice the difference when the sentence tells the important news first. |
|
Clear is good; simple can be mind-numbing, so vary your sentence structures. |
Imagine an entire report full of this: Profits were up. This is good. Production increased by six percent. Employees received bonuses in two of our quarters. The stock split. Even though you are reading excellent news, you are about to keel over from the monotony, aren't you? Writing cleanly and concisely doesn't mean writing like a robot. Think about how the small nuggets of information relate to one another, and combine them in sentences that make sense, put the important news first, and show that you take pride in writing well. |
We are happy to report that profits are up, and our shares have split because of a six-percent increase in production. As a result, our hard-working employees were rewarded with bonuses in two of four quarters. Not only is it possible to read this passage without dozing off, it also gives more information by showing the relationship among the pieces of information given. |
Finally, watch for wordiness. As you write and edit, ask yourself whether you are using several words when there’s one perfectly good one that would suffice.
| Type of Redundancy | Example | Revision |
|
Redundant pairs |
each and every first and foremost full and complete |
each first complete |
|
Redundant expressions |
the month of July fellow colleagues personal opinion past memories |
July colleagues opinion memories |
|
Wordy Phrases |
at a later time on a daily basis due to the fact that in reference to |
later daily because about |
|
Nominalizations |
take into consideration make a recommendation make an effort perform a review |
consider recommend try review |
Positive Tone
As we already stated, business writing should be clear and concise. Take care, however, that your document does not turn out as an endless series of short, choppy sentences. Keep in mind also that "concise" does not have to mean "blunt" – you still need to think about your tone and the audience for whom you are writing. Consider the following examples:
After carefully reviewing this proposal, we have decided to prioritize other projects this quarter.
Nobody liked your project idea, so we are not going to give you any funding.
The first version is a weaker statement, emphasizing facts not directly relevant to its point. The second version provides the information in a simple and direct manner. But you don't need to be an expert on style to know that the first phrasing is diplomatic and respectful (even though it's less concise) as compared with the second version, which is unnecessarily harsh and likely to provoke a negative reaction.
Unless there is a specific reason not to, use positive language wherever you can. Positive language benefits your writing in two ways. First, it creates a positive tone , and your writing is more likely to be well-received. Second, it clarifies your meaning, as positive statements are more concise. Take a look at the following negatively worded sentences and then their positive counterparts, below .
Examples of Negative and Positive Sentences
- Negative: Your car will not be ready for pick up until Friday.
- Positive: Your car will be ready for pick up on Friday.
- Negative: Your vacation is not approved until the manager clears it.
- Positive: Your vacation will be approved when the manager clears it.
- Negative: Don't forget to turn in your request for reimbursement.
- Positive: Remember to turn in your request for reimbursement.
Source: Photo by Brooke Cagle on Unsplash
Pronouns
Personal pronouns (like I, we, and you) are important in letters and memos. In such documents, it is perfectly appropriate to refer to yourself as I and to the reader as you. Be careful, however, when you use the pronoun we in a business letter that is written on company stationery since it commits your company to what you have written. When stating your opinion, use I; when presenting company policy, use we.
Active and Passive Voice
The best writers strive to achieve a style that is so clear that their messages cannot be misunderstood. One way to achieve a clear style is to minimize your use of the passive voice because it not only makes your writing dull but also can be ambiguous or overly impersonal. To communicate professionally, you need to know when and how to use either active or passive voice. Although most contexts prefer the active voice , the passive voice may be the best choice in certain situations. Generally, though, passive voice tends to be awkward, vague, and wordy.
To use active voice, make the noun that performs the action the subject of the sentence and pair it directly with an action verb .
Read these two sentences:
- The administrative assistant provided copies of the contract for everyone present.
- Everyone present was provided with a copy of the contract by the administrative assistant.
In the first sentence, provided is an action verb that is paired with the subject, the administrative assistant . If you ask yourself, “Who provided the copies?” the answer is the administrative assistant . The other noun in the sentence— everyone — did not provide anything.
Now look at the second sentence. The action verb is provided . If you ask yourself, “Who provided the copies?” the answer, again, is the administrative assistant . But, in this sentence, the writer placed everyone —not the administrative assistant —in the subject position. When the doer of the action is not the subject, the sentence is in passive voice. In passive voice constructions, the doer of the action usually follows the word by as the indirect object of a prepositional phrase, and the action verb is typically partnered with a version of the verb to be .
Examples
Example 1 : The timing and allocation of resources will be determined by the project manager.
-
The nouns in the subject position are "timing and allocation."
-
The form of the verb to be is the word "will be."
-
The action verb is the word "determined."
-
The doer of the action is "the project manager."
Example 2 : More opportunities as well as challenges are created for members of the accounting profession by growing globalization.
-
The nouns in the subject position are "opportunities and challenges."
-
The form of the verb to be is the word "are."
-
The action verb is "created."
-
The doer of the action is "growing globalization."
Now, try to convert these sentences into active voice.
Generally, use active voice as much as you can. Sometimes, however, passive voice is the best option. Consider the following situations when it is acceptable to use passive voice:
-
When you do not know who or what is responsible for the action.
-
Example: Our front-door lock was picked.
-
Rationale: If you do not know who picked the lock on your front door, you cannot say who did it. You could say a thief broke in, but that would be an assumption; you could, theoretically, find out that the lock was picked by a family member who had forgotten to take a key.
-
Example: Our front-door lock was picked.
-
When the person or thing that performed the action is not important.
-
Example: The park was flooded all week.
-
Rationale: Although you know that the rainwater flooded the park, saying so would not be important.
-
Example: The park was flooded all week.
-
When you do not want to place credit, responsibility, or blame.
-
Example: A mistake was made in the investigation that resulted in the wrong person being on trial.
-
Rationale: Even if you think you know who is responsible for the problem, you might not want to expose the person.
-
Example: A mistake was made in the investigation that resulted in the wrong person being on trial.
-
When you want to maintain the impression of objectivity.
-
Example: It was noted that only first-grades chose to eat the fruit.
-
Rationale: Research reports in certain academic disciplines attempt to remove the researcher from the results to avoid saying, for example, "I noted that only first graders..."
-
Example: It was noted that only first-grades chose to eat the fruit.
Active or Passive?
- The Human Resource Director was hired last week.
- All employees are required to submit their timesheets this Friday.
- Key stakeholders need to attend the meeting in Philadelphia next month.
- The presenter has explained the theory clearly and thoroughly.
Hint: You can figure this out by asking yourself, “Is the doer in the subject position paired with an action verb?” If you answer yes, the sentence uses active voice.
Lists
Lists can consist of words, phrases, or even sentences. Lists are useful in business writing because they are a fast way to draw attention to several items. They can be found embedded in sentences or arranged vertically. In business documents, we should always try to arrange lists vertically because the vertical arrangement adds emphasis and makes the information stand out. They also add white space, which helps the reader locate the list easily in the document and to focus on the information.
Horizontal (Embedded List) vs. Vertical List
The store needs several items to process the refund for the incorrect billing. If you have the receipt, we’ll need that. After you find the receipt, circle the incorrect payment and add the voided check to the envelope. Remember that a stamped return envelope will get your money back more quickly. Please be sure to add that.
OR
To process your refund, the store needs several pieces of documentation. Please do the following:
- Circle the incorrect items on the original receipt.
- Prepare a voided check.
- Provide a self-addressed, stamped envelope.
- Mail all of these items to this address: ACMT Products, PO Box 145, Shippensburg, PA 17257.
Note that a vertical list must be properly introduced with a sentence so that the context of the list would be clear to the reader. Depending on the nature of the items listed, you will need to decide between a bulleted list and a numbered list . Bullets are usually used when the order or sequence does not matter. Numbers are used when we wish to emphasize the order, sequence, or quantity of listed items. Instructions, for example, must use numbered lists to clearly indicate the sequence of the steps.
Bulleted List vs. Numbered List
Follow these tips for effective time management:
- Use a planner or calendar to be mindful of deadlines.
- Divide big projects into smaller sections.
- Set a time limit to complete a task.
OR
Follow these three tips for effective time management:
- Use a planner or calendar to be mindful of deadlines.
- Divide big projects into smaller sections.
- Set a time limit to complete a task.
Remember that we use a period at the end of each listed item only when we are listing complete sentences.
Parallelism
Parallel construction of sentences, lists, and even headings makes messages much easier for the reader to absorb. Sometimes, for the newer writer, it might be easier to think of a predictable rhythm or format when working on how to achieve parallelism. Think of the beat of poetry or songs and how it makes the words easy to remember and predict. As a writer, you can use that same structure to your advantage.
Compare the following sentences:
- Yara loves running, to swim, and biking.
- Yara loves running, swimming, and biking.
Was the second sentence easier to comprehend than the first? The second sentence uses parallelism. All three verbs end in “ing,” whereas in the first sentence, two of the action words end in “ing” and one does not. While the meaning of the first sentence comes through, it’s easy to trip up over the mismatched action words (or verbs).
The application of parallelism improves writing style and readability, and it makes sentences easier to process.
Compare the following examples:
-
Lacking parallelism: "She likes cooking, jogging, and to read."
- Parallel: "She likes cooking, jogging, and reading."
- Parallel: "She likes to cook, jog, and read."
-
Lacking parallelism: "He likes to swim and running."
- Parallel: "He likes to swim and to run."
- Parallel: "He likes swimming and running."
Once again, the examples above combine different action words. To make them parallel, the sentences are rewritten using the same types of action word. You could argue that the first sentence is correct in that "cooking," jogging," and "to read" are all grammatically valid conclusions to "She likes." However, when you put them together, the lack of parallelism leads to a sentence that is hard to follow.
Here are a few more examples of parallelism in which the elements are all different lengths and types:
- Jackson and Krista are cooking dinner, David and Rogelio are setting the table, and Ollie and Ron are picking up dessert. (The parallel elements in this sentence are independent clauses that could stand alone. We could make sentences out of each clause before the comma.)
- Juana looked for her phone under the table, on top of the bookcase, and inside the cupboard. (The parallel elements are prepositional phrases, or words that indicate location, in this sentence.)
- Mandy and Torrence watched The Godfather , Mary Poppins , and a PBS documentary about pelicans. (The parallel elements in this sentences are nouns, or things.)
Bias-Free Language
Business writers work to be clear and direct in meaning, and drawing attention to details about race, age, country of origin, disability, and gender in the workplace might cause conscious or unconscious bias.
Let’s look at some examples and ways to fix them. A simple rule for bias-free writing is to consider whether personal details need to be included to get the point across.
| Avoid | Try Instead |
| Franklin is the new African-American accountant. | Franklin is the new accountant. |
| For someone nearing retirement, she caught on to that new software quickly. | She caught on to that new software quickly. |
| Abdul has some of the highest call center ratings even though his Saudi accent is strong. | Abdul has some of the highest call center ratings. |
| John is one of our most active employees even though he must use a wheelchair. | John is one of our most active employees. |
| Did the cleaning woman bring new trash bags? | Did the cleaner bring new trash bags? |
| Do we have enough manpower to finish this project? | Do we have enough workforce to finish this project? |
Gender Bias
Writing in a non-sexist way requires the ability to recognize sexism in the first place. The next hurdle is to figure out a way to eliminate any inherent sexism without disrupting the flow of the piece. Here are a few techniques to help avoid bias.
The first way to avoid gender bias in your writing is to use gender-neutral words when referring to individuals in various positions:
| Avoid | Try Instead |
| businessman, businesswoman | business executive |
| chairman, chairwoman | chairperson |
| the common man | the average person |
| salesman, saleswoman | salesperson, sales clerk, marketer |
The next thing to be aware of is the use of gendered pronouns. While some still use he as a generic pronoun, this shows a strong bias towards male individuals. Instead you can use “he or she” (“his or her,” etc) as the pronoun for a generic noun. This is an okay solution, but it can get clunky in large doses: "Every employee should check with his or her supervisor that his or her report was properly filed." Or, you can try to make the subject plural, using "they" instead.
While they is typically treated as a plural pronoun, when an individual has expressed a desire to be identified with gender-neutral pronouns ( they/their/theirs ), it is grammatically correct to use they as a singular pronoun. In fact, American Psychological Association (APA) now recognizes "they" as a generic third-person pronoun in English. Using this pronoun helps us avoid gender assumptions and become inclusive writers.
| Avoid | Try Instead |
|
Every employee should file his report by the end of the day. |
All employees should file their reports by the end of the day. OR Every employee should file their report by the end of the day. |
|
When filing the report, each employee should make sure he or she included yesterday's data. |
When filing the report, employees should make sure they included yesterday's data. OR When filing the report, each employee should make sure they included yesterday's data. |
|
Any author knows that his first draft won't be good. |
All authors know that their first drafts won't be good. OR Any author knows that their first draft won't be good. |
Race and Ethnicity Bias
When speaking about a racial or ethnic group, deciding which term to use can be a tricky subject because the ascribed meaning to particular terms and labels can frequently change. When choosing between terms to refer to a group, it is best to ask a member of that group what they prefer.
As a general rule in a business setting, do not mention a person's race or ethnicity unless it is directly relevant to the situation.
Disability Bias
As a general rule, avoid using labeled nouns when talking about people with disabilities. Try to use emotionally neutral expressions rather than ones that assign a role, such as victim .
| Avoid | Try Instead |
| the disabled | the people with disabilities |
| the schizophrenic | the person diagnosed with schizophrenia |
| an AIDS victim | a person with AIDS |
| a person suffering from epilepsy | a person with epilepsy |
General Business Writing Style Tips
- When revising and editing a document, evaluate it for the quality of its content, organization, style and readability. Then add to it, reorganize, and trim as necessary to meet the needs of the target audience. Always think of the audience.
- Determine the level of formality based on the audience and the situation.
- Express your ideas in a positive manner.
- Avoid big words and lengthy, complicated sentences.
- Use lists to emphasize and to make navigation easier.
- Use active voice often; use passive voice only when the situation requires it.
- Check that your writing is free of bias.
All links live as of July 2021.
This work "Business Writing Style" is a derivative of “ Professional Communications ” by the Olds College OER Development Team, " Communication at Work " by Jordan Smith, and " Business Communication Skills for Managers " by Lumen Learning used under a CC BY license. "Business Writing Style" is licensed under CC BY 4.0 by Iva Balic.


25.4: Newborn Resuscitation
By the end of this section, you will be able to:
- Discuss the indications for oxygen and assisted ventilation in a newborn
- Identify the importance of temperature monitoring and maintenance
- Describe how to safely administer surfactant to a newborn
The goal of neonatal care at birth is to support the transition from the womb to extrauterine life. “The most important priority for newborn survival is the establishment of adequate lung inflation and ventilation after birth” (American Heart Association [AHA], 2020). Newborns who cannot breathe on their own need timely interventions from the administration of oxygen to full resuscitation.
Temperature
A newborn’s temperature is monitored frequently after birth to maintain a temperature between 36.5° C and 37.5° C (97.7° F and 99.5° F) through admission and stabilization (Department of Reproductive Health and Research [RHR], World Health Organization [WHO], 1997). A measured axillary temperature below 36.5° C is considered hypothermia and is associated with increased neonatal mortality and morbidity (AHA, 2020; Laptook et al., 2018) and can easily be prevented with the use of warmers, drying the newborn, swaddling, or skin-to-skin contact if further resuscitation is not needed. A hypothermic newborn is at risk of hypoglycemia, respiratory distress, metabolic acidosis, and jaundice (Weiner, 2021).
Oxygen and Ventilation Therapy
Most newborns will spontaneously breathe within 30 to 60 seconds after birth. Simple drying and tactile stimulation may encourage ventilation , or effective breaths that result in chest rise with air entry to the lungs (AHA, 2020) (see Figure 22.4). If the newborn does not start breathing within that first minute, bradycardia, a heart rate under 100 beats per minute in a neonate, will be ongoing. The nurse should clear the airway, mouth, and nose, if needed. Providing positive pressure ventilation (PPV) , with breaths at a rate of 40 to 60 per minute, is the treatment to both improve heart rate and facilitate ventilation for the newborn. As appropriate ventilation occurs, the heart rate will increase. This increasing heart rate is the first reassuring sign during resuscitation measures. A three-lead cardiac monitor or electrocardiogram is the recommended tool for assessment rather than direct auscultation or readings from pulse oximetry (AHA, 2020; Balest, 2022). For neonates, respiratory failure occurs first, followed by cardiac arrest, while in adults this is reversed. This physiologic response of the newborn requires that resuscitation prioritize PPV (Ersdal et al., 2012; Pallapothu, et al., 2023). “Delays in initiating ventilatory support in newly born infants increase the risk of death” (AHA, 2020).
Continued increased respiratory effort, tachycardia or bradycardia, and central cyanosis all indicate a need for supplemental oxygen . An oxygen saturation under 92 percent or an arterial oxygen pressure (PaO2) under 60 substantiates the necessity of oxygen administration (Vento & Saugstad, 2019). Supplemental oxygen is administered via nasal cannula with humidified and warmed air to prevent drying of the nares and cold stress to the neonate (Figure 25.12).
Supportive ventilation for the newborn may continue beyond the delivery and move from PPV to noninvasive nasal continuous positive airway pressure (CPAP) . If the newborn is unable to protect or maintain their own airway, intubation and a ventilator are required to both ventilate and oxygenate. Ventilation is the physical delivery of breath to the lungs, while oxygenation is the exchange of gases at the cellular level. Continuous pulse oximetry and frequent monitoring of the patient are required when using respiratory supportive devices. Too much oxygen can be dangerous to the neonate. Careful titration of oxygen and monitoring of saturation reduce the risk of complications of oxygen therapy such as retinopathy of prematurity (ROP) and bronchopulmonary dysplasia (BPD) (Bancalari & Schade, 2022; Sahni & Mowes, 2022).
Mechanical ventilation , the use of a ventilator , is necessary any time hypoxemia or hypercapnia cannot be corrected with other interventions. Mechanical ventilation may be necessary for infants who have apnea with bradycardia, ineffective respiratory effort, shock, asphyxia, infection, meconium aspiration syndrome , or respiratory distress syndrome (RDS) . High-frequency ventilation (HFV) provided with jet ventilators , oscillators , or high-frequency flow interrupters , gives very frequent small breaths at low pressures to the neonate compared to traditional mechanical ventilators. HFV decreases the risk of barotrauma to the infant lungs and the risk of BPD (Ethawi et al., 2016).
Newborn Care: Part 3
See Newborn Care: Part 2 for a review of the patient data.
| Flow Chart |
Newborn assessment data at 30 minutes of age
Data obtained after transfer to transitional nursery
Data obtained 60 minutes after nursing actions
|
| Provider’s Orders |
Transfer to transitional (intermediate care) nursery
VS every 30 minutes Observe respiratory status closely Place under radiant warmer Continuous pulse oximetry Continuous oxygen per oxygen hood NPO Monitor intake and output until discharge Chest x-ray |
Escalated Therapies
Nitric oxide (NO) is a strong direct pulmonary dilator when delivered as a gas via inhalation. It is used to decrease pulmonary hypertension, pulmonary vasoconstriction, acidosis, and hypoxemia and also to treat meconium aspiration syndrome, congenital diaphragmatic hernia , persistent pulmonary hypertension, and sepsis (Barrington et al., 2017; Vento & Saugstad, 2019).
Another extreme, complex, and expensive life-support method, called extracorporeal membrane oxygenation (ECMO) , involves a modified form of heart-lung bypass. ECMO allows for treatment of any disease or trauma that has resulted in intractable hypoxemia due to severe cardiac and/or respiratory failure (Figure 25.13). ECMO essentially provides oxygen to the lungs and body while the lungs are treated for any underlying disease process or insult. ECMO does require anticoagulation that can escalate the risk of intraventricular hemorrhage and is contraindicated in very small or preterm infants under 34 weeks’ gestation (Amodeo et al., 2021).
The Cincinnati Children’s Hospital Medical Center provides updates on neonatal resuscitation and describes the function of ECMO for neonates.
Neonatal Resuscitation
A quick visual assessment allows the nurse to identify newborns who need resuscitation at birth or soon after. Newborns who are breathing and/or crying are best cared for skin-to-skin with their parent. These infants do not need routine tactile stimulation or suctioning, even if the amniotic fluid was notable for meconium. Suctioning the airway should be done only as necessary because doing it routinely can cause bradycardia (Wyckoff et al., 2020). This is an evidence-based approach. Previously, newborns were intubated and suctioned for meconium. Studies within the published literature identified that the risks did not outweigh the benefits, and this practice was changed. Is the newborn breathing and crying? Do they have good muscle tone? If not, the newborn needs assistance. The nurse clears the airway with suction, keeps the infant warm, dries them, and attempts to reposition the airway so that the infant can breathe on their own. If breathing is not spontaneous, the next step is to start external ventilation. If that is unsuccessful, the nurse calls for assistance and begins resuscitation (American Heart Association [AHA], 2020).
The American Heart Association (AHA) has a “Top 10” list of priorities for health-care professionals during resuscitation of neonates. Guidelines from the AHA are evidence based and peer reviewed and are updated regularly to give the most accurate resuscitation information.
Risk factors associated with neonates requiring resuscitation include
- no, or limited, prenatal care;
- gestational age < 36 weeks or ≥ 41 weeks;
- multiple gestation;
- forceps- or vacuum-assisted delivery;
- emergency cesarean delivery;
- meconium-stained amniotic fluid;
- shoulder dystocia, breech, or other abnormal presentation;
- abnormal heart rate in the fetus;
- infection in the infant or birthing person (Balest, 2022); and
- maternal drug consumption, chronic or acute use.
Surfactant Administration
A surfactant is any agent that decreases surface tension between two surfaces, thereby improving the exchange of oxygen and carbon dioxide. Pulmonary surfactant decreases the surface tension between the gaseous-aqueous interface in the lungs. Pulmonary surfactant is a surface-active phospholipid secreted by the alveolar epithelium and produced by the alveolar type-II (AT-II) cells of the lungs (Moraes et al., 2022).
Sterile surfactant is collected from animals and administered to newborns at risk of not having, or not having enough of, their own surfactant. Sterile surfactant is delivered via an endotracheal tube. Lung-surfactant development starts at 24 weeks’ gestation, but not until at least 32 weeks does the fetus make adequate amounts of it (Sarfaroj, 2021).
Surfactant can be used with oxygen and/or ventilation. Several doses are given in series via the endotracheal tube. After administration, the infant is monitored for side effects, the most severe being patent ductus arteriosus and pulmonary hemorrhage.
Surfactant
Many clinical trials over the past decades have shown that surfactant replacement therapy is a safe and an effective treatment that significantly decreases the occurrence of air leaks and pulmonary interstitial emphysema along with ventilatory requirements.
Generic Name: beractant
Trade Name: Survanta
Action: provides exogenous surfactant to promote lung maturity
-
Route/Dosage:
airway, 4 mL/kg, variable frequency
- Premature neonates: Endotracheal: 4 mL/kg (100 mg phospholipids/kg) as soon as possible after birth, preferably within 15 minutes; as many as four doses may be administered during the first 48 hours of life, no more frequently than every 6 hours; usually requires no more frequent dosing than every 12 hours unless surfactant is being inactivated by an infectious process (Sanchez Luna, et al., 2022).
- Administration : through an endotracheal tube using a 5 French end-hole catheter: The infant should be stable before proceeding with administration. Insert a 5 French end-hole catheter into the infant's endotracheal tube. Administer the dose in four 1 mL/kg aliquots. Each quarter-dose is instilled over 2 to 3 seconds followed by at least 30 seconds of manual ventilation or until stable; each quarter-dose is administered with the infant in a different position; slightly downward inclination with head turned to the right, then repeat with head turned to the left; then slightly upward inclination with head turned to the right; then repeat with head turned to the left. Following administration of one full dose, withhold suctioning for 1 hour unless signs of significant airway obstruction occur.
- Indications: lung immaturity; reduce the severity of RDS in premature infants
- Adverse Reactions/Side Effects: oxygen desaturation, transient bradycardia, alterations in blood pressure
- Nursing Implications: Frequent monitoring of the patient. Diuresis may occur with improvement. Newborn may be weaned off ventilation and oxygenation support as oxygenation improves (Vallerand & Sanoski, 2019; Vento & Saugstad, 2019).
- Parent/Family Education: Provide information about the underlying reason for administration. The newborn does not have their own supply and are being given an outside source of surfactant.


2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
-
- Last updated
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One simple graph, the stem-and-leaf graph or stemplot , comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example, 23 has stem two and leaf three. The number 432 has stem 43 and leaf two. Likewise, the number 5,432 has stem 543 and leaf two. The decimal 9.3 has stem nine and leaf three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.
Example \(\PageIndex{1}\)
For Susan Dean's spring pre-calculus class, scores for the first exam were as follows (smallest to largest):
33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94; 96; 100
| Stem | Leaf |
|---|---|
| 3 | 3 |
| 4 | 2 9 9 |
| 5 | 3 5 5 |
| 6 | 1 3 7 8 8 9 9 |
| 7 | 2 3 4 8 |
| 8 | 0 3 8 8 8 |
| 9 | 0 2 4 4 4 4 6 |
| 10 | 0 |
The stemplot shows that most scores fell in the 60s, 70s, 80s, and 90s. Eight out of the 31 scores or approximately 26% \(\left(\frac{8}{31}\right)\) were in the 90s or 100, a fairly high number of As.
Exercise \(\PageIndex{2}\)
For the Park City basketball team, scores for the last 30 games were as follows (smallest to largest):
32; 32; 33; 34; 38; 40; 42; 42; 43; 44; 46; 47; 47; 48; 48; 48; 49; 50; 50; 51; 52; 52; 52; 53; 54; 56; 57; 57; 60; 61
Construct a stem plot for the data.
Answer
| Stem | Leaf |
|---|---|
| 3 | 2 2 3 4 8 |
| 4 | 0 2 2 3 4 6 7 7 8 8 8 9 |
| 5 | 0 0 1 2 2 2 3 4 6 7 7 |
| 6 | 0 1 |
The stemplot is a quick way to graph data and gives an exact picture of the data. You want to look for an overall pattern and any outliers. An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500) while others may indicate that something unusual is happening. It takes some background information to explain outliers, so we will cover them in more detail later.
Example \(\PageIndex{3}\)
The data are the distances (in kilometers) from a home to local supermarkets. Create a stemplot using the data:
1.1; 1.5; 2.3; 2.5; 2.7; 3.2; 3.3; 3.3; 3.5; 3.8; 4.0; 4.2; 4.5; 4.5; 4.7; 4.8; 5.5; 5.6; 6.5; 6.7; 12.3
Do the data seem to have any concentration of values?
HINT: The leaves are to the right of the decimal.
Answer
The value 12.3 may be an outlier. Values appear to concentrate at three and four kilometers.
| Stem | Leaf |
|---|---|
| 1 | 1 5 |
| 2 | 3 5 7 |
| 3 | 2 3 3 5 8 |
| 4 | 0 2 5 5 7 8 |
| 5 | 5 6 |
| 6 | 5 7 |
| 7 | |
| 8 | |
| 9 | |
| 10 | |
| 11 | |
| 12 | 3 |
Query \(\PageIndex{1}\)
Exercise \(\PageIndex{4}\)
The following data show the distances (in miles) from the homes of off-campus statistics students to the college. Create a stem plot using the data and identify any outliers:
0.5; 0.7; 1.1; 1.2; 1.2; 1.3; 1.3; 1.5; 1.5; 1.7; 1.7; 1.8; 1.9; 2.0; 2.2; 2.5; 2.6; 2.8; 2.8; 2.8; 3.5; 3.8; 4.4; 4.8; 4.9; 5.2; 5.5; 5.7; 5.8; 8.0
Answer
| Stem | Leaf |
|---|---|
| 0 | 5 7 |
| 1 | 1 2 2 3 3 5 5 7 7 8 9 |
| 2 | 0 2 5 6 8 8 8 |
| 3 | 5 8 |
| 4 | 4 8 9 |
| 5 | 2 5 7 8 |
| 6 | |
| 7 | |
| 8 | 0 |
The value 8.0 may be an outlier. Values appear to concentrate at one and two miles.
Example \(\PageIndex{5}\): side-by-side stem-and-leaf plot
A side-by-side stem-and-leaf plot allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of leaves share the same stem. The leaves are to the left and the right of the stems. Tables \(\PageIndex{1}\) and \(\PageIndex{2}\) show the ages of presidents at their inauguration and at their death. Construct a side-by-side stem-and-leaf plot using this data.
| President | Age at Inauguration | President | Age | President | Age |
|---|---|---|---|---|---|
| Washington | 57 | Lincoln | 52 | Hoover | 54 |
| J. Adams | 61 | A. Johnson | 56 | F. Roosevelt | 51 |
| Jefferson | 57 | Grant | 46 | Truman | 60 |
| Madison | 57 | Hayes | 54 | Eisenhower | 62 |
| Monroe | 58 | Garfield | 49 | Kennedy | 43 |
| J. Q. Adams | 57 | Arthur | 51 | L. Johnson | 55 |
| Jackson | 61 | Cleveland | 47 | Nixon | 56 |
| Van Buren | 54 | B. Harrison | 55 | Ford | 61 |
| W. H. Harrison | 68 | Cleveland | 55 | Carter | 52 |
| Tyler | 51 | McKinley | 54 | Reagan | 69 |
| Polk | 49 | T. Roosevelt | 42 | G.H.W. Bush | 64 |
| Taylor | 64 | Taft | 51 | Clinton | 47 |
| Fillmore | 50 | Wilson | 56 | G. W. Bush | 54 |
| Pierce | 48 | Harding | 55 | Obama | 47 |
| Buchanan | 65 | Coolidge | 51 | Trump | 70 |
| President | Age | President | Age | President | Age |
|---|---|---|---|---|---|
| Washington | 67 | Lincoln | 56 | Hoover | 90 |
| J. Adams | 90 | A. Johnson | 66 | F. Roosevelt | 63 |
| Jefferson | 83 | Grant | 63 | Truman | 88 |
| Madison | 85 | Hayes | 70 | Eisenhower | 78 |
| Monroe | 73 | Garfield | 49 | Kennedy | 46 |
| J. Q. Adams | 80 | Arthur | 56 | L. Johnson | 64 |
| Jackson | 78 | Cleveland | 71 | Nixon | 81 |
| Van Buren | 79 | B. Harrison | 67 | Ford | 93 |
| W. H. Harrison | 68 | Cleveland | 71 | Reagan | 93 |
| Tyler | 71 | McKinley | 58 | ||
| Polk | 53 | T. Roosevelt | 60 | ||
| Taylor | 65 | Taft | 72 | ||
| Fillmore | 74 | Wilson | 67 | ||
| Pierce | 64 | Harding | 57 | ||
| Buchanan | 77 | Coolidge | 60 |
Answer
| Ages at Inauguration | Ages at Death | |
|---|---|---|
| 9 9 8 7 7 7 6 3 2 | 4 | 6 9 |
| 8 7 7 7 7 6 6 6 5 5 5 5 4 4 4 4 4 2 1 1 1 1 1 0 | 5 | 3 6 6 7 7 8 |
| 9 5 4 4 2 1 1 1 0 | 6 | 0 0 3 3 4 4 5 6 7 7 7 8 |
| 7 | 0 0 1 1 1 4 7 8 8 9 | |
| 8 | 0 1 3 5 8 | |
| 9 | 0 0 3 3 |
Exercise \(\PageIndex{6}\)
The table shows the number of wins and losses the Atlanta Hawks have had in 42 seasons. Create a side-by-side stem-and-leaf plot of these wins and losses.
| Losses | Wins | Year | Losses | Wins | Year |
|---|---|---|---|---|---|
| 34 | 48 | 1968–1969 | 41 | 41 | 1989–1990 |
| 34 | 48 | 1969–1970 | 39 | 43 | 1990–1991 |
| 46 | 36 | 1970–1971 | 44 | 38 | 1991–1992 |
| 46 | 36 | 1971–1972 | 39 | 43 | 1992–1993 |
| 36 | 46 | 1972–1973 | 25 | 57 | 1993–1994 |
| 47 | 35 | 1973–1974 | 40 | 42 | 1994–1995 |
| 51 | 31 | 1974–1975 | 36 | 46 | 1995–1996 |
| 53 | 29 | 1975–1976 | 26 | 56 | 1996–1997 |
| 51 | 31 | 1976–1977 | 32 | 50 | 1997–1998 |
| 41 | 41 | 1977–1978 | 19 | 31 | 1998–1999 |
| 36 | 46 | 1978–1979 | 54 | 28 | 1999–2000 |
| 32 | 50 | 1979–1980 | 57 | 25 | 2000–2001 |
| 51 | 31 | 1980–1981 | 49 | 33 | 2001–2002 |
| 40 | 42 | 1981–1982 | 47 | 35 | 2002–2003 |
| 39 | 43 | 1982–1983 | 54 | 28 | 2003–2004 |
| 42 | 40 | 1983–1984 | 69 | 13 | 2004–2005 |
| 48 | 34 | 1984–1985 | 56 | 26 | 2005–2006 |
| 32 | 50 | 1985–1986 | 52 | 30 | 2006–2007 |
| 25 | 57 | 1986–1987 | 45 | 37 | 2007–2008 |
| 32 | 50 | 1987–1988 | 35 | 47 | 2008–2009 |
| 30 | 52 | 1988–1989 | 29 | 53 | 2009–2010 |
Answer
| Number of Wins | Number of Losses | |
|---|---|---|
| 3 | 1 | 9 |
| 9 8 8 6 5 | 2 | 5 5 9 |
| 8 7 6 6 5 5 4 3 1 1 1 1 0 | 3 | 0 2 2 2 2 4 4 5 6 6 6 9 9 9 |
| 8 8 7 6 6 6 3 3 3 2 2 1 1 0 | 4 | 0 0 1 1 2 4 5 6 6 7 7 8 9 |
| 7 7 6 3 2 0 0 0 0 | 5 | 1 1 1 2 3 4 4 6 7 |
| 6 | 9 |
Another type of graph that is useful for specific data values is a line graph . In the particular line graph shown in Example, the x -axis (horizontal axis) consists of data values and the y -axis (vertical axis) consists of frequency points . The frequency points are connected using line segments.
Example \(\PageIndex{7}\)
In a survey, 40 mothers were asked how many times per week a teenager must be reminded to do his or her chores. The results are shown in Table and in Figure.
| Number of times teenager is reminded | Frequency |
|---|---|
| 0 | 2 |
| 1 | 5 |
| 2 | 8 |
| 3 | 14 |
| 4 | 7 |
| 5 | 4 |
Exercise \(\PageIndex{8}\)
In a survey, 40 people were asked how many times per year they had their car in the shop for repairs. The results are shown in Table. Construct a line graph.
| Number of times in shop | Frequency |
|---|---|
| 0 | 7 |
| 1 | 10 |
| 2 | 14 |
| 3 | 9 |
Answer
Figure \(\PageIndex{2}\): A line graph showing the number of times a car is in the shop on the x-axis and frequency on the y-axis.Bar graphs consist of bars that are separated from each other. The bars can be rectangles or they can be rectangular boxes (used in three-dimensional plots), and they can be vertical or horizontal. The bar graph shown in Example \(\PageIndex{9}\) has age groups represented on the x -axis and proportions on the y -axis .
Example \(\PageIndex{9}\)
By the end of 2011, Facebook had over 146 million users in the United States. Table shows three age groups, the number of users in each age group, and the proportion (%) of users in each age group. Construct a bar graph using this data.
| Age groups | Number of Facebook users | Proportion (%) of Facebook users |
|---|---|---|
| 13–25 | 65,082,280 | 45% |
| 26–44 | 53,300,200 | 36% |
| 45–64 | 27,885,100 | 19% |
Answer
Figure \(\PageIndex{3}\): This is a bar graph that matches the supplied data. The x-axis shows age groups and the y-axis show the percentages of Facebook usersExercise \(\PageIndex{10}\)
The population in Park City is made up of children, working-age adults, and retirees. Table shows the three age groups, the number of people in the town from each age group, and the proportion (%) of people in each age group. Construct a bar graph showing the proportions.
| Age groups | Number of people | Proportion of population |
|---|---|---|
| Children | 67,059 | 19% |
| Working-age adults | 152,198 | 43% |
| Retirees | 131,662 | 38% |
Answer
Figure \(\PageIndex{4}\): This is a bar graph that matches the supplied data. The x-axis shows age groups, and the y-axis shows the percentages of Park City's population.Example \(\PageIndex{11}\)
The columns in Table contain: the race or ethnicity of students in U.S. Public Schools for the class of 2011, percentages for the Advanced Placement examine population for that class, and percentages for the overall student population. Create a bar graph with the student race or ethnicity (qualitative data) on the x -axis, and the Advanced Placement examinee population percentages on the y -axis.
| Race/Ethnicity | AP Examinee Population | Overall Student Population |
|---|---|---|
| 1 = Asian, Asian American or Pacific Islander | 10.3% | 5.7% |
| 2 = Black or African American | 9.0% | 14.7% |
| 3 = Hispanic or Latino | 17.0% | 17.6% |
| 4 = American Indian or Alaska Native | 0.6% | 1.1% |
| 5 = White | 57.1% | 59.2% |
| 6 = Not reported/other | 6.0% | 1.7% |
Solution
Figure \(\PageIndex{5}\): This is a bar graph that matches the supplied data. The x-axis shows race and ethnicity, and the y-axis shows the percentages of AP examinees.Exercise \(\PageIndex{12}\)
Park city is broken down into six voting districts. The table shows the percent of the total registered voter population that lives in each district as well as the percent total of the entire population that lives in each district. Construct a bar graph that shows the registered voter population by district.
| District | Registered voter population | Overall city population |
|---|---|---|
| 1 | 15.5% | 19.4% |
| 2 | 12.2% | 15.6% |
| 3 | 9.8% | 9.0% |
| 4 | 17.4% | 18.5% |
| 5 | 22.8% | 20.7% |
| 6 | 22.3% | 16.8% |
Answer
Figure \(\PageIndex{6}\): This is a bar graph that matches the supplied data. The x-axis shows Park City voting districts, and the y-axis shows the percentages of the registered voter population.Summary
A stem-and-leaf plot is a way to plot data and look at the distribution. In a stem-and-leaf plot, all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends. That is, finding a general pattern in data sets including temperature, sales, employment, company profit or cost over a period of time. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Some bar graphs present bars clustered in groups of more than one (grouped bar graphs), and others show the bars divided into subparts to show cumulative effect (stacked bar graphs). Bar graphs are especially useful when categorical data is being used.
References
- Burbary, Ken. Facebook Demographics Revisited – 2001 Statistics, 2011. Available online at http://www.kenburbary.com/2011/03/fa...-statistics-2/ (accessed August 21, 2013).
- “9th Annual AP Report to the Nation.” CollegeBoard, 2013. Available online at http://apreport.collegeboard.org/goa...omoting-equity (accessed September 13, 2013).
- “Overweight and Obesity: Adult Obesity Facts.” Centers for Disease Control and Prevention. Available online at http://www.cdc.gov/obesity/data/adult.html (accessed September 13, 2013).
Contributors
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Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


15.3E: Whooping Cough
- Describe the mechanism of action and causes of pertussis causing bacteria
Pertussis
Pertussis, also known as whooping cough, is an infection of the respiratory system characterized by a “whooping” sound that an afflicted person makes when breathing inwards. Only 50% of patients actually display the classic sound as they attempt to draw breath over a partially closed glottis. In the U.S., the infection was responsible for 5,000 to 10,000 deaths per year before a vaccine was developed and made available. Vaccination has transformed this. Between 1985 and 1988, fewer than 100 children died from pertussis. In 2000, according to the WHO, around 39 million people worldwide were being infected annually. Of these, about 297,000 died.
Causes of Pertussis
Pertussis is caused by the bacteria, Bordetella pertussis, a gram-negative, aerobic coccobacillus capsulate of the genus Bordetella. Bordetella pertussis infects its host by colonizing lung epithelial cells. The bacterium contains a surface protein, filamentous haemagglutinin adhesin, which binds to the sulfatides found on the cilia of epithelial cells. Once anchored, the bacterium produces tracheal cytotoxin, which stops the cilia from beating. This prevents the cilia from clearing debris from an organism ‘s lungs, and the body responds by sending the host into a coughing fit. These coughs expel some bacteria into the air, which are free to infect other hosts. There does not appear to be a zoonotic reservoir for B. pertussis. Humans are its only host. The bacterium is spread by airborne droplets, and its incubation period is one to two weeks.
B. pertussis has the ability to inhibit the function of a host’s immune system, through virulence factors. Its virulence factors include pertussis toxin, filamentous hæmagglutinin, pertactin, fimbria, and tracheal cytotoxin. The pertussis toxin, or PTx, inhibits G protein coupling that regulates an adenylate cyclase-mediated conversion of ATP to cyclic AMP. The end result is that phagocytes convert too much ATP to cyclic AMP, which can cause disturbances in cellular signaling mechanisms. This prevents phagocytes from correctly responding to an infection. PTx, formerly known as lymphocytosis -promoting factor, causes a decrease in the entry of lymphocytes into lymph nodes. This can lead to a condition known as lymphocytosis, which is a large increase in the number of lymphocytes in an organism’s blood.
Key Points
- Whooping cough is caused by the bacteria Bordetella pertussis, which infects the respiratory system.
- There is no zoonotic reservoir of Bordetella pertussis, meaning that humans appear to be the only host of this bacteria.
- Bordetella pertussis produces a number of virulence factors, notably Ptx, which inhibits the ability of phagocytes to respond to infections. This helps Bordetella pertussis spread throughout a host.
Key Terms
- zoonotic : of or relating to zoonosis, the transmission of an infectious disease between species.
- glottis : an organ of speech, located in the larynx, and consisting of the true vocal cords and the opening between them
- lymphocytes : type of white blood cells in the vertebrate immune system