4.7: Add and Subtract Fractions with Common Denominators
- Model fraction addition
- Add fractions with a common denominator
- Model fraction subtraction
- Subtract fractions with a common denominator
Before you get started, take this readiness quiz.
- Simplify: \(2x + 9 + 3x − 4\). If you missed this problem, review Example 2.2.10 .
- Draw a model of the fraction \(\dfrac{3}{4}\). If you missed this problem, review Example 4.1.2 .
- Simplify: \(\dfrac{3 + 2}{6}\). If you missed this problem, review Example 4.3.12 .
Model Fraction Addition
How many quarters are pictured? One quarter plus \(2\) quarters equals \(3\) quarters.
Figure \(\PageIndex{1}\)
Remember, quarters are really fractions of a dollar. Quarters are another way to say fourths. So the picture of the coins shows that
\[\begin{split} \dfrac{1}{4} \qquad \qquad \qquad \dfrac{2}{4} \qquad & \qquad \qquad \dfrac{3}{4} \\ one \; quarter + two \; quarters &= three\; quarters \end{split} \nonumber \]
Let’s use fraction circles to model the same example, \(\dfrac{1}{4} + \dfrac{2}{4}\).
| Start with one \(\dfrac{1}{4}\) piece. | \(\dfrac{1}{4}\) | |
| Add two more \(\dfrac{1}{4}\) pieces. | \(+ \dfrac{2}{4}\) | |
| The result is \(\dfrac{3}{4}\). | \(\dfrac{3}{4}\) |
So again, we see that
\[\dfrac{1}{4} + \dfrac{2}{4} = \dfrac{3}{4} \nonumber \]
Use a model to find the sum \(\dfrac{3}{8} + \dfrac{2}{8}\).
Solution
| Start with three \(\dfrac{1}{8}\) pieces. | \(\dfrac{3}{8}\) | |
| Add two \(\dfrac{1}{8}\) pieces. | \(+ \dfrac{2}{8}\) | |
| How many \(\dfrac{1}{8}\) pieces are there? | \(\dfrac{5}{8}\) |
There are five \(\dfrac{1}{8}\) pieces, or five-eighths. The model shows that \(\dfrac{3}{8} + \dfrac{2}{8} = \dfrac{5}{8}\).
Use a model to find each sum. Show a diagram to illustrate your model. \[\dfrac{1}{8} + \dfrac{4}{8} \nonumber \]
- Answer
-
\(\dfrac{5}{8}\)
Use a model to find each sum. Show a diagram to illustrate your model. \[\dfrac{1}{6} + \dfrac{4}{6} \nonumber \]
- Answer
-
\(\dfrac{5}{6}\)
Add Fractions with a Common Denominator
Example \(\PageIndex{1}\) shows that to add the same-size pieces—meaning that the fractions have the same denominator—we just add the number of pieces.
If \(a\), \(b\), and \(c\) are numbers where \(c ≠ 0\), then
\[\dfrac{a}{c} + \dfrac{b}{c} = \dfrac{a + b}{c}\]
To add fractions with a common denominator, add the numerators and place the sum over the common denominator.
Find the sum: \(\dfrac{3}{5} + \dfrac{1}{5}\).
Solution
| Add the numerators and place the sum over the common denominator. | \(\dfrac{3 + 1}{5}\) |
| Simplify. | \(\dfrac{4}{5}\) |
Find each sum: \(\dfrac{3}{6} + \dfrac{2}{6}\).
- Answer
-
\(\dfrac{5}{6}\)
Find each sum: \(\dfrac{3}{10} + \dfrac{7}{10}\).
- Answer
-
\(1\)
Find the sum: \(\dfrac{x}{3} + \dfrac{2}{3}\).
Solution
| Add the numerators and place the sum over the common denominator. | \(\dfrac{x + 2}{3}\) |
Note that we cannot simplify this fraction any more. Since \(x\) and \(2\) are not like terms, we cannot combine them.
Find the sum: \(\dfrac{x}{4} + \dfrac{3}{4}\).
- Answer
-
\(\dfrac{x+3}{4}\)
Find the sum: \(\dfrac{y}{8} + \dfrac{5}{8}\).
- Answer
-
\(\dfrac{y+5}{8}\)
Find the sum: \(− \dfrac{9}{d} + \dfrac{3}{d}\).
Solution
We will begin by rewriting the first fraction with the negative sign in the numerator.
\[− \dfrac{a}{b} = \dfrac{−a}{b} \nonumber \]
| Rewrite the first fraction with the negative in the numerator. | \(\dfrac{-9}{d} + \dfrac{3}{d}\) |
| Add the numerators and place the sum over the common denominator. | \(\dfrac{-9 + 3}{d}\) |
| Simplify the numerator. | \(\dfrac{-6}{d}\) |
| Rewrite with negative sign in front of the fraction. | \(- \dfrac{6}{d}\) |
Find the sum: \(− \dfrac{7}{d} + \dfrac{8}{d}\).
- Answer
-
\(\dfrac{1}{d}\)
Find the sum: \(− \dfrac{6}{m} + \dfrac{9}{m}\).
- Answer
-
\(\dfrac{3}{m}\)
Find the sum: \(\dfrac{2n}{11} + \dfrac{5n}{11}\).
Solution
| Add the numerators and place the sum over the common denominator. | \(\dfrac{2n + 5n}{11}\) |
| Combine like terms. | \(\dfrac{7n}{11}\) |
Find the sum: \(\dfrac{3p}{8} + \dfrac{6p}{8}\).
- Answer
-
\(\dfrac{9p}{8}\)
Find the sum: \(\dfrac{2q}{5} + \dfrac{7q}{5}\).
- Answer
-
\(\dfrac{9q}{5}\)
Find the sum: \(− \dfrac{3}{12} + \left(− \dfrac{5}{12}\right)\).
Solution
| Add the numerators and place the sum over the common denominator. | \(\dfrac{-3 + (-5)}{12}\) |
| Add. | \(\dfrac{-8}{12}\) |
| Simplify the fraction. | \(-\dfrac{2}{3}\) |
Find each sum: \(− \dfrac{4}{15} + \left(− \dfrac{6}{15}\right)\).
- Answer
-
\(-\dfrac{2}{3}\)
Find each sum: \(− \dfrac{5}{21} + \left(− \dfrac{9}{21}\right)\).
- Answer
-
\(-\dfrac{2}{3}\)
Model Fraction Subtraction
Subtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into \(12\) slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or \(\dfrac{7}{12}\) of the pizza) left in the box. If Leonardo eats \(2\) of these remaining pieces (or \(\dfrac{2}{12}\) of the pizza), how much is left? There would be \(5\) pieces left (or \(\dfrac{5}{12}\) of the pizza).
\[\dfrac{7}{12} - \dfrac{2}{12} = \dfrac{5}{12} \nonumber \]
Let’s use fraction circles to model the same example, \(\dfrac{7}{12} − \dfrac{2}{12}\). Start with seven \(\dfrac{1}{12}\) pieces. Take away two \(\dfrac{1}{12}\) pieces. How many twelfths are left?
Figure \(\PageIndex{2}\)
Again, we have five twelfths, \(\dfrac{5}{12}\).
Use fraction circles to find the difference: \(\dfrac{4}{5} − \dfrac{1}{5}\).
Solution
Start with four \(\dfrac{1}{5}\) pieces. Take away one \(\dfrac{1}{5}\) piece. Count how many fifths are left. There are three \(\dfrac{1}{5}\) pieces left.
Use a model to find each difference. Show a diagram to illustrate your model. \(\dfrac{7}{8} − \dfrac{4}{8}\)
- Answer
-
\(\dfrac{3}{8}\), models may differ.
Use a model to find each difference. Show a diagram to illustrate your model. \(\dfrac{5}{6} − \dfrac{4}{6}\)
- Answer
-
\(\dfrac{1}{6}\), models may differ.
Subtract Fractions with a Common Denominator
We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.
If \(a\), \(b\), and \(c\) are numbers where \(c ≠ 0\), then
\[\dfrac{a}{c} - \dfrac{b}{c} = \dfrac{a-b}{c}\]
To subtract fractions with a common denominator, we subtract the numerators and place the difference over the common denominator.
Find the difference: \(\dfrac{23}{24} − \dfrac{14}{24}\).
Solution
| Subtract the numerators and place the difference over the common denominator. | \(\dfrac{23 - 14}{24}\) |
| Simplify the numerator. | \(\dfrac{9}{24}\) |
| Simplify the fraction by removing common factors. | \(\dfrac{3}{8}\) |
Find the difference: \(\dfrac{19}{28} − \dfrac{7}{28}\).
- Answer
-
\(\dfrac{3}{7}\)
Find the difference: \(\dfrac{27}{32} − \dfrac{11}{32}\).
- Answer
-
\(\dfrac{1}{2}\)
Find the difference: \(\dfrac{y}{6} − \dfrac{1}{6}\).
Solution
| Subtract the numerators and place the difference over the common denominator. | \(\dfrac{y - 1}{6}\) |
The fraction is simplified because we cannot combine the terms in the numerator.
Find the difference: \(\dfrac{x}{7} − \dfrac{2}{7}\).
- Answer
-
\(\dfrac{x-2}{7}\)
Find the difference: \(\dfrac{y}{14} − \dfrac{13}{14}\).
- Answer
-
\(\dfrac{y-13}{14}\)
Find the difference: \(− \dfrac{10}{x} − \dfrac{4}{x}\).
Solution
Remember, the fraction \(− \dfrac{10}{x}\) can be written as \(\dfrac{−10}{x}\).
| Subtract the numerators. | \(\dfrac{-10 - 4}{x}\) |
| Simplify. | \(\dfrac{-14}{x}\) |
| Rewrite with the negative sign in front of the fraction. | \(- \dfrac{14}{x}\) |
Find the difference: \(− \dfrac{9}{x} − \dfrac{7}{x}\).
- Answer
-
\(-\dfrac{16}{x}\)
Find the difference: \(− \dfrac{17}{a} − \dfrac{5}{a}\).
- Answer
-
\(-\dfrac{22}{a}\)
Now lets do an example that involves both addition and subtraction.
Simplify: \(\dfrac{3}{8} + \left(- \dfrac{5}{8}\right) − \dfrac{1}{8}\).
Solution
| Combine the numerators over the common denominator. | \(\dfrac{3 + (-5) - 1}{8}\) |
| Simplify the numerator, working left to right. | \(\dfrac{-2 - 1}{8}\) |
| Subtract the terms in the numerator. | \(\dfrac{-3}{8}\) |
| Rewrite with the negative sign in front of the fraction. | \(- \dfrac{3}{8}\) |
Simplify: \(\dfrac{2}{5} + \left(− \dfrac{4}{5}\right) − \dfrac{3}{5}\).
- Answer
-
\(-1\)
Simplify: \(\dfrac{5}{9} + \left(− \dfrac{4}{9}\right) − \dfrac{7}{9}\).
- Answer
-
\(-\dfrac{2}{3}\)
Access Additional Online Resources
- Adding Fractions With Pattern Blocks
- Adding Fractions With Like Denominators
- Subtracting Fractions With Like Denominators
Key Concepts
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Fraction Addition
- If \(a,b,\) and \(c\) are numbers where \(c\neq 0\), then \(\dfrac{a}{c} + \dfrac{b}{c} = \dfrac{a+b}{c}\)
- To add fractions, add the numerators and place the sum over the common denominator.
-
Fraction Subtraction
- If \(a,b,\) and \(c\) are numbers where \(c\neq 0\), then \(\dfrac{a}{c} - \dfrac{b}{c} = \dfrac{a-b}{c}\)
- To subtract fractions, subtract the numerators and place the difference over the common denominator.
Practice Makes Perfect
Model Fraction Addition
In the following exercises, use a model to add the fractions. Show a diagram to illustrate your model.
- \(\dfrac{2}{5} + \dfrac{1}{5}\)
- \(\dfrac{3}{10} + \dfrac{4}{10}\)
- \(\dfrac{1}{6} + \dfrac{3}{6}\)
- \(\dfrac{3}{8} + \dfrac{3}{8}\)
Add Fractions with a Common Denominator
In the following exercises, find each sum.
- \(\dfrac{4}{9} + \dfrac{1}{9}\)
- \(\dfrac{2}{9} + \dfrac{5}{9}\)
- \(\dfrac{6}{13} + \dfrac{7}{13}\)
- \(\dfrac{9}{15} + \dfrac{7}{15}\)
- \(\dfrac{x}{4} + \dfrac{3}{4}\)
- \(\dfrac{y}{3} + \dfrac{2}{3}\)
- \(\dfrac{7}{p} + \dfrac{9}{p}\)
- \(\dfrac{8}{q} + \dfrac{6}{q}\)
- \(\dfrac{8b}{9} + \dfrac{3b}{9}\)
- \(\dfrac{5a}{7} + \dfrac{4a}{7}\)
- \(\dfrac{-12y}{8} + \dfrac{3y}{8}\)
- \(\dfrac{-11x}{5} + \dfrac{7x}{5}\)
- \(− \dfrac{1}{8} + \left(− \dfrac{3}{8}\right)\)
- \(− \dfrac{1}{8} + \left(− \dfrac{5}{8}\right)\)
- \(− \dfrac{3}{16} + \left(− \dfrac{7}{16}\right)\)
- \(− \dfrac{5}{16} + \left(− \dfrac{9}{16}\right)\)
- \(− \dfrac{8}{17} + \dfrac{15}{17}\)
- \(− \dfrac{9}{19} + \dfrac{17}{19}\)
- \(− \dfrac{6}{13} + \left(− \dfrac{10}{13}\right) + \left(- \dfrac{12}{13}\right)\)
- \(− \dfrac{5}{12} + \left(− \dfrac{7}{12}\right) + \left(- \dfrac{11}{12}\right)\)
Model Fraction Subtraction
In the following exercises, use a model to subtract the fractions. Show a diagram to illustrate your model.
- \(\dfrac{5}{8} − \dfrac{2}{8}\)
- \(\dfrac{5}{6} − \dfrac{2}{6}\)
Subtract Fractions with a Common Denominator
In the following exercises, find the difference.
- \(\dfrac{4}{5} − \dfrac{1}{5}\)
- \(\dfrac{4}{5} − \dfrac{3}{5}\)
- \(\dfrac{11}{15} − \dfrac{7}{15}\)
- \(\dfrac{9}{13} − \dfrac{4}{13}\)
- \(\dfrac{11}{12} − \dfrac{5}{12}\)
- \(\dfrac{7}{12} − \dfrac{5}{12}\)
- \(\dfrac{4}{21} − \dfrac{19}{21}\)
- \(- \dfrac{8}{9} − \dfrac{16}{9}\)
- \(\dfrac{y}{17} − \dfrac{9}{17}\)
- \(\dfrac{x}{19} − \dfrac{8}{19}\)
- \(\dfrac{5y}{8} − \dfrac{7}{8}\)
- \(\dfrac{11z}{13} − \dfrac{8}{13}\)
- \(- \dfrac{8}{d} − \dfrac{3}{d}\)
- \(- \dfrac{7}{c} − \dfrac{7}{c}\)
- \(- \dfrac{23}{u} − \dfrac{15}{u}\)
- \(- \dfrac{29}{v} − \dfrac{26}{v}\)
- \(- \dfrac{6c}{7} − \dfrac{5c}{7}\)
- \(- \dfrac{12d}{11} − \dfrac{9d}{11}\)
- \(\dfrac{-4r}{13} − \dfrac{5r}{13}\)
- \(\dfrac{-7s}{3} − \dfrac{7s}{3}\)
- \(- \dfrac{3}{5} − \left(- \dfrac{4}{5}\right)\)
- \(- \dfrac{3}{7} − \left(- \dfrac{5}{7}\right)\)
- \(- \dfrac{7}{9} − \left(- \dfrac{5}{9}\right)\)
- \(- \dfrac{8}{11} − \left(- \dfrac{5}{11}\right)\)
Mixed Practice
In the following exercises, perform the indicated operation and write your answers in simplified form.
- \(− \dfrac{5}{18} \cdot \dfrac{9}{10}\)
- \(− \dfrac{3}{14} \cdot \dfrac{7}{12}\)
- \(\dfrac{n}{5} − \dfrac{4}{5}\)
- \(\dfrac{6}{11} − \dfrac{s}{11}\)
- \(- \dfrac{7}{24} − \dfrac{2}{24}\)
- \(- \dfrac{5}{18} − \dfrac{1}{18}\)
- \(\dfrac{8}{15} \div \dfrac{12}{5}\)
- \(\dfrac{7}{12} \div \dfrac{9}{28}\)
Everyday Math
- Trail Mix Jacob is mixing together nuts and raisins to make trail mix. He has \(\dfrac{6}{10}\) of a pound of nuts and \(\dfrac{3}{10}\) of a pound of raisins. How much trail mix can he make?
- Baking Janet needs \(\dfrac{5}{8}\) of a cup of flour for a recipe she is making. She only has \(\dfrac{3}{8}\) of a cup of flour and will ask to borrow the rest from her next-door neighbor. How much flour does she have to borrow?
Writing Exercises
- Greg dropped his case of drill bits and three of the bits fell out. The case has slots for the drill bits, and the slots are arranged in order from smallest to largest. Greg needs to put the bits that fell out back in the case in the empty slots. Where do the three bits go? Explain how you know.
Bits in case: \(\dfrac{1}{16}, \dfrac{1}{8}\), ___, ___, \(\dfrac{5}{16}, \dfrac{3}{8}\), ___, \(\dfrac{1}{2}, \dfrac{9}{16}, \dfrac{5}{8}\).
Bits that fell out: \(\dfrac{7}{16}, \dfrac{3}{16}, \dfrac{1}{4}\).
- After a party, Lupe has \(\dfrac{5}{12}\) of a cheese pizza, \(\dfrac{4}{12}\) of a pepperoni pizza, and \(\dfrac{4}{12}\) of a veggie pizza left. Will all the slices fit into 1 pizza box? Explain your reasoning.
Self Check
(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
(b) On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?
Contributors and Attributions
-
Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at<EMAIL_ADDRESS>."


12.3: PT Phase Diagrams
Let’s now discuss the pressure–temperature diagram of a typical substance, as reported in Figure \(\PageIndex{1}\). Each of the lines reported in the diagram represents an equilibrium between two phases, and therefore it represents a condition that reduces the number of degrees of freedom to one. The lines can be determined using the Clapeyron equation, Equation 12.1.8 . The interpretation of each line is as follows:
Liquid \(\rightleftarrows\) Gas equilibrium
For this equilibrium we can use Trouton’s rule , Equation 7.1.5, and write: \[ \Delta_{\text{vap}} S = S_{\text{g}}-S_{\text{l}} \cong 88 \; \dfrac{\text{kJ}}{\text{mol}} > 0\quad \text{always}, \label{12.3.1} \]
where the entropy of vaporization is always positive, even for cases where the Trouton’s rule is violated. The difference in molar volumes is easily obtained, since the volume of the gas is always much greater than the volume of the liquid:
\[ \overline{V}_{\text{g}} - \overline{V}_{\text{l}} \cong \overline{V}_{\text{g}} = 22.4\; \dfrac{\text{L}}{\text{mol}} >0\quad \text{always}. \label{12.3.2} \]
Replacing these values in the Clapeyron equation, we obtain:
\[ \dfrac{dP}{dT}=\dfrac{88}{22.4}\left( \dfrac{0.0831}{8.31} \right) = 0.004\;\text{bar} > 0 \quad \text{always}, \label{12.3.3} \]
which is always positive,regardless of violations to the Trouton’s rule. Notice how small this value is, meaning that the liquid–gas equilibrium curve is mostly flat as \(T\rightarrow 0\).
Solid \(\rightleftarrows\) Gas equilibrium
If we look at the signs of each quantity, this case is similar to the previous one: \[ \begin{equation} \begin{aligned} \Delta_{\text{subl}} S &> 0 \quad \text{always} \\ \Delta_{\text{subl}} \overline{V }&> 0 \quad \text{always} \\ \\ \dfrac{dP}{dT} &> 0 \quad \text{always}. \end{aligned} \end{equation}\label{12.3.4} \]
However, the Trouton’s rule is not valid for the solid–gas equilibrium, and \(\dfrac{dP}{dT}\) will be larger than for the previous case.
Solid \(\rightleftarrows\) Liquid equilibrium
The final curve is for the solid-liquid equilibrium, for which we have:
\[ \Delta_{\text{fus}} S = \dfrac{\Delta_{\text{fusion}} H}{T_{\text{m}}} > 0 \quad \text{always}, \label{12.3.5} \]
since fusion is always an exothermic process, \((\Delta_{\text{fus}} H>0)\). On the other side:
\[ \Delta_{\text{fusion}} \overline{V} = \overline{V}_{\text{l}} - \overline{V}_{\text{s}} > 0 \quad \text{generally}. \nonumber \]
In other words, the difference of the molar volume of the liquid and that of the solid is positive for most substances, but it might be negative (for example for \(\mathrm{H}_2\mathrm{O}\)). As such:
\[ \dfrac{dP}{dT} > 0 \quad \text{generally}. \label{12.3.6} \]
For \(\mathrm{H}_2\mathrm{O}\) and a few other substances, \(\dfrac{dP}{dT}<0\), an anomalous behavior that has crucial consequences for the existence of life on earth.\(^1\) For this importance, this behavior is also depicted in Figure \(\PageIndex{1}\) using a dashed green line.
Since the differences in molar volumes between the solid and the liquid phases are usually small (changes are generally of the order of \(10^{-3}\;\mathrm{L}\)), \(\dfrac{dP}{dT}\) is always much larger than for the previous two cases. The resulting lines for the solid–liquid equilibria are still almost vertical, regardless of the signs of their angular coefficients.
The triple point and the critical point
The only point in the \(PT\) diagram where all the three phases coexist is called the triple point. The number of degrees of freedom at the triple point for every 1-component diagram is \(f=1-3+2=0\). The fact that the triple point has zero degrees of freedom means that its coordinates, \({T_{\text{tp}},P_{\text{tp}},\overline{V}_{\text{tp}}}\), are uniquely determined for each chemical substance. For this reason, the value of the triple point of water was fixed by definition—rather than measured—until 2019. This definition was necessary to establish the base unit of the thermodynamic temperature scale in the SI (the Kelvin).\(^2\)
In addition to the triple point where the solid, liquid, and gas phases meet, a triple point may involve more than one condensed phase. Triple points are common for substances with multiple solid phases (polymorphs), involving either two solid phases and a liquid one or three solid phases. Helium is a special case that presents a triple point involving two different fluid phases, called the lambda point. Since the number of degrees of freedom cannot be negative, the Gibbs phase rule for a 1-component diagram sets the limit to how many phases can coexist to just three. Therefore, quadruple points (or higher coexistence points) are not possible for pure substances, even for polymorphs.\(^3\)
Another point with a fixed position in the \(PT\) diagram is the critical point, \({T_{\text{c}},P_{\text{c}},\overline{V}_{\text{c}}}\). We have already given the definition of the critical temperature in Definition: Critical Temperature . This point represents the end of the liquid–gas equilibrium curve. This point is also semantically important to define different regions of the phase diagram, as in Figure \(\PageIndex{1}\). A gas whose pressure and temperature are below the critical point is called a vapor . A gas whose temperature is above the critical one and the pressure is below its critical one is called a supercritical fluid . Finally, a liquid whose pressure is above the critical point is called a compressible liquid .\(^4\)
- As is well explained by Wikipedia : “The unusual density curve and lower density of ice than of water is vital to life—if water were most dense at the freezing point, then in winter the very cold water at the surface of lakes and other water bodies would sink, lakes could freeze from the bottom up, and all life in them would be killed. Furthermore, given that water is a good thermal insulator (due to its heat capacity), some frozen lakes might not completely thaw in summer.[34] The layer of ice that floats on top insulates the water below. Water at about 4 °C (39 °F) also sinks to the bottom, thus keeping the temperature of the water at the bottom constant.”
- For more information on the 2019 redefinition of the SI units, see this Wikipedia page .
- Notice that quadruple points are possible for 2-component diagrams.
- Notice that the temperature of a liquid must be below the critical point, otherwise it is no longer a liquid but rather a supercritical fluid.


9.14: Grouping Objects
Learning Objectives
- Group objects
- Modify grouped objects
PowerPoint allows you to insert shapes or objects and position them in various ways in a slide. In the previous module you learned how to arrange objects. Now we’ll walk through how to group objects. The main reasons to group objects are to make it easier to move, align or resize objects together. In this example we assume objects have already been arranged and now need to be grouped.
Group Objects
- Open a slide in a PowerPoint presentation containing various shapes or objects arranged in the slide.
-
Start from a corner of the slide, hold the left-mouse button down and drag it to include all objects to be included in a group.
- Release the mouse button and all the objects should be showing that they have been selected by each object showing its rotate arrow, resizing dots, etc.
-
On the
Home
tab, select the
Arrange
button, and in
Group Objects
, select
Group
.
-
Now all the selected objects will be in one group and can be moved, resized, rotated, copied, flipped or rearranged as one group.
Modify Group Objects
Once objects are grouped, they can be modified in a variety of ways including ungrouping and regrouping. We’ll walk through a few steps of how to modify within a group object.
Text
If a group object has resized by either enlarging or shrinking and there is text involved within the group, check to see if it now needs to be modified. When a group is resized, text retains its original font size. To resize it, triple click on the text and all text in an object is selected. A menu will appear to change the size to fit the object.
Shapes
Within a group, an individual object can be moved around without affecting the other objects. To move a specific object in a group, select the object and drag it to a new position.
Ungroup/Regroup
If after repositioning or adjusting a group you no longer want the objects to act as one group, go back to the Home, Arrange, Group Objects, selecting Ungroup. If you decide that you’d rather have them as a group again, select all the objects and select the Regroup option.
Note
In Office 365 PowerPoint, grouping can be done with all kinds of objects; video, audio, pictures, shapes, etc. It was not possible in earlier PowerPoint versions to group video and pictures together.
Contributors and Attributions
- Grouping Objects. Authored by : Sherri Pendleton. Provided by : Lumen Learning. License : CC BY: Attribution


12.1: The Development of Self in Early Adulthood
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- Last updated
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Learning Objectives
By the end of this section, you will be able to:
- Identify common developmental tasks of emerging and early adulthood
- Explain the role of cultural change in the development of self during emerging and early adulthood
- Describe how personality may evolve and solidify across emerging and early adulthood
Tell me about yourself. Chad had been mulling over this question in the few days since his blind date. It’s such a simple question, but he had a hard time answering it as he attempted to figure out what, exactly, this prospective partner might find interesting to know about him. Did they want to know that he considers himself friendly, introverted, trustworthy, and hardworking? Or that he’s a total foodie, a D&D fan, and someone who hopes to learn to scuba dive someday? Who is he?
In this section, we focus on the development of self and personality in emerging and early adulthood. The self encompasses all our personal characteristics (APA, 2023.) It is the way we see ourselves, represent ourselves, and relate to others. The self is considered a broader and more complex part of our development than our personality or identity (discussed later in this chapter). We’ll also examine developmental tasks and life events at this stage and the way they shape our sense of self. Finally, we’ll consider the frameworks of Erikson and other theorists who explain why our sense of self changes as we move into adulthood, and how that change relates to our personality traits.
Developmental Tasks: Growing Independence and Role Change
Between the ages of 18 and 29, U.S. adults may experience several significant life changes, such as leaving the parental home, completing school, entering the workforce, forming a committed romantic relationship, and becoming a parent. Many if not all these events require or result in increasing independence and role change that in turn contribute to the development of self. In preparation for these tasks, developmental psychologist Jeffrey Arnett (2000) suggested that “emerging adulthood” (ages 18–25) is characterized by a period of extensive exploration of new roles and adult commitments. Young adults place more priority on personal growth-oriented opportunities that have the potential to increase their social relationships, status, and vocational success, compared to older adults who place greater priority on their health and prosocial engagement. Regardless of age, it is how attainable we perceive our goals to be that predicts our well-being (Bühler et al., 2019). Scales and colleagues (2015) assert that successful development means more than just completing a developmental task or reaching a personal goal, but also being able to develop with a “thriving orientation,” reflected by growth in a young adult’s well-being and maturity as they encounter changing roles and contexts. Based on this perspective, Scales and colleagues conducted an extensive review of cross-cultural research and identified eight dimensions of well-being that reflect a “successful young adulthood: physical health, psychological and emotional well-being, life skills, ethical behavior, healthy family and social relationships, educational attainment, constructive educational and occupational engagement, civic engagement” (Scales et al., 2015) (Figure 12.2).
Scales and colleagues intended this list to be inclusive enough to reflect developmental success in early adulthood for a variety of people, but the way we measure or interpret each dimension is filtered through our own cultural context. For example, young adults from more traditional communities or collectivistic cultures may view the pathway to developing “healthy family relationships” as living in and contributing to their parents’ household, whereas other young adults might measure it by their ability to leave the parental home and support themselves. Let’s take a closer look at the way cultural changes influence our perspective of developmental success in early adulthood.
The Social Clock and the Cultural Context of Social Development
Cultural expectations about normative behavior and achievements are often associated with age and create a social clock by which we judge the progress of ourselves and others (Neugarten et al., 1965). Social clock expectations do not necessarily reflect what is real or typical but instead are idealized milestones. For example, in the United States a widespread expectation is that college education should begin immediately after high school graduation and be completed within four years, by age 22. In reality, fewer than half of U.S. college students complete their college education within this timeframe (U.S. Department of Education, 2019).
Social clock milestones are set by a person’s culture and generation, as well as their age. Take the developmental task of leaving your parents’ home. The number of young U.S. adults who live with their parents has increased somewhat over the last 75 years, and young men are more likely to do so than young women (Hatfield, 2023), but the percentage has peaked during times of national emergency, such as during the Great Depression (48 percent) and the start of the COVID-19 pandemic in 2020 (52 percent) (Fry et al., 2020). (Figure 12.3).
Currently one-third of U.S. adults aged 18-34 live with their parents. Compare that number with recent reports from the European Union, where in many countries such as Italy, Greece, and Croatia, two-thirds of young adults live at home with their parents (Figure 12.4).
If we measure success in young adulthood by the person’s well-being in their changing roles and contexts, what happens when a young adult or others perceive them to be on or off time with their social clock? In many cultures, most developmental tasks of young adulthood are considered positive (such as graduation) (Shanahan & Busseri, 2019), and not completing them may be seen negatively.
Self-evaluation based on completion of developmental tasks in young adulthood appears to be cross-cultural. In both the culture of Turkey and the culture of Switzerland, young adults report greater life satisfaction when they achieve these goals. What differs across cultures are the developmental priorities: Life satisfaction of Turkish young adults is positively affected by on-time achievement of traditional family tasks such as marriage and parenthood, whereas Swiss young adults were more focused on individual achievements such as education and independent living (Pekel-Uludağlı & Akbaş, 2019; Krings et al., 2008). These differing priorities are echoed by interviews with diverse young adults in the United States. Those from immigrant families and ethnic and racial minorities are more likely to view the transition to adulthood as preparation for “the roles and responsibilities of interdependence,” such as living within or contributing to an intergenerational family household or business, than to prioritize individuality and independence (Swartz et al., 2017, p. 280).
Overall, today’s young adults appear to care about the traditional goals prescribed by their social clocks such as career and marriage, but they also pursue personal priorities like independence, maturity, and confidence. Those in the United States report that normative milestones like graduating and starting a career matter to them but are not prerequisites to adult maturity, and thus they can be flexible about when they complete them (Swartz et al., 2017). Based on hundreds of interviews around the country, Swartz and colleagues (2017) concluded that today’s young adults “felt fairly comfortable with the uncertainty and ambiguity – social status-wise – of the transition to adulthood. They took it as almost natural and inevitable, nearly desiring and celebrating the lack of certainty for its flexibility, freedom, and openness” (p. 4).
This generational shift in young adults’ perspective on the social clock is likely an adaptation to the rapid pace of cultural change. In addition to staying longer in their parents’ home, they are also prolonging their education, marrying later, having children later, changing jobs more frequently, and even remaining dependent on their parent’s healthcare plan longer than previous generations (Vespa, 2017; Centers for Medicare and Medicaid Services, 2023). What accounts for these changes? Young adults are responding to the changing circumstances of the world around them that have sometimes created more opportunities but also set up more potential obstacles (Swartz et al., 2017). That said, many young adults still might feel some stress or anxiety if those in their close friend or social group seem to be achieving developmental tasks before they do. Feeling "off time" from your social group - particularly if you are behind their schedule - can create some invisible pressure to adhere to the social clock.
Opportunities and Obstacles
Today’s young adults can search for educational and employment opportunities, dating partners, and new homes without getting out of bed. They can learn, work, and maintain personal connections online. Access to education, information, and social connection has increased, and the methods by which young adults interact with their world have changed.
Young U.S. adults are also living in an increasingly diverse nation. According to the U.S. Census Diversity Index, in 2010 the chance that two randomly chosen individuals would be from different racial or ethnic groups was just over half, at 54.9 percent (U.S. Census Bureau, 2020) (Figure 12.5). By 2020 it was 61.6 percent, given greater diversity among younger than older age groups (Menchaca et al., 2023; U.S. Census Bureau, 2020). This growing diversity is reflected in the increasing variety of experiences in emerging adulthood, and it disrupts the assumptions of a one-size-fits-all social clock. However, sometimes a young person’s possible pathways are limited by economic, social, and cultural constraints, which we must also consider when navigating the shifting cultural landscape.
Economic conditions can impede young adults’ progress on developmental goals like continuing their education and living independently. Over the last 40 years, the United States and other nations have increasingly evolved into knowledge economies in which financial success depends largely on technological skill and innovation, scientific knowledge and progress, and intellectual breakthroughs (Berkes & Gaetani, 2023). The industries that accomplish these tasks rely on a more highly educated workforce. Not surprisingly, then, 74 percent of the high school class of 2023 reported they wanted to go to college (Bauer-Wolf, 2023). However, only 66 percent expect to attend, and in many states like Arizona, Idaho, and Utah, the percentage that enroll is 50 percent or lower (NCHEMS, 2018). Many cite cost as a major barrier. Even when adjusting for inflation, the average cost of attending a 4-year college has increased 180 percent in the last 40 years (McGurran & Hahn, 2023). Higher education isn’t the only avenue to independence with financial barriers: With sky-rocketing home prices, interest rates, and utility costs, a recent report concluded that housing hasn’t been so unaffordable in the United States since 1984 (Bahney, 2023).
Robbins and Wilner (2001) coined the term quarter-life crisis to describe feelings of helplessness, panic, indecision, and apprehension that may accompany the expectations of emerging adulthood. In a meta-analysis of research published over the last ten years, Hasyim and colleagues (2024) identified both individual and environmental factors that may influence whether a young adult experiences these feelings (Figure 12.6). Inflexibly committing to goals without space for reflection can make young people feel trapped and anxious. This anxiety can be lowered by perceived social support and spirituality. However, when young adults perceived their family or community as exerting too much influence, pressure, or judgment, it increased the likelihood of negative experiences during the early adult transition, particularly for adults from families with collectivistic cultural values.
Faced with so many challenges and choices, however, young adults are particularly good at adaptive decision-making. They can efficiently review and integrate information in task-specific ways (Lindow & Lang, 2022). Perhaps that is why, contrary to the looming threat of the quarter-life crisis, reported life satisfaction typically increases for most over the course of young adulthood (Switek & Easterlin, 2018). Even when he used the term crisis within his own work, Erikson did not mean “impending catastrophe” but rather “a necessary turning point” (Erikson, 1968, p. 16). And consistent with the research, relationships with others are important to developmental success during that turning point in time.
Life Hacks: Thriving During the Quarter-Life Crisis
Looking back, young adults who have been through the “quarter-life crisis” provide the following advice (Dabis & Yates, 2014):
- Change your environment. Even a temporary change in surroundings like a visit home or a short vacation can provide space to reset and reflect.
- Practice self-awareness. Workplace psychologists call this process “taking stock” (Panchal & Jackson, 2007). Take time to review your situation. Pay attention when something doesn’t feel right and consider how to leverage your strengths.
- Be decisive. Have confidence in your feelings and follow through with your decisions. Practicing self-assurance doesn’t mean staying committed to bad situations, but rather following your gut. And sometimes that means changing what you are doing.
- Stay positive. Tell yourself it will be okay. Let go of your own negative thoughts, challenge the negative voices of others, and reject toxic environments.
- Practice resilience. Few things in life go as planned. Get comfortable with a little trial and error. Be prepared to “tweak” and “adapt” as you go.
- Think about your finances. While money doesn’t buy happiness, it does provide stability. Spend carefully, save what you can, and think long-term.
- Find support. Friends, family, coworkers, and community members in whom you can confide and with whom you can share feelings and find acceptance are a bedrock in times of change and uncertainty.
The Role of Intimacy
Many classic theories about the development of self in early adulthood focus on the value of establishing committed and meaningful relationships with others. We begin this section with Erikson’s early adult challenge of intimacy vs. isolation and the perspectives of other thinkers such as psychologists George Valliant and Daniel Levinson and writer Gail Sheehy.
Theory of Psychosocial Development
Erikson’s theory of psychosocial development in early adulthood is called intimacy vs. isolation , reflecting the challenge of establishing close and trusting relationships with others. While these relationships might include romantic or sexual ones, Erikson was clear that psychological intimacy can be achieved in any relationship in which you demonstrate “ the ability to fuse your identity with someone else’s without the fear that you are going to lose something yourself” (Evans, 1967, p. 48), and that trusting partnerships can be found in the context of “friendship, combat, leadership, love, and inspiration” (Erikson, 1959, p. 101) (Figure 12.7).
Erikson asserted that intimacy, whether with a close friend, fellow soldier, or romantic partner, requires a commitment that builds trust, but also vulnerability and willingness to sacrifice and compromise. Those unwilling to experience it are likely to become psychologically and socially isolated. On the surface this developmental challenge can appear to undermine the need for increasing independence and self-sufficiency that characterizes many of the developmental tasks discussed earlier. However, research on early adulthood is clear: Social connectedness is key to a successful early adult transition. Indeed, early adulthood is associated with increasing feelings of family obligation, and those who report feeling needed and useful to their friends and family are more likely to also report receiving greater support and experiencing higher well-being during the early-adult transition (Fuligni & Pederson, 2002; Fuligni et al., 2022) (Figure 12.8).
Related Theories of Early Adult Development
Based on his 60-year longitudinal study of more than 500 men as they embarked on adulthood, psychologist George Valliant (1977, 1993, 2002) affirmed Erikson’s developmental framework and the early adult challenge of intimacy vs. isolation, in particular as it applied to men in the cohort Valliant studied. But Valliant added two new elements: First, he inserted a transitional stage at the end of early adulthood that he called “career consolidation,” a time to reconcile the early-adulthood tasks of intimacy and career exploration and a bridge to the generative priorities of middle adulthood.
Second, Valliant documented that adults cope with the stress and anxieties of developmental tasks by using defense mechanisms, which vary in their effectiveness and maturity. In the context of intimacy vs. isolation, Valliant identified “affiliation” as one of the most mature and healthy coping mechanisms. Affiliation allows us to reduce the anxiety of developmental tasks by confiding in others and being willing to ask for and receive their help and support in solving problems. On the other hand, Valliant described “help-rejecting complaining” as an immature defense mechanism that keeps others at a distance at the expense of healthy development. Adults employing this response to anxiety will complain about their problems and yet reject offers to help, judging the suggestions as useless or “not good enough” (Di Giuseppe & Perry, 2021).
Psychologist Daniel Levinson also saw developmental value in establishing connections with others in early adulthood. Calling the developmental stages “eras,” Levinson’s Seasons of Life theory of adult development describes a transitional period of exploration between ages 17 and 22. During this time, young adults modify their relationships with friends and family to develop the independence needed to progress into the era of early adulthood. Levinson’s early adulthood era is characterized by pursuing life goals, such as leaving the parent’s home, as well as starting a career and marriage. Levinson suggests that the path to achieving these goals can be facilitated by a close mentoring relationship with a role model who can guide and support the young adult’s emerging independence and maturity, particularly in the workplace.
Like Valliant’s, Levinson’s theory was originally based on a longitudinal study of adult men. With his collaborator and wife Judy, however, Levinson later conducted a smaller-scale study on a cohort of career women born between 1936 and 1947, to examine the validity of his theory as applied to women. After her husband’s death, Judy Levinson published the results of this work in The Seasons of a Woman’s Life (1996). While the study found many similarities in men’s and women’s transitions and eras of early adulthood, it found women faced greater obstacles in reconciling education, career, and family responsibilities. They also met with greater gender discrimination in their career development, and they found it more difficult to establish effective mentoring relationships in the workplace because available mentors were usually men. As a result, many of the women studied described their husbands as their primary source of career mentoring and support, exhibiting a more direct link between the developmental tasks of intimacy and career development than their men counterparts did.
While Daniel Levinson was framing his theory of adult development in men, writer Gail Sheehy was researching the lives of men and women in their 20’s, 30s, and 40’s to explore the reality of adult development in the 20 th century. In the book Passages (1976) , based on her work, Sheehy colorfully mapped out the decades of adulthood:
- “Tryout Twenties”: Age 18-30 is a “provisional adulthood” where there is room to explore options during a “prolonged adolescence,” when young people are still defined by others’ expectations.
- “Turbulent Thirties”: Age 30-40 is the first experience of true adulthood, in which individuals take on real adult roles and responsibility and challenge the idealistic aspirations of early adulthood.
- “Flourishing Forties:” Age 40-50 begins a “second adulthood,” fueled by a midlife crisis during which adults take stock of the goals and achievements of their “first adulthood” and attempt to realign their priorities to confidently and optimistically pursue meaningful goals in the second half of life.
The book was wildly popular for Sheehy’s engaging and relatable insights and was eventually named by the Library of Congress as one of the most influential books of its time. Twenty years later, Sheehy published the follow-up New Passages (1995), in which she more carefully examined the latter half of adulthood from her own perspective as an older adult. In this sequel, Sheehy noted that societal and cultural changes had created noticeable cohort differences in the developmental experience of adults from different generations, and that earlier conceptions of the stages of adulthood were outdated. She rejected the one-size-fits-all description of adult development that she and others had earlier endorsed, instead drawing attention to the way longer lifespans create increased opportunities for modern adults to “customize our own life cycle” in a way not possible decades earlier.
Personality Traits: Evidence for Stability and Change
While the development of self in adulthood is, in part, an adaptation to the developmental tasks encountered at this stage of life, our personality is also inextricably tied to our sense of self. The Five-Factor Model (FFM) is the most widely accepted framework psychologists use for describing individual differences in personality. With it they can measure where individuals fall on a continuum of five traits: Openness to experience, Conscientiousness, Extraversion, Agreeableness, and Neuroticism (OCEAN). According to the originators of this model, these traits reflect biologically based tendencies that interact with environmental influences such as culture to predict how we will respond to life changes such as the challenges of early adulthood. All this interaction culminates in our evolving sense of self.
The Five-Factor model views our individual personality traits as relatively stable predispositions more likely to drive development rather than to develop themselves (Roberts & Davis, 2016). For example, during early adulthood, a person high in extraversion might explore careers that require regularly working with large groups of people. In this example, personality is influencing the developmental task of career exploration. Exploring careers well-suited to our individual personality traits in early adulthood is advisable, especially because research shows that the level of a given individual personality trait tends to remain stable over time relative to its level in others, a phenomenon known as rank-order stability . That is, a person who demonstrates high levels of extraversion isn’t likely to become very introverted over time. In fact, rank-order stability increases during early adulthood (Ferguson, 2010).
However, even if a person’s ranking on a personality trait isn’t likely to change substantially with age, that doesn’t mean it cannot respond to life events with small but adaptive changes. A mean-level change describes the extent to which the level of a personality trait can fluctuate over the lifespan. This fluctuation may occur in response to cultural changes, historical events, and role changes. For example, the developmental tasks of emerging adulthood may explain why research finds mean level changes such as an increase in emotional stability and conscientiousness during early adulthood (Roberts & Davis, 2016). According to the social investment theory of personality development , as young people begin to commit to adult roles, including romantic relationships and school and work responsibilities, their personality responds with small but measurable increases in agreeableness, conscientious, and openness and decreases in neuroticism (Roberts et al., 2006, 2016; Wagner et al., 2015; Schwaba et al., 2018; Schwaba et al., 2019). They may react to the responsibilities of school and work with an increase in the goal-oriented organization found in the trait of conscientiousness. This association has been supported cross-culturally (Bleidorn et al., 2013). The increase or decrease of certain traits with age to effectively adapt to the demands of development is known as the maturity principle of personality development .
Young adults may also draw on stable support systems, both internal and external, to facilitate their development. Personality has a remarkable ability to both direct the trajectory of developmental tasks in early adulthood and adapt to changing roles and responsibilities. It is like a sturdy rubber band that can support our sense of self while also stretching to meet our changing needs.
Link to Learning
Where do you rank on the Big 5 personality traits? Take this Big Five Personality Test self-assessment to learn more about your level of openness, conscientiousness, extraversion, agreeableness, and neuroticism. Consider how your level of each trait might have enabled or adapted to the developmental tasks or roles relevant to your life right now.
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25.1: Adrenergics and Anticholinergics
By the end of this section, you should be able to:
- 25.1.1 Discuss the use of adrenergic and anticholinergic drugs used to treat lower respiratory disorders.
- 25.1.2 Explain the indications, actions, adverse reactions, and interactions of adrenergic and anticholinergic drugs used to treat lower respiratory disorders.
- 25.1.3 Describe nursing implications of adrenergic and anticholinergic drugs used to treat lower respiratory disorders.
- 25.1.4 Explain the client education related to adrenergic and anticholinergic drugs used to treat lower respiratory disorders.
Adrenergics
Adrenergic drugs, also known as sympathomimetic drugs, are a class of medications that that bind to adrenergic receptors throughout the body. These receptors are stimulated by the neurotransmitters norepinephrine and epinephrine , also known as adrenaline. Adrenergic drugs mimic the effects of these neurotransmitters or enhance their activity, resulting in a wide range of physiological responses. These medications can act on different types of adrenergic receptors, including alpha-adrenergic receptors and beta-adrenergic receptors, producing diverse effects on various organ systems. Adrenergic drugs are used to manage several conditions, such as asthma, and they play a crucial role in bronchodilation (Farzam et al., 2022).
Beta Adrenergics
Beta-adrenergic drugs target beta-adrenergic receptors in the sympathetic nervous system. These receptors are found in various tissues, including the heart, lungs, and smooth muscles, and lead to smooth muscle relaxation.
One type of beta-adrenergic receptor, beta 2, is predominantly found in the smooth muscles of the lungs, bronchioles, and blood vessels. Stimulating these receptors leads to bronchodilation and vasodilation. Medications like albuterol, levalbuterol, and salmeterol are frequently used in the treatment of respiratory conditions, such as asthma and COPD, that cause bronchoconstriction.
Albuterol is a short-acting beta-2 adrenergic agonist and is primarily used to treat and manage respiratory conditions such as asthma, COPD, and exercise-induced bronchospasm. Albuterol works by engaging or stimulating the beta-2 adrenergic receptors, relaxing the smooth muscles in the airways and leading to bronchodilation and improved airflow. Albuterol is often used as a rescue medication for acute asthma attacks and as maintenance therapy for COPD (Hsu & Bajaj, 2023).
Levalbuterol and salmeterol are also beta-adrenergic agonists and are used to treat asthma and COPD. Levalbuterol is a short-acting beta-2 agonist , and salmeterol is a long-acting beta-2 agonist . Salmeterol is used as a maintenance therapy to prevent asthma and should not be used for immediate relief of an asthma attack, whereas levalbuterol is used similarly to albuterol.
Table 25.1 lists common beta adrenergics used for lower respiratory system disorders and typical routes and dosing for adult and pediatric clients .
| Drug | Routes and Dosage Ranges |
|
Albuterol
( Accuneb , Proventil , Ventolin ) |
In adults for acute episodes of bronchospasm or prevention of asthmatic symptoms:
2 inhalations (2.5 mg per inhalation) every 4–6 hours. Some clients may only need 1 inhalation every 4 hours.
In adults for exercise-induced bronchospasm prevention: 2 inhalations (2.5 mg per inhalation) 15 minutes prior to exercise. In children age 2–12: 1.25 mg or 0.63 mg 3–4 times daily via nebulization. |
|
Levalbuterol
( Xopenex ) |
Adults:
0.63 mg every 6–8 hours by nebulization.
Children 6–11: 0.31 mg 3 times per day by nebulization, not to exceed 0.63 mg 3 times a day. |
|
Salmeterol
( Serevent ) |
For bronchodilation and prevention of asthma symptoms:
1 inhalation (50 mcg) twice daily, 12 hours apart, in combination with inhaled corticosteroids.
For exercise-induced bronchospasm: 1 inhalation (50 mcg) 30 minutes prior to exercise. For COPD: 1 inhalation (50 mcg) twice daily 12 hours apart. |
Adverse Effects and Contraindications
Common adverse effects include tremors, nervousness, headache, and tachycardia. Cold symptoms, migraine, chest pain, bronchitis, and nausea have also been reported. Clients with severe cardiac disease should use albuterol only at the direction of their health care provider due to systemic effects on heart rate and blood pressure (DailyMed, Albuterol sulfate , 2023).
Table 25.2 is a drug prototype table for beta adrenergics featuring albuterol. It lists drug class, mechanism of action, adult and pediatric dosage , indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Beta adrenergic Mechanism of Action Relaxes bronchial, uterine, and vascular smooth muscle by stimulating beta-2 receptors |
Drug Dosage
In adults for acute episodes of bronchospasm or prevention of asthmatic symptoms: 2 inhalations (2.5 mg per inhalation) every 4–6 hours. Some clients may only need 1 inhalation every 4 hours. In adults for exercise-induced bronchospasm prevention: 2 inhalations (2.5 mg per inhalation) 15 minutes prior to exercise. In children ages 2–12: 1.25 mg or 0.63 mg 3–4 times daily via nebulization. |
|
Indications
Prevention and relief of bronchospasm Prevention of exercise-induced bronchospasm Therapeutic Effects Bronchodilation Relief of bronchospasm |
Drug Interactions
Antiarrhythmics Beta blockers CNS stimulants Food Interactions No significant interactions |
|
Adverse Effects
Tremor Nervousness Tachycardia Headache |
Contraindications
Hypersensitivity Caution: Cardiac disorder Hyperthyroidism Diabetes Severe cardiac disease |
Alpha- and Beta-Adrenergic Agonists
Alpha- and beta-adrenergic agonists stimulate both alpha- and beta-adrenergic receptors. Alpha-adrenergic receptors are found primarily in smooth muscles, regulating vasoconstriction and blood pressure. Beta-adrenergic receptors are present in the heart, lungs, and other tissues and control heart rate, bronchodilation, and metabolic processes.
Ephedrine, a sympathomimetic drug, acts as a nonselective alpha- and beta-adrenergic agonist , meaning it stimulates both types of receptors. The ability of ephedrine to activate both receptor types makes it a widely used drug for conditions such as asthma and nasal congestion as well as low blood pressure. However, its usage requires caution due to potential side effects and interactions with other medications (Drugbank Online, 2023).
Epinephrine is used often as an emergency treatment for allergic reactions and respiratory distress including anaphylaxis. It works by relaxing and opening air passages to allow for easier breathing. It can be given as an oral inhalation, intravenously, subcutaneously, and as an intramuscular injection (Dalal & Grujic, 2023). Epinephrine can cause anxiety, tremors, palpitations, nausea, and headache.
Table 25.3 lists common alpha and beta adrenergics used for lower respiratory system disorders and typical routes and dosing for adult clients.
| Drug | Routes and Dosage Ranges |
|
Ephedrine
( Emerphed , Corphedra ) |
1–2 tablets (12.5 mg each) every 4 hours as needed. Maximum dose: 12 tablets in 24 hours. |
|
Epinephrine
( Adrenalin , Auvi-Q , Epipen , Primatene Mist ) |
Inhalation:
1 inhalation as needed. Wait 1 minute, then take second inhalation. Wait at least 4 hours between doses. Maximum dose: 8 inhalations in 24 hours.
Intramuscular or subcutaneous: 0.3–0.5 mg (0.3–0.5 mL) of undiluted epinephrine administered in the anterolateral aspect of the thigh, repeated every 5–10 minutes as necessary. Maximum dose: 0.5 mg (0.5 mL) per injection. Intended for severe exacerbation and/or when inhalation is not available. |
Adverse Effects and Contraindications
Ephedrine can cause an increase in heart rate and blood pressure, insomnia, and tremors. Clients who have hypersensitivity or who have been taking a monoamine oxidase inhibitor (MAOI) should not use ephedrine (DailyMed, Ephedrine hydrochloride , 2022).
Epinephrine can cause anxiety, restlessness, and headache. Clients may also report chest pain, high blood pressure, dizziness, and difficulty sleeping.
Table 25.4 is a drug prototype table for alpha and beta adrenergics featuring ephedrine. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Adrenergic Mechanism of Action Relaxes bronchial smooth muscle by stimulating beta-2 receptors Stimulates alpha- and beta-adrenergic receptors in the sympathetic nervous system |
Drug Dosage
1–2 tablets (12.5 mg per tablet) every 4 hours as needed. Maximum dose: 12 tablets in 24 hours. |
|
Indications
Mild/intermittent asthma Therapeutic Effects Bronchodilation Relief of bronchospasm |
Drug Interactions
Alpha blockers Beta blockers Cardiac glycosides MAOIs Food Interactions No significant interactions |
|
Adverse Effects
Nervousness Palpitations Tachycardia Headache |
Contraindications
Angle-closure glaucoma Heart failure Intermittent asthma Cardiovascular disease Hypertension Stroke Caution: Bronchial asthma or emphysema with degenerative heart disease |
Anticholinergics
Anticholinergic drugs block the action of acetylcholine at muscarinic receptors, which are found in numerous organs and tissues throughout the body. They produce a range of effects such as relaxation of smooth muscles, reduction in secretions, and inhibition of parasympathetic responses. These medications are useful in the treatment of various conditions, including respiratory disorders, overactive bladder, gastrointestinal disorders, and certain neurological conditions.
Safety Alert
Side Effects of Anticholinergics
Anticholinergics should be used with caution due to potential side effects, especially in older adults , who may be more susceptible to adverse reactions like cognitive impairment and increased risk of falls.
Two commonly used respiratory anticholinergics are ipratropium bromide and tiotropium. Ipratropium bromide, often administered via inhalation, acts as a bronchodilator by blocking the action of acetylcholine at the muscarinic receptors in the airways. This helps to relax the smooth muscles and widen the air passages, providing relief from symptoms such as wheezing and shortness of breath in conditions like asthma and COPD.
Tiotropium, also an inhalation medication, is a long-acting anticholinergic that provides sustained bronchodilation by binding specifically to the muscarinic receptors in the airways. It is primarily used for the long-term maintenance treatment of COPD to reduce symptoms and improve lung function.
Table 25.5 lists common anticholinergics used for lower respiratory system disorders and typical routes and dosing for adult clients.
| Drug | Routes and Dosage Ranges |
|
Ipratropium bromide
( Atrovent ) |
Metered-dose inhaler
(17 mcg):
4–8 inhalations with spacer every 20 minutes for 3 doses, then hourly as needed for up to 3 hours.
Nebulization (500 mcg) : 3–4 times daily, with doses 6–8 hours apart. |
|
Tiotropium
( Spiriva ) |
Hand inhaler:
2 inhalations of the powder contents of 1 Spiriva capsule, once daily.
Spiriva Respimat inhaler: For COPD: 2 inhalations (2.5 mcg each) per device actuation once daily. For asthma: 2 inhalations (1.25 mcg each) once daily. |
Adverse Effects and Contraindications
Side effects of both drugs can include dry mouth, headache, nervousness or dizziness, blurred vision, constipation, and cough. Clients with hypersensitivity, narrow-angle glaucoma, and urinary retention should avoid these drugs; they can cause urinary retention and exacerbate symptoms.
Table 25.6 is a drug prototype table for anticholinergics featuring ipratropium bromide. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Anticholinergic Mechanism of Action Inhibits vagally mediated reflexes by antagonizing acetylcholine at muscarinic receptors on bronchial smooth muscle |
Drug Dosage
Metered-dose inhaler (17 mcg): 4–8 inhalations with spacer every 20 minutes for 3 doses, then hourly as needed for up to 3 hours. Nebulization (500 mcg) : 3–4 times daily, with doses 6–8 hours apart. |
|
Indications
Bronchospasm Relief of acute asthmatic symptoms (when combined with albuterol) Therapeutic Effects Bronchodilation Relief of bronchospasm |
Drug Interactions
Other anticholinergics Food Interactions No significant interactions |
|
Adverse Effects
Dizziness Urinary retention Palpitations Tachycardia Blurred vision Constipation Dry mouth |
Contraindications
Hypersensitivity Caution: Angle-closure glaucoma Bladder neck obstruction Prostatic hyperplasia |
Link to Learning
In this link to learning, Alila Medical Media presents information on the pharmacology and action of adrenergics. This educational video with animation discusses the different types of adrenergic receptors and the different types of drugs that act on them.
Nursing Implications
The nurse should do the following for clients who are taking adrenergic or anticholinergic drugs:
- Prior to administering, assess the client’s medical history, current drug list, and allergies.
- Assess the client’s baseline respiratory function.
- Ensure the drug is prepared appropriately using aseptic technique, and verify dosage prior to administration.
- Monitor the client’s response to the drug, including any changes in breathing effort, rate, and oxygen saturation.
- 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 an adrenergic or anticholinergic drug should:
- Take the drug as prescribed without skipping doses or stopping therapy.
- Prime the inhaler prior to use by shaking it and spraying into the air for a total of 4 sprays. Clean it after use by rinsing it with water and allowing it to dry.
- Wait at least 15 seconds between inhalations if more than one is required.
- Inform the health care provider of worsening symptoms including shortness of breath, cough, chest tightness, and wheezing.
- Create an asthma action plan. The Asthma and Allergy Foundation of America provides an example.
The client taking an adrenergic or anticholinergic drug should not:
- Use more medication than was prescribed by the health care provider.
- Wash or place a powder inhaler in water.
Unfolding Case Study
Part A
Read the following clinical scenario to answer the questions that follow. This case study will evolve throughout the chapter.
Harold Watson is a 65-year-old client who presents to his primary care physician with complaints of worsening shortness of breath, chronic cough, and increased sputum production over the past few months. He reports that these symptoms have significantly impacted his daily activities, and he has also noticed a decrease in his ability to perform simple tasks around the house. Harold reports that he quit smoking 10 years ago but was a heavy smoker for 30 years. He reports smoking roughly one pack of cigarettes per day when he was smoking.
History
Hypertension
Current Medications
Metoprolol 100 mg daily
| Vital Signs | Physical Examination | |
|---|---|---|
| Temperature: | 98.7°F |
|
| Blood pressure: | 145/90 mm Hg | |
| Heart rate: | 92 beats/min | |
| Respiratory rate: | 20 breaths/min | |
| Oxygen saturation: | 91% on room air | |
| Height: | 5'6" | |
| Weight: | 175 lb |
Based on the assessment of Harold, what diagnosis should the nurse anticipate from the health care provider?
- Answer
-
COPD
Based on Harold’s past medical history of chronic obstructive pulmonary disease (COPD) and the physical examination, which of the following medications would be the highest priority to administer to him?
- Answer
-
Salmeterol


31.4: Practice Solving Equations and Representing Situations with Equations
Lesson
Let's solve equations by doing the same to each side.
Exercise \(\PageIndex{1}\): Number Talk: Subtracting From Five
Find the value of each expression mentally.
\(5-2\)
\(5-2.1\)
\(5-2.17\)
\(5-2\frac{7}{8}\)
Exercise \(\PageIndex{2}\): Row Game: Solving Equations Practice
Solve the equations in one column. Your partner will work on the other column.
Check in with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error and correct it.
| column A | column B |
|---|---|
| \(18=2x\) | \(36=4x\) |
| \(17=x+9\) | \(13=x+5\) |
| \(8x=56\) | \(3x=21\) |
| \(21=\frac{1}{4}x\) | \(28=\frac{1}{3}x\) |
| \(6x=45\) | \(8x=60\) |
| \(x+4\frac{5}{6}=9\) | \(x+3\frac{5}{5}=8\) |
| \(\frac{5}{7}x=55\) | \(\frac{3}{7}x=33\) |
| \(\frac{1}{5}=6x\) | \(\frac{1}{3}=10x\) |
| \(2.17+x=5\) | \(6.17+x=9\) |
| \(\frac{20}{3}-\frac{10}{9}x\) | \(\frac{14}{5}=\frac{7}{15}x\) |
| \(14.88+x=17.05\) | \(3.91+x=6.08\) |
| \(3\frac{3}{4}x=1\frac{1}{4}\) | \(\frac{7}{5}x=\frac{7}{15}\) |
Exercise \(\PageIndex{3}\): Choosing Equations to Match Situations
Circle all of the equations that describe each situation. If you get stuck, consider drawing a diagram. Then find the solution for each situation.
-
Clare has 8 fewer books than Mai. If Mai has 26 books, how many books does Clare have?
- \(26-x=8\)
- \(x=26+8\)
- \(26-8=x\)
- \(x=\underline{\qquad}\)
-
A coach formed teams of 8 from all the players in a soccer league. There are 14 teams. How many players are in the league?
- \(y=14\div 8\)
- \(\frac{y}{8}=14\)
- \(\frac{1}{8}y=14\)
- \(y=14\cdot 8\)
- \(y=\underline{\qquad}\)
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Kiran scored 223 more points in a computer game than Tyler. If Kiran scored 409 points, how many points did Tyler score?
- \(223=409-z\)
- \(409-223=z\)
- \(409+223=z\)
- \(409=223+z\)
- \(z=\underline{\qquad}\)
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Mai ran 27 miles last week, which was three times as far as Jada ran. How far did Jada run?
- \(3w=27\)
- \(w=\frac{1}{3}\cdot 27\)
- \(w=27\div 3\)
- \(w=3\cdot 27\)
- \(w=\underline{\qquad}\)
Are you ready for more?
Mai’s mother was 28 when Mai was born. Mai is now 12 years old.  How old will they be then?
Summary
Writing and solving equations can help us answer questions about situations.
Suppose a scientist has \(13.68\) liters of acid and needs \(16.05\) liters for an experiment. How many more liters of acid does she need for the experiment?
- We can represent this situation with the equation:
\(13.68+x=16.05\)
- When working with hangers, we saw that the solution can be found by subtracting 13.68 from each side. This gives us some new equations that also represent the situation:
\(x=16.05-13.68\)
- Finding a solution in this way leads to a variable on one side of the equal sign and a number on the other. We can easily read the solution—in this case, 2.37—from an equation with a letter on one side and a number on the other. We often write solutions in this way.
\(x=2.37\)
Let’s say a food pantry takes a \(54\)-pound bag of rice and splits it into portions that each weigh \(\frac{3}{4}\) of a pound. How many portions can they make from this bag?
- We can represent this situation with the equation:
\(\frac{3}{4}x=54\)
- We can find the value of \(x\) by dividing each side by \(\frac{3}{4}\). This gives us some new equations that represent the same situation:
\(x=54\div\frac{3}{4}\)
- The solution is 72 portions.
\(x=72\)
Glossary Entries
Definition: Coefficient
A coefficient is a number that is multiplied by a variable.
For example, in the expression \(3x+5\), the coefficient of \(x\) is \(3\). In the expression \(y+5\), the coefficient of \(y\) is \(1\), because \(y=1\cdot y\).
Definition: Solution to an Equation
A solution to an equation is a number that can be used in place of the variable to make the equation true.
For example, 7 is the solution to the equation \(m+1=8\), because it is true that \(7+1=8\). The solution to \(m+1=8\) is not \(9\), because \(9+1\neq 8\).
Definition: Variable
A variable is a letter that represents a number. You can choose different numbers for the value of the variable.
For example, in the expression \(10-x\), the variable is \(x\). If the value of \(x\) is 3, then \(10-x=7\), because \(10-3=7\). If the value of \(x\) is \(6\), then \(10-x=4\), because \(10-6=4\).
Practice
Exercise \(\PageIndex{4}\)
Select all the equations that describe each situation and then find the solution.
-
Kiran’s backpack weighs 3 pounds less than Clare’s backpack. Clare’s backpack weighs 14 pounds. How much does Kiran’s backpack weigh?
- \(x+3=14\)
- \(3x=14\)
- \(x=14-3\)
- \(x=14\div 3\)
-
Each notebook contains 60 sheets of paper. Andre has 5 notebooks. How many sheets of paper do Andre’s notebooks contain?
- \(y=60\div 5\)
- \(y=5\cdot 60\)
- \(\frac{y}{5}=60\)
- \(5y=60\)
Exercise \(\PageIndex{5}\)
Solve each equation.
- \(2x=5\)
- \(y+1.8=14.7\)
- \(6=\frac{1}{2}z\)
- \(3\frac{1}{4}=\frac{1}{2}+w\)
- \(2.5t=10\)
Exercise \(\PageIndex{6}\)
For each equation, draw a tape diagram that represents the equation.
- \(3\cdot x=18\)
- \(3+x=18\)
- \(17-6=x\)
(From Unit 6.1.1)
Exercise \(\PageIndex{7}\)
Find each product.
\((21.2)\cdot (0.02)\qquad (2.05)\cdot (0.004)\)
(From Unit 5.3.4)
Exercise \(\PageIndex{8}\)
For a science experiment, students need to find 25% of 60 grams.
- Jada says, “I can find this by calculating \(\frac{1}{4}\) of 60.”
- Andre says, “25% of 60 means \(\frac{25}{100}\cdot 60\).”
Do you agree with either of them? Explain your reasoning.
(From Unit 3.4.4)


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-
Why does oil palm (>Elaeis guineensis, LC) cultivation represent a significant threat to biodiversity in Africa? (In addition to your own research, it might also be useful to read Box 6.1.)
-
Read Harris et al. (2009) on the decline of the world’s mass wildlife migrations. Which lost African migration appeals to you most and why? What species were involved? What numbers of animals were involved? How do you think this migration can be revived?
-
Which ecosystem in your region would you consider the most damaged, and which would you consider the most pristine? Can you explain why these two ecosystems have such different fates?
-
Do you agree with the idea that human population growth is the primary driver of extinctions today? Why? How do we balance protecting biodiversity with providing for a growing human population, and the right of people to have children?


14.6: County and City Government
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Learning Objectives
By the end of this section, you will be able to:
- Identify the differences between county and municipal governments in terms of their responsibilities and funding sources
- Describe the two primary types of municipal government and the three basic types of county government
County and city governments make up an important component of the overall structure of the government. Not only do they affect citizens directly; it is also easier for citizens to interact with local government officials because their offices and the community’s school board or city council meetings are often close by. Despite this fact, voter turnout in local elections tends to be lower than in state and national elections. Municipal and county governments differ in structure and purpose in several ways.
County Government
County governments serve a larger geographical area than cities and towns, but a smaller area than states. They are created by the state government and typically operate under provisions set out in the state constitution. As such, they are essentially administrative units of the state. Census estimates from 2012 indicate that there are just over three thousand counties in the United States. 82 County systems usually take one of three basic forms: the commission system, the council-administrator system, and the council-elected executive system.
The most common form of county government is the commission system. Under this structure, an elected commission, which generally consists of a small number of commissioners, serves as the governing body within the county, performing all legislative and executive functions. These include adopting a budget, passing county resolutions, and hiring and firing county officials. 83
Under the council-administrator system, the voters elect council members to serve for a specified period of time, and the council in turn appoints an administrator to oversee the operation of the government. The administrator serves at the directive of the council and can be terminated by the council. The goal of this arrangement is to divide administrative and policymaking responsibilities between the elected council and the appointed administrator. 84
Under a council-elected executive system, the voters elect both the members of the council and the executive. The executive performs functions similar to those of the state governor. For instance, the executive can veto the actions of the council, draft a budget, and provide suggestions regarding public policy. 85
Although the tasks they perform can vary from state to state, most counties have a courthouse that houses county officials, such as the sheriff, the county clerk, the assessor, the treasurer, the coroner, and the engineer. These officials carry out a variety of important functions and oversee the responsibilities of running a county government. For instance, the county coroner investigates the cause of death when suspicious circumstances are present. The county clerk oversees the registration of voters and also certifies election results for the county. In addition, this officeholder typically keeps the official birth, death, and marriage records. The county treasurer oversees the collection and distribution of funds within the county, while the county assessor conducts property tax evaluations and informs individual citizens or business owners of their right to contest the appraised value of their property. Finally, a county engineer will oversee the maintenance and construction of county infrastructure. 86 In short, counties help to maintain roads and bridges, courthouses and jails, parks and pools, and public libraries, hospitals, and clinics. 87 To provide these services, county governments typically rely on property tax revenue, a portion of sales tax receipts, and funds from intergovernmental transfers by way of federal or state grants.
City Government
Municipal governments oversee the operation and functions of cities and towns. Census estimates for 2012 show just over 19,500 municipal governments and nearly 16,500 township governments in the United States. 88 The vast majority of municipal governments operate on one of two governing models: a mayor-council system or a council-manager system.
Under the mayor-council system voters elect both a mayor and members of the city council. The city council performs legislative functions and the mayor the executive functions. Under this system, the mayor may be given a great deal of authority or only limited powers. 89 Under a strong mayor system, the mayor will be able to veto the actions of the council, appoint and fire the heads of city departments, and produce a budget. Under a weak mayor system, the mayor has little authority compared to the council and acts in a ceremonial capacity as a spokesperson for the city. 90
In a council-manager system of government, either the members of the city council are elected by voters along with a mayor who presides over the council, or the voters elect members of the city council and the mayor is chosen from among them. In either case, the city council will then appoint a city manager to carry out the administrative functions of the municipal government. This frees the city council to address political functions such as setting policy and formulating the budget. 91
Municipal governments are responsible for providing clean water as well as sewage and garbage disposal. They must maintain city facilities, such as parks, streetlights, and stadiums (Figure 14.19). In addition, they address zoning and building regulations, promote the city’s economic development, and provide law enforcement, public transportation, and fire protection. Municipal governments typically rely on property tax revenue, user fees from trash collection and the provision of water and sewer services, a portion of sales tax receipts, and taxes on business.
Link to Learning
The International City/County Management Association (ICMA) provides networking opportunities, professional development, and statistical data in order to support local government leaders and other individuals throughout the world. Visit the ICMA Leadership page to learn what makes a better leader and how you might improve your local community.


16.3: Other Aromatic Substitutions
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Objectives
After completing this section, you should be able to
- write a balanced equation for the halogenation (F, Cl, Br, I) of benzene in the presence of a suitable catalyst or promoter.
- draw the resonance contributors for the carbocation which is formed during the reaction of chlorine or bromine with benzene.
- write the equation for the nitration and sulfonation of benzene.
- write the detailed mechanism for the nitration and sulfonation of benzene.
- write the equation for the reduction of an aromatic nitro compound to an amine.
- identify aromatic sulfonation as being a reversible process, and describe the conditions under which the forward and reverse reactions are favoured.
- write the equation for the desulfonation of an aromatic sulfonic acid.
- identify aromatic sulfonic acids as being key intermediates in the manufacture of sulfa drugs.
Key Terms
Make certain that you can define, and use in context, the key term below.
- nitronium ion, (NO +2 )
Study Notes
You should be careful to remember that iodine and fluorine cannot be introduced into an aromatic ring by the method used for bromine and chlorine. On its own, iodine is unreactive with aromatic rings, but one method for aromatic iodination is treatment in the presence of a copper salt such as copper(II)chloride where I2 is oxidized to the more electrophilic species I + .
In contrast, fluorine is too reactive, so it cannot be used directly for aromatic flourination. However, fluorinating agents like 1-(chloromethyl)-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane ditetrafluoroborate (also known as F-TEDA-BF 4 ) sold commercially as Sectfluor® offer convenient sources of “F + ” for this type of reaction.
F-TEDA-BF 4
The overall equation for the formation of nitronium ions by the action of sulfuric acid on nitric acid is
$\ce{\sf{HNO3 + 2H2SO4 <=> H3O+ + NO2+ + HSO4- }}$
The ability of compounds such as nitronium tetrafluoroborate to bring about the nitration of aromatic compounds is good evidence in support of the proposed mechanism.
The nitration of an aromatic ring is an important synthetic pathway to generating arylamines. The reaction below shows one common method of reducing the nitro group. (Amines are examined in more detail in Chapter 24.)
Halogenation of Benzene
Halogenation is an example of electrophillic aromatic substitution. In electrophilic aromatic substitutions, a benzene is attacked by an electrophile which results in substition of hydrogens. However, halogens are not electrophillic enough to break the aromaticity of benzenes, which require a catalyst to activate.
Activation of Halogen
(where X= Br or Cl, we will discuss further in detail later why other members of the halogen family Flourine and Iodine are not used in halogenation of benzenes)
Hence, Halogen needs the help and aid of Lewis Acidic Catalysts to activate it to become a very strong electrophile. Examples of these activated halogens are Ferric Hallides (FeX 3 ) Aluminum Halides (AlX 3 ) where X= Br or Cl. In the following examples, the halogen we will look at is Bromine.
In the example of bromine, in order to make bromine electrophillic enough to react with benzene, we use the aid of an aluminum halide such as aluminum bromide.
With aluminum bromide as a Lewis acid, we can mix Br 2 with AlBr 3 to give us Br + . The presence of Br + is a much better electrophile than Br 2 alone. Bromination is acheived with the help of AlBr 3 (Lewis acid catalysts) as it polarizes the Br-Br bond. The polarization causes polarization causes the bromine atoms within the Br-Br bond to become more electrophillic. The presence of Br + compared to Br 2 alone is a much better electrophille that can then react with benzene.
As the bromine has now become more electrophillic after activation of a catalyst, an electrophillic attack by the benzene occurs at the terminal bromine of Br-Br-AlBr 3. This allows the other bromine atom to leave with the AlBr 3 as a good leaving group, AlBr 4 -.
After the electrophilic attack of bromide to the benzene, the hydrogen on the same carbon as bromine substitutes the carbocation in which resulted from the attack. Hence it being an electrophilic aromatic SUBSTITUTION. Since the by-product aluminum tetrabromide is a strong nucleophile, it pulls of a proton from the Hydrogen on the same carbon as bromine.
In the end, AlBr 3 was not consumed by the reaction and is regenerated. It serves as our catalyst in the halogenation of benzenes.
Dissociation Energies of Halogens and its Effect on Halogenation of Benzenes
The electrophillic bromination of benzenes is an exothermic reaction. Considering the exothermic rates of aromatic halogenation decreasing down the periodic table in the Halogen family. Flourination is the most exothermic and Iodination would be the least. Being so exothermic, a reaction of flourine with benzene is explosive! For iodine, electrophillic iodination is generally endothermic, hence a reaction is often not possible. Similar to bromide, chlorination would require the aid of an activating presence such as Alumnium Chloride or Ferric Chloride. The mechanism of this reaction is the same as with Bromination of benzene.
Nitration and sulfonation of benzene are two examples of electrophilic aromatic substitution. The nitronium ion (NO 2 + ) and sulfur trioxide (SO 3 ) are the electrophiles and individually react with benzene to give nitrobenzene and benzenesulfonic acid respectively.
Nitration of Benzene
The source of the nitronium ion is through the protonation of nitric acid by sulfuric acid, which causes the loss of a water molecule and formation of a nitronium ion.
Sulfuric Acid Activation of Nitric Acid
The first step in the nitration of benzene is to activate HNO 3 with sulfuric acid to produce a stronger electrophile, the nitronium ion.
Because the nitronium ion is a good electrophile, it is attacked by benzene to produce Nitrobenzene.
Mechanism
(Resonance forms of the intermediate can be seen in the generalized electrophilic aromatic substitution)
Sulfonation of Benzene
Sulfonation is a reversible reaction that produces benzenesulfonic acid by adding sulfur trioxide and fuming sulfuric acid. The reaction is reversed by adding hot aqueous acid to benzenesulfonic acid to produce benzene.
Mechanism
To produce benzenesulfonic acid from benzene, fuming sulfuric acid and sulfur trioxide are added. Fuming sulfuric acid, also refered to as oleum , is a concentrated solution of dissolved sulfur trioxide in sulfuric acid. The sulfur in sulfur trioxide is electrophilic because the oxygens pull electrons away from it because oxygen is very electronegative. The benzene attacks the sulfur (and subsequent proton transfers occur) to produce benzenesulfonic acid.
Reverse Sulfonation
Sulfonation of benzene is a reversible reaction. Sulfur trioxide readily reacts with water to produce sulfuric acid and heat. Therefore, by adding heat to benzenesulfonic acid in diluted aqueous sulfuric acid the reaction is reversed.
Further Applications of Nitration and Sulfonation
Nitration is used to add nitrogen to a benzene ring, which can be used further in substitution reactions. The nitro group acts as a ring deactivator. Having nitrogen present in a ring is very useful because it can be used as a directing group as well as a masked amino group. The products of aromatic nitrations are very important intermediates in industrial chemistry.
Because sulfonation is a reversible reaction, it can also be used in further substitution reactions in the form of a directing blocking group because it can be easily removed. The sulfonic group blocks the carbon from being attacked by other substituents and after the reaction is completed it can be removed by reverse sulfonation. Benzenesulfonic acids are also used in the synthesis of detergents, dyes, and sulfa drugs. Bezenesulfonyl Chloride is a precursor to sulfonamides, which are used in chemotherapy.
Exercises
Exercise \(\PageIndex{1}\)
1. What is/are the required reagent(s)for the following reaction:
- Answer
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SO 3 and H 2 SO 4 (fuming)
Exercise \(\PageIndex{2}\)
What is the product of the following reaction:
- Answer
-
Exercise \(\PageIndex{3}\)
Why is it important that the nitration of benzene by nitric acid occurs in sulfuric acid?
- Answer
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Sulfuric acid is needed in order for a good electrophile to form. Sulfuric acid protonates nitric acid to form the nitronium ion (water molecule is lost). The nitronium ion is a very good electrophile and is open to attack by benzene. Without sulfuric acid the reaction would not occur.
Exercise \(\PageIndex{4}\)
Write a detailed mechanism for the sulfonation of benzene, including all resonance forms.
- Answer
-
Exercise \(\PageIndex{5}\)
Draw an energy diagram for the nitration of benzene. Draw the intermediates, starting materials, and products. Label the transition states.
- Answer
-
Exercise \(\PageIndex{6}\)
In each case, how many products would be possible for the bromination of p -xylene, o -xylene, and m -xylene?
- Answer
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Exercise \(\PageIndex{7}\)
If toluene is treated with D 2 SO 4 all the hydrogen’s are replaced with deuterium. Explain.
- Answer
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The deuterium is added to the ring. When the ring “re-aromatizes” the base scavenges the hydrogen before the deuterium and therefore is left on the ring. Continues for the rest of the hydrogen on the ring.
References
- Laali, Kenneth K., and Volkar J. Gettwert. “Electrophilic Nitration of Aromatics in Ionic Liquid Solvents.” The Journal of Organic Chemistry 66 (Dec. 2000): 35-40. American Chemical Society.
- Malhotra, Ripudaman, Subhash C. Narang, and George A. Olah. Nitration: Methods and Mechanisms. New York: VCH Publishers, Inc., 1989.
- Sauls, Thomas W., Walter H. Rueggeberg, and Samuel L. Norwood. “On the Mechanism of Sulfonation of the Aromatic Nucleus and Sulfone Formation.” The Journal of Organic Chemistry 66 (1955): 455-465. American Chemical Society.
- Vollhardt, Peter. Organic Chemistry : Structure and Function. 5th ed. Boston: W. H. Freeman & Company, 2007.