22.2: Cardiac Emergency Drugs
By the end of this section, you should be able to:
- 22.2.1 Identify the characteristics of drugs used to treat cardiac emergencies.
- 22.2.2 Explain the indications, actions, adverse reactions, and interactions of drugs used to treat cardiac emergencies.
- 22.2.3 Describe nursing implications of drugs used to treat cardiac emergencies.
- 22.2.4 Explain the client education related to drugs used to treat cardiac emergencies.
The goal of treatment for a client with AMI or unstable angina is restoring the blood supply to the affected area of the heart muscle. Drugs can help either supply more oxygen to the heart (temporarily) or reduce the heart’s demand for oxygen. If there is stenosis (narrowing) in a coronary artery, the definitive treatment is having the client undergo stent placement or, if stenting is not an option, coronary artery bypass grafting. It is very important that this treatment not be delayed because it can save heart tissue. Thrombolytic therapy may also be used to dissolve an occlusive clot that is causing the coronary ischemia or infarction. Thrombolytic therapy is discussed in Anticoagulant, Antiplatelet, and Thrombolytic Drugs.
Acute Myocardial Infarction and Unstable Angina Drugs
Four classifications of drugs may be used in emergency situations for AMI and unstable angina: aspirin, oxygen, nitroglycerin, and, occasionally, morphine. In either AMI or unstable angina, the most important thing to consider is blood supply to the heart. If the cardiac cells are not receiving blood, they will become ischemic and eventually will die. Each of the medications is used to enhance oxygen-rich blood flow to the heart.
Aspirin
Salicylic acid ( aspirin ) has been used for mild pain relief for more than 100 years. (Pain Response Drugs discusses aspirin as a nonopioid analgesic.) It was also found to work as an antiplatelet drug; therefore, it is useful in suspected AMI and unstable angina. Aspirin irreversibly binds to receptors on platelets, which prevents them from sticking to other platelets. Because platelet aggregation is the first step in blood clotting, if this can be reduced, then the heart may receive more blood.
Adverse Effects and Contraindications
Aspirin can cause gastritis and bleeding in the stomach, other parts of the gastrointestinal tract, brain, and spinal cord.
Contraindications to aspirin are allergy to nonsteroidal anti-inflammatory drugs (NSAIDs), asthma, hemophilia, and other blood clotting disorders. Pediatric clients who have suspected viral illnesses should not take aspirin because Reye’s syndrome, a potentially fatal complication, could develop. As a precaution, aspirin is generally not used in pediatric clients .
Table 22.1 is a drug prototype table for aspirin used in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Salicylic acid Mechanism of Action Irreversibly binds with receptors on platelets, which makes them unable to bind with other platelets |
Drug Dosage
For acute myocardial infarction or unstable angina: 325 mg orally (chewed) once. (If client is unable to take orally, administer rectal suppository form.) |
|
Indications
Mild pain Platelet inhibition in suspected AMI or unstable angina Therapeutic Effects Platelet inhibition Relief of mild pain |
Drug Interactions
Anticoagulants Food Interactions Alcohol Tobacco |
|
Adverse Effects
Gastrointestinal upset/gastritis Gastrointestinal bleeding |
Contraindications
Allergy to NSAIDs Asthma Hemophilia Pediatric clients (risk of developing Reye’s syndrome) |
Nursing Implications
The nurse should do the following for clients who are taking aspirin:
- Assess the client’s allergies and verify that they are not allergic to any of the NSAIDs.
- Assess for signs and symptoms of bleeding.
- In the event of suspected AMI or unstable angina, direct the client to chew the aspirin and then swallow it.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client taking aspirin in an emergency situation should:
- Inform the health care team if they have an allergy to aspirin or other NSAIDs or have a diagnosis of asthma.
- Chew the aspirin tablet before swallowing.
See Anticoagulant, Antiplatelet, and Thrombolytic Drugs for full client teaching guidelines on the use of aspirin in nonemergency situations.
FDA Black Box Warning
Aspirin
The risk of serious bleeding in the stomach, gastrointestinal tract, brain, and spinal cord is increased with aspirin and other NSAIDs .
Concomitant use of aspirin greater than 100 mg per day can reduce the efficacy of ticagrelor (an antiplatelet medication) and should be avoided.
Oxygen
In an AMI or unstable angina, the cardiac cells are deprived of oxygen . When cells are deprived of oxygen, they eventually will die. Supplemental oxygen may be used if the client’s oxygen saturation is less than 94% on room air. In the past, oxygen was used immediately for clients with suspected AMI or unstable angina; however, it was not found to be beneficial if used in clients who were already maintaining an oxygen saturation of 95% or more (Hofmann et al., 2017). Oxygen is typically delivered via nasal cannula starting at 2 L/min and can be titrated to 6 L/min. If the client requires a higher dose to maintain oxygen saturation greater than 94%, then other methods of oxygen delivery should be used.
Nitroglycerin
Nitroglycerin is a nitrate and a first-line treatment for clients with AMI or unstable angina. Nitroglycerin is converted to nitrous oxide, which ultimately causes smooth muscles around arteries to relax. Smooth muscle relaxation causes vasodilation. In AMI or unstable angina, the cardiac myocytes are not receiving enough oxygen, and vasodilation allows more oxygen to be delivered to hypoxic cells. In emergency situations, nitroglycerin is administered either sublingually or intravenously.
Antihypertensive and Antianginal Drugs discusses nitrates more extensively.
Adverse Effects and Contraindications
Adverse effects include orthostatic hypotension, tachycardia, paradoxical bradycardia, flushing, peripheral edema, nausea and vomiting, headache, and blurred vision.
Contraindications include allergies to nitrates, concomitant use of phosphodiesterase (PDE) inhibitors such as tadalafil and sildenafil, history of right ventricular infarction, and hypertrophic cardiomyopathy.
Nitrates should be used cautiously in clients who are on chronic diuretic therapy, have low systolic blood pressure, have autonomic nervous system dysregulation, or are pregnant or breastfeeding.
Safety Alert
Nitroglycerin
Nitrates can cause hypotension. In an emergency situation, make sure the client is sitting or lying down before administering nitroglycerin.
Table 22.2 is a drug prototype table for nitroglycerin use in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Nitrate Mechanism of Action Converts to nitric oxide, which ultimately causes smooth muscle relaxation and vasodilation |
Drug Dosage
For acute myocardial infarction or unstable angina: Sublingual: 0.15–0.6 mg as needed for chest pain every 5 min up to 3 times. Intravenous (IV): 5–10 mcg/min up to 100 mcg/min. |
|
Indications
For acute relief of pain in suspected acute myocardial infarction or unstable angina Therapeutic Effects Relieves pain Increases delivery of oxygen to cardiac tissue |
Drug Interactions
Avanafil Riociguat Sildenafil Tadalafil Vardenafil Food Interactions Alcohol Tobacco |
|
Adverse Effects
Orthostatic hypotension Tachycardia Paradoxical bradycardia Flushing Peripheral edema Nausea and vomiting Headache Blurred vision |
Contraindications
Allergy to nitrates Hypersensitivity Increased intracranial pressure Cardiomyopathy History of right ventricular infarction Shock Caution: Chronic diuretic therapy Low systolic blood pressure Autonomic system dysregulation Pregnancy Lactation |
Nursing Implications
Refer to Antihypertensive and Antianginal Drugs for a full list of nursing implications for clients prescribed nitrates. In the event of suspected AMI or unstable angina, the health care provider may order sublingual nitroglycerin until an IV line is in place. If the client is receiving IV nitroglycerin, the nurse will receive orders to titrate the nitroglycerin based on pain level and blood pressure.
The nurse should do the following for clients who are receiving nitroglycerin intravenously for chest pain:
- Place the client on continuous cardiac monitoring.
- Monitor vital signs frequently, particularly blood pressure, because nitroglycerin can cause significant hypotension.
- If symptomatic hypotension occurs, do not give the nitroglycerin and inform the health care provider.
- Frequently assess pain level.
- Assess for headache and give pain medication for it as ordered.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client receiving nitroglycerin for unstable angina or AMI should:
-
Alert the nurse if any of these occur:
- Their chest pain changes (either improves or worsens)
- They feel faint
- They experience nausea or vomiting
See Antihypertensive and Antianginal Drugs for full client teaching guidelines on nitroglycerin, including client home usage.
Morphine
Morphine is a potent, fast-acting opioid agonist . It binds to opioid receptors in the central and peripheral nervous systems to modulate (decrease) the pain response. Morphine also can help relieve anxiety, which may lower heart rate and reduce the heart’s demand for oxygen. For many years, morphine was a first-line drug in the emergency management of AMI and unstable angina, but now it is used if nitroglycerin cannot control the chest pain (Hermiz & Sedhai, 2023). Pain Response Drugs covers opioid agonists in depth.
Adverse Effects and Contraindications
Opioids must be managed carefully due to their potential adverse effects, which include respiratory depression, respiratory arrest, apnea, circulatory depression, shock, cardiac arrest, sedation, lightheadedness, dizziness, nausea, vomiting, and constipation.
Opioids should not be used if the client has a known hypersensitivity to morphine, respiratory depression, acute or severe asthma, hypercarbia, or a paralytic ileus.
Safety Alert
Opioid Analgesics
Morphine can cause respiratory depression, respiratory arrest, cardiac arrest, and shock. Nurses must monitor the client frequently (reassess at least every 5–10 minutes) when using morphine to control pain.
Table 22.3 is a drug prototype table for opioid agonists featuring morphine. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Opioid agonist Mechanism of Action Primarily a mu opioid receptor agonist that causes modulation of pain in the central and peripheral nervous systems |
Drug Dosage
For acute myocardial infarction if optimal nitroglycerin does not control chest pain: 4–8 mg IV initially, then 2–8 mg IV repeated every 5–15 minutes if needed for complete pain relief. |
|
Indications
For management of pain not responsive to nonnarcotic analgesics Therapeutic Effects Relieves pain |
Drug Interactions
Central nervous system depressants:
Cimetidine Anticholinergics Food Interactions Alcohol |
|
Adverse Effects
Respiratory depression Respiratory arrest Apnea Circulatory depression Shock Cardiac arrest Sedation Lightheadedness Dizziness Nausea Vomiting Constipation |
Contraindications
Known hypersensitivity to morphine Respiratory depression Acute or severe bronchial asthma or hypercarbia Paralytic ileus |
Nursing Implications
The nurse should do the following for clients who are receiving morphine for chest pain:
- Place the client on continuous cardiac monitoring.
- Assess the client’s vital signs and level of consciousness before administering morphine intravenously.
- Reassess vital signs and level of consciousness frequently after administering morphine intravenously.
- If the client’s respiratory rate is less than 10 breaths/min, inform the health care provider.
- Assess the client’s pain frequently.
- Reassess the client’s pain 15 minutes after administering morphine.
- Ensure that a morphine reversal agent (naloxone) is available.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client receiving morphine for unstable angina or AMI should:
-
Alert the nurse if any of these occur:
- Their chest pain changes (either improves or worsens)
- They feel sleepy, dizzy, or lightheaded
- They experience nausea or vomiting
See Pain Response Drugs for full client teaching guidelines on morphine.
FDA Black Box Warning
Morphine
Life-threatening respiratory depression, addiction, abuse, and misuse can occur with morphine use. Concomitant use of morphine with benzodiazepines or other central nervous system depressants may result in profound sedation and/or respiratory depression.
Dysrhythmia Drugs
There is a saying in cardiac nursing that there are only three problems with the conduction system: The heart can beat too fast, too slow, or not at all.
This is an oversimplification, but each one of these problems can lead to hemodynamic instability and potentially death. Once again, the importance of cardiac output cannot be emphasized enough. Cardiac output is a function of heart rate and stroke volume. If the heart rate is too fast, then ventricular filling cannot occur, and cardiac output is affected. If the heart rate is too slow, then not enough blood will be pumped, and cardiac output is affected. If there is no heart rate at all, then, of course, there is no cardiac output.
The cardiac conduction system—specifically, the SA node—determines the heart rate. The SA node is influenced by the sympathetic and parasympathetic nervous systems. As with all other tissues in the body, it must have a blood supply, and it needs the correct amount of electrolytes (sodium, potassium, calcium, and chloride) to function optimally. The cardiac conduction system (see Figure 22.4) includes the SA node, the AV node, the bundle of His, and the Purkinje fibers.
Although the main pacemaker of the heart is the SA node, other areas of the conduction system generate electrical impulses. The SA node generates impulses at 60–100 beats/min, the AV node at 40–60 beats/min, and the ventricles at 20–40 beats/min. Typically, the conduction system will conduct the fastest rate, which is why the system normally follows the SA node impulses.
Cardiac conduction can be categorized by area of the heart: atrial conduction and ventricular conduction. Most conduction problems in the atria are not life-threatening, but supraventricular tachycardia, atrial fibrillation with rapid ventricular response, and sick sinus syndrome (which can cause hemodynamically unstable bradycardia) can cause hemodynamic instability and potentially death. Ventricular dysrhythmias nearly always cause hemodynamic instability and will lead to death if not treated rapidly. Ventricular dysrhythmias include ventricular tachycardia, pulseless ventricular tachycardia, and ventricular fibrillation.
Emergency dysrhythmias discussed in this chapter include:
- Asystole : Complete cessation of electrical activity in the heart
- Atrial fibrillation with rapid ventricular response : Rapid electrical stimulation and conduction that cause the atria to have unorganized contraction (fibrillation) and the ventricles to beat rapidly
- Symptomatic bradycardia : Heart rate less than 60 beats per minute that negatively affects cardiac output
- Pulseless electrical activity : Life-threatening dysrhythmia in which the electrical system conducts impulses but the cardiac myocytes do not respond
- Pulseless ventricular tachycardia : Life-threatening dysrhythmia in which the ventricles contract so rapidly that a pulse cannot be detected
- Supraventricular tachycardia : Rapid heart rate that originates from above the ventricles
- Ventricular fibrillation : Life-threatening dysrhythmia originating in the ventricles in which ventricles are not coordinated in their contraction, leading to minimal cardiac output
- Ventricular tachycardia : Dysrhythmia that originates from the ventricles and causes them to contract rapidly; if it becomes fast enough, it can turn into pulseless ventricular tachycardia, which is life-threatening
The drugs described in this section are used in emergency situations to restore hemodynamic stability and improve cardiac conduction. Antiarrhythmic drugs that are used long term are discussed in Antidysrhythmic Drugs.
Adenosine
Adenosine is a class V antidysrhythmic drug. It is used to convert supraventricular tachycardia into normal sinus rhythm (the regular conduction pattern of the heart). Adenosine affects how potassium and calcium move into and out of the myocardial conduction cells that affect the resting membrane potential, causing conduction to take longer. This is useful in disrupting supraventricular tachycardia and gives the heart the opportunity to restart in normal sinus rhythm.
Adverse Effects and Contraindications
Adenosine may cause flushing of the skin, palpitations, chest pain, hypotension, lightheadedness, nausea, sweating, nervousness, numbness, and apprehension. It decreases conduction through the AV node and may produce short-lasting heart block. It is important to note that the benefit of adenosine in a life-threatening event outweighs the risk of adverse effects.
Contraindications to adenosine include second- or third-degree heart block (except in clients with a pacemaker), sinus node disease (sick sinus syndrome or symptomatic bradycardia), and known hypersensitivity to adenosine.
Table 22.4 is a drug prototype table for adenosine use in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Class V antiarrhythmic Mechanism of Action Affects potassium and calcium channels in the myocardial conducting cells, significantly slowing heart rate |
Drug Dosage
For supraventricular tachycardia: 6 mg rapid IV bolus (administered over 1–2 seconds); if supraventricular tachycardia is not eliminated, administer 12 mg rapid IV bolus. The 12 mg dose may be repeated once if required. |
|
Indications
To convert supraventricular tachycardia to normal sinus rhythm Therapeutic Effects Slows nerve impulses in the heart |
Drug Interactions
Methylxanthines (caffeine, theophylline) Dipyridamole Carbamazepine Food Interactions Caffeine |
|
Adverse Effects
Flushing of skin Palpitations Chest pain Hypotension Lightheadedness Nausea Sweating Nervousness Numbness Apprehension Short-lasting heart block due to decreased conduction through the AV node |
Contraindications
Second- or third-degree heart block (except in clients with a pacemaker) Sinus node disease (sick sinus syndrome or symptomatic bradycardia) Known hypersensitivity to adenosine |
Clinical Tip
Adenosine
Adenosine has a very short half-life and should be administered as a rapid IV bolus directly into a vein, followed by a rapid saline flush.
Nursing Implications
The nurse should do the following for clients who are receiving adenosine intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor vital signs frequently.
- Administer adenosine as an IV push directly into a vein over 1–2 seconds.
- Administer a rapid saline bolus immediately after administering adenosine.
- Be prepared to administer a second dose.
- If the client is alert, inform them that they may feel chest pain once the bolus is given. The chest pain should subside quickly (in less than 1 minute).
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
In supraventricular tachycardia, the client may not be conscious because of decreased cardiac output.
If alert and oriented, the client receiving adenosine should:
- Inform the health care team if they have a known heart block or sick sinus syndrome.
Amiodarone
Amiodarone is a class III antiarrhythmic drug used for hemodynamically unstable ventricular tachycardia, ventricular fibrillation, and other dysrhythmias. It blocks potassium and calcium channels from opening, which slows down cardiac conduction and therefore slows heart rate. Antidysrhythmic Drugs covers the use of amiodarone in the management of chronic dysrhythmias.
Adverse Effects and Contraindications
Amiodarone can cause hypotension, bradycardia, atrioventricular block, hepatic injury, heart rhythm disturbances, pulmonary injury, loss of vision, thyroid injury, hypersensitivity, anorexia, nausea, vomiting, and photosensitivity. It is important to note that the benefit of amiodarone in a life-threatening event outweighs the risk of adverse effects.
Contraindications to amiodarone include known hypersensitivity, cardiogenic shock, marked sinus bradycardia, and second- or third-degree AV block (unless the client has an implanted pacemaker).
Table 22.5 is a drug prototype table for amiodarone use in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Class III antiarrhythmic Mechanism of Action Blocks potassium and calcium channels in the cardiac conducting cells, slowing the heart rate |
Drug Dosage
For hemodynamically unstable ventricular tachycardia or ventricular fibrillation: 150 mg IV bolus given over 10 minutes, then 360 mg IV infused over the next 6 hours, then 540 mg IV infused over the next 18 hours; dosage should be titrated after 24 hours. |
|
Indications
For ventricular fibrillation and hemodynamically unstable ventricular tachycardia Therapeutic Effects Slows nerve impulses in the heart |
Drug Interactions
Drugs that prolong the QT interval (increased risk of torsade de pointes):
Warfarin (increases effect) HMG-CoA reductase inhibitors/statin drugs (increases effect; risk of myopathy) Protease inhibitors St. John’s wort Food Interactions Grapefruit/grapefruit juice |
|
Adverse Effects
Anorexia Nausea and vomiting Hypotension Bradycardia and atrioventricular block Hepatic injury Dysrhythmias Photosensitivity Pulmonary injury Loss of vision Thyroid injury Hypersensitivity |
Contraindications
Known hypersensitivity Cardiogenic shock Marked sinus bradycardia Second- or third-degree AV block (unless the client has an implanted pacemaker) |
Safety Alert
Amiodarone
Amiodarone can cause pulmonary toxicity and swelling in the lungs.
Nursing Implications
The nurse should do the following for clients who are receiving amiodarone intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor vital signs frequently.
- Monitor level of consciousness.
- Monitor laboratory values and report abnormal findings to the health care provider.
- Have resuscitative equipment and drugs immediately available.
- Monitor for adverse effects of amiodarone infusion.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client receiving amiodarone should:
- Inform the health care provider of nausea, which may be an early indication of liver damage.
Clients with ventricular fibrillation or hemodynamically unstable ventricular tachycardia are typically no longer conscious. See Antidysrhythmic Drugs for client teaching guidelines for amiodarone in less acute situations.
FDA Black Box Warning
Amiodarone
Amiodarone can cause pulmonary toxicity and swelling in the lungs.
Atropine
Atropine is a first-line drug used for treating symptomatic bradycardia. It is an anticholinergic drug, which means it blocks receptors in the parasympathetic nervous system. The heart is constantly stimulated by both the parasympathetic nervous system (PNS) and the sympathetic nervous system (SNS). It reacts to whichever system is sending more impulses. If the PNS signals are blocked, then the heart receives fewer signals from acetylcholine, the primary neurotransmitter of the PNS. Because of fewer signals from the PNS, the SNS signaling is stronger, which increases the heart rate.
Adverse Effects and Contraindications
Atropine can cause tachycardia, acute glaucoma, pyloric obstruction, and complete urinary retention. It is important to note that the benefit of atropine in a life-threatening event outweighs the risk of adverse effects.
There are no contraindications to the use of atropine.
Table 22.6 is a drug prototype table for atropine use in emergency situations. 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 cholinergic nerves, resulting in decreased parasympathetic stimulation |
Drug Dosage
For symptomatic bradycardia: 1 mg IV every 3–5 minutes; maximum dose: 3 mg. |
|
Indications
Symptomatic bradycardia Treatment of organophosphorus poisoning Therapeutic Effects Increased heart rate |
Drug Interactions
Mexiletine Food Interactions No significant interactions |
|
Adverse Effects
Tachycardia Acute glaucoma Pyloric obstruction Complete urinary retention |
Contraindications
None |
Nursing Implications
The nurse should do the following for clients receiving atropine intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor vital signs frequently.
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
In symptomatic bradycardia, the client may not be conscious because of decreased cardiac output.
If alert and oriented, the client receiving atropine should:
- Inform the health care team if they feel different (better or worse) after the initial dose.
- Inform the health care team if they feel a fast heart rate or racing heart after the dose.
Diltiazem
Diltiazem is a nondihydropyridine Calcium channel blocker and a class IV antiarrhythmic drug. Nondihydropyridine calcium channel blockers inhibit calcium flow into cardiac myocytes, which results in decreased force of contractions and decreased heart rate. Therefore, diltiazem is useful for treating supraventricular tachycardia and atrial fibrillation with rapid ventricular response. In addition, calcium channel blockers cause vasodilation and can reduce blood pressure. Antihypertensive and Antianginal Drugs discusses the use of calcium channel blockers in hypertension.
Adverse Effects and Contraindications
Diltiazem can cause asystole; atrial flutter; first-, second-, and third-degree atrioventricular block; bradycardia; chest pain; congestive heart failure; sinus pause; sinus node dysfunction; syncope; ventricular dysrhythmia; ventricular fibrillation; ventricular tachycardia; dizziness; allergic reaction; Stevens–Johnson syndrome; and angioedema. It is important to note that the benefit of diltiazem in a life-threatening event outweighs the risk of adverse effects.
Contraindications include sick sinus syndrome, unless the client has a pacemaker; second- or third-degree heart block, unless the client has a pacemaker; severe hypotension and/or cardiogenic shock; hypersensitivity; ventricular tachycardia; and AMI.
Diltiazem should not be administered concurrently with IV beta-adrenergic blockers.
Table 22.7 is a drug prototype table for diltiazem use in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Nondihydropyridine calcium channel blocker; class IV antiarrhythmic drug Mechanism of Action Inhibits calcium ions from entering the cell, resulting in decreased force of cardiac contraction and vascular smooth muscle relaxation |
Drug Dosage
For paroxysmal supraventricular tachycardia or atrial fibrillation with rapid ventricular response: 0.25 mg/kg actual body weight IV bolus over 2 minutes. If response inadequate, 0.35 mg/kg actual body weight IV bolus administered over 2 minutes. Subsequent bolus doses may be administered as needed according to the health care provider’s discretion. After initial bolus(es), continuous IV infusion may be needed, starting at 10 mg/hour for up to 24 hours. |
|
Indications
Atrial fibrillation with rapid ventricular response Supraventricular tachycardia Therapeutic Effects Slows heart rate Lowers blood pressure |
Drug Interactions
Beta-adrenergic blockers may increase incidence of bradycardia Food Interactions Alcohol |
|
Adverse Effects
Allergic reaction Angioedema Asystole Atrial flutter First-degree atrioventricular block Second-degree atrioventricular block Third-degree atrioventricular block Bradycardia Chest pain Congestive heart failure Hypotension Sinus pause Sinus node dysfunction Syncope Ventricular dysrhythmia Ventricular fibrillation Ventricular tachycardia Dizziness Stevens–Johnson syndrome |
Contraindications
Sick sinus syndrome (unless client has pacemaker) Second- or third-degree heart block (unless client has pacemaker) Severe hypotension and/or cardiogenic shock Hypersensitivity Ventricular tachycardia Acute myocardial infarction |
Nursing Implications
The nurse should do the following for clients receiving diltiazem intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor blood pressure frequently.
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
In supraventricular tachycardia or atrial fibrillation with rapid ventricular response, the client may not be conscious because of decreased cardiac output.
If alert and oriented, the client receiving diltiazem should:
- Inform the health care team if they have a known heart block or sick sinus syndrome.
See Antidysrhythmic Drugs for client teaching guidelines for diltiazem in less acute situations.
Epinephrine
Epinephrine ( adrenaline ) is a hormone that stimulates the SNS during the fight-or-flight response. SNS stimulation results in a faster heart rate, increased cardiac output, and pulmonary dilation (for increased oxygen intake), among other things. Epinephrine is a nonselective adrenergic agonist , which means it stimulates all receptors in the SNS. Epinephrine is used in a variety of emergency situations. In cardiac emergencies, epinephrine is used in ventricular fibrillation, pulseless ventricular tachycardia, asystole, and pulseless electrical activity.
Adverse Effects and Contraindications
Epinephrine can cause anxiety and excitability, headache, fear, heart palpitations, tachycardia, supraventricular tachycardia, ventricular arrhythmias, hypertension, cerebral hemorrhage, hemiplegia, subarachnoid hemorrhage, anginal pain in clients with angina, pulmonary edema, hypoglycemia, hypokalemia, and lactic acidosis. It is important to note that the benefit of epinephrine in a life-threatening event outweighs the risk of adverse effects.
Contraindications to epinephrine include cardiac dilation, coronary artery insufficiency, and shock during general anesthesia. Epinephrine contains sodium bisulfate, which may cause an allergic reaction.
Table 22.8 is a drug prototype table for epinephrine use in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Adrenergic agonist (nonselective) Mechanism of Action Binds to sympathetic nervous system receptors and stimulates the sympathetic nervous system, which causes increased heart rate, increased blood pressure, and increased oxygen intake in the lungs |
Drug Dosage
For ventricular fibrillation, pulseless ventricular tachycardia, asystole, and pulseless electrical activity: 0.1–1 mg IV bolus (using 0.1 mg/mL concentration) repeated every 5 minutes as necessary during cardiac resuscitation. For anaphylaxis: 0.3–0.5 mg intramuscularly (using 1 mg/mL concentration), repeated every 5–10 minutes as needed. |
|
Indications
Emergency treatment of type I hypersensitivity reactions (anaphylaxis), ventricular fibrillation, pulseless ventricular tachycardia, asystole, and pulseless electrical activity Emergency treatment of anaphylaxis Therapeutic Effects Increases heart rate Increases blood pressure Bronchodilation |
Drug Interactions
Other sympathomimetic (adrenergic stimulant) drugs such as isoproterenol Digoxin Other medications may potentiate the effects:
Use with caution in clients taking monoamine oxidase inhibitors Food Interactions No significant interactions |
|
Adverse Effects
Anxiety Excitability Headache Fear Heart palpitations Tachycardia Supraventricular tachycardia Ventricular arrhythmias Myocardial ischemia Hypertension Cerebral hemorrhage Hemiplegia Subarachnoid hemorrhage Anginal pain in clients with angina Pulmonary edema Hypoglycemia Hypokalemia Lactic acidosis |
Contraindications
Cardiac dilation Coronary artery insufficiency Shock during general anesthesia |
Nursing Implications
The nurse should do the following for clients receiving epinephrine intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor blood pressure frequently. (Often, blood pressure is measured continuously when client is in shock.)
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
In ventricular fibrillation, pulseless ventricular tachycardia, asystole, or pulseless electrical activity, the client will be unconscious. In anaphylaxis, the client may be unconscious.
If alert and oriented, the client receiving epinephrine should:
- Inform the health care team if they have a change in status (better or worse) after medication administration.
- Inform the health care team if they notice a change in their breathing.
Lidocaine
Lidocaine is classified as a local anesthetic agent, but it is also a class Ib antiarrhythmic drug used in acute ventricular dysrhythmias. Lidocaine blocks sodium channels, which slows the cardiac action potential and causes the electrical stimulation threshold to be higher. The higher stimulation threshold causes the cardiac conduction cells to be less likely to conduct action potentials, which ultimately treats ventricular tachyarrhythmias.
Adverse Effects and Contraindications
Lidocaine can cause respiratory depression and arrest, unconsciousness, convulsions, tremors, twitching, vomiting, blurred or double vision, drowsiness, dizziness, light-headedness, agitation, confusion, paresthesia, and dysarthria. It is important to note that the benefit of lidocaine in a life-threatening event outweighs the risk of adverse effects.
Contraindications to lidocaine include a history of hypersensitivity, Stokes–Adams syndrome, Wolff–Parkinson–White syndrome, and heart block.
Table 22.9 is a drug prototype table for lidocaine use in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications. Lidocaine as a topical anesthetic is not addressed in this section.
|
Drug Class
Class Ib antiarrhythmic Mechanism of Action Blocks sodium channels in cardiac conducting cells, which ultimately causes slowed conduction and decreased heart rate |
Drug Dosage
For ventricular arrhythmias: 1–1.5 mg/kg IV bolus at 25–50 mg/min. Continuous IV infusion may be needed; usual dosing is 1–4 mg/min. |
|
Indications
Emergency management of ventricular arrhythmias Therapeutic Effects Decreases heart rate |
Drug Interactions
Other antiarrhythmic drugs (cardiac effects may be additive or antagonistic, which may lead to toxic effects) Propranolol, metoprolol, nadolol (increase the serum concentration of lidocaine) Food Interactions No significant interactions |
|
Adverse Effects
Respiratory depression Respiratory arrest Unconsciousness Convulsions Tremors Twitching Vomiting Blurred or double vision Drowsiness Dizziness Light-headedness Agitation Confusion Cardiovascular arrest Bradycardia, which may lead to cardiovascular arrest Hypotension Ventricular fibrillation Ventricular tachycardia Asystole Allergic reaction, including anaphylaxis |
Contraindications
History of known reaction Stokes – Adams syndrome Wolff – Parkinson – White syndrome Severe sinoatrial heart block Severe atrioventricular heart block Severe intraventricular heart block |
Nursing Implications
The nurse should do the following for clients receiving lidocaine intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor blood pressure frequently.
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- For continuous IV lidocaine infusion, closely monitor the rate and provide continuous ECG monitoring.
- Monitor for adverse effects of lidocaine infusion
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client receiving lidocaine should:
- Inform the health care provider of tremors, twitching, nausea, vomiting, blurred or double vision, dizziness, lightheadedness, or confusion.
In acute ventricular arrhythmias, clients are typically no longer conscious. See Antidysrhythmic Drugs for client teaching guidelines for lidocaine in less acute situations.
Procainamide
Procainamide is a class Ia antiarrhythmic drug that binds to sodium channels, reducing the speed of conduction. It is used in life-threatening ventricular arrhythmias.
Adverse Effects and Contraindications
Procainamide can cause hypotension, asystole, ventricular fibrillation, lupus erythematosus–like syndrome, pleural effusions, pericarditis, neutropenia, thrombocytopenia, hemolytic anemia, agranulocytosis, dizziness, weakness, and elevated liver enzyme levels.
Prolonged use of procainamide often leads to a positive antinuclear antibody (ANA) test; if this occurs, the risk–benefit ratio of procainamide use should be reassessed. It is important to note that the benefit of procainamide in a life-threatening event generally outweighs the risk of adverse effects.
Contraindications to the use of procainamide include a history of hypersensitivity, complete heart block, atrial fibrillation or flutter, congestive heart failure, lupus erythematosus, torsade de pointes, myasthenia gravis, and sulfite sensitivity.
Table 22.10 is a drug prototype table for procainamide use in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Class Ia antiarrhythmic Mechanism of Action Antagonizes cardiac cell sodium channels, which ultimately slows the heart rate |
Drug Dosage
For life-threatening ventricular arrhythmias: Loading dose 10–17 mg/kg at a rate of 20–50 mg/min. Maintenance therapy may be indicated; dosing is variable. |
|
Indications
Emergency management of ventricular arrhythmias Therapeutic Effects Decreases heart rate |
Drug Interactions
Digitalis derivatives Other class Ia antiarrhythmic drugs Other antiarrhythmic drugs (may prolong the QT interval) Food Interactions No significant interactions |
|
Adverse Effects
Hypotension Asystole Ventricular fibrillation Lupus erythematosus–like syndrome Pleural effusion Pericarditis Neutropenia Thrombocytopenia Hemolytic anemia Agranulocytosis Dizziness Weakness Elevated liver enzyme levels |
Contraindications
History of hypersensitivity Complete heart block Atrial fibrillation or flutter Congestive heart failure Lupus erythematosus Torsade de pointes Myasthenia gravis Sulfite sensitivity |
Nursing Implications
The nurse should do the following for clients receiving procainamide intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor blood pressure frequently.
- Monitor level of consciousness.
- Have other resuscitative equipment and drugs available.
- Monitor laboratory values, including ANA titer and liver enzyme levels, and report abnormal results to the health care provider
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client receiving procainamide should:
- Inform the health care provider of generalized rheumatic pain, dizziness, or weakness.
In acute ventricular arrhythmias, clients are typically no longer conscious. See Antidysrhythmic Drugs for client teaching guidelines for procainamide in less acute situations.
FDA Black Box Warning
Procainamide
Prolonged administration of procainamide often leads to the development of a positive antinuclear antibody (ANA) test, with or without symptoms of a lupus erythematosus–like syndrome. If a positive ANA titer develops, the benefit versus risks of continued procainamide therapy should be assessed.
Dopamine and Dobutamine
After a cardiac event, clients often may still have hypotension or be in shock even after the immediate emergency is over. They may need medications to stabilize their blood pressure so that tissues are perfused. Dopamine and dobutamine are two drugs that help achieve and maintain hemodynamic stability.
Dopamine
Endogenous (naturally occurring in the body) dopamine is a hormone that plays a role in stimulating the SNS. Dopamine , an inotropic agent , is converted into epinephrine within the bloodstream. Dopamine binds to alpha-1, alpha-2, beta-1, and dopaminergic receptors. Adrenergic stimulation of alpha-1 and alpha-2 receptors causes vasoconstriction, which leads to increased blood pressure. Adrenergic stimulation of beta-1 receptors directly increases the heart rate.
Exogenous (synthetic) dopamine mimics the body’s own dopamine to the same effect. Dopamine is used in profound hypotension and shock to increase cardiac output by increasing the rate and force of contraction and blood pressure by vasoconstriction. At low doses (0.5–2 mcg/kg/min), dopamine causes vasodilation and can be used to increase urinary output. At intermediate doses (2–10 mcg/kg/min), it increases heart rate and stroke volume, which leads to increased cardiac output. At high doses, dopamine causes vasoconstriction, which increases blood pressure.
Adverse Effects and Contraindications
Dopamine can cause ventricular arrhythmia, atrial fibrillation, ectopic beats, tachycardia, anginal pain, palpitations, cardiac conduction abnormalities, widened QRS complex, bradycardia, hypotension, hypertension, vasoconstriction, dyspnea, azotemia, headache, and anxiety. Extravasation of dopamine into the tissue around an IV site may cause necrosis, sloughing, and potentially gangrene. It is important to note that the benefit of dopamine in a life-threatening event outweighs the risk of adverse effects.
Contraindications to the use of dopamine include pheochromocytoma, uncorrected tachyarrhythmias or ventricular fibrillation, and allergy to metabisulfite.
Safety Alert
Dopamine
Dopamine may cause peripheral ischemia in clients with a history of occlusive vascular disease.
Dopamine is a potent drug. It should be administered only in an intensive care area with proper monitoring available.
Table 22.11 is a drug prototype table for dopamine use in emergency situations. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Inotrope Mechanism of Action Converts to epinephrine in the bloodstream, which ultimately causes vasoconstriction and increased rate and force of contraction |
Drug Dosage
For hemodynamic instability: Initiate titration at 2–5 mcg/kg/min and titrate as directed by health care provider. Titration parameters include blood pressure and signs of tissue perfusion (adequate urine output). |
|
Indications
Emergency management of hypotension and shock Therapeutic Effects Increases heart rate |
Drug Interactions
Monoamine oxidase inhibitors Tricyclic antidepressants Beta-adrenergic blockers (may antagonize the effects) Alpha-adrenergic blockers (may antagonize the effects) Haloperidol Cyclopropane or halogenated hydrocarbon anesthetics Other vasopressors and oxytocic drugs Phenytoin Food Interactions No significant interactions |
|
Adverse Effects
Ventricular arrhythmia Atrial fibrillation Ectopic beats Tachycardia Anginal pain Palpitations Cardiac conduction abnormalities Widened QRS complex Bradycardia Hypotension Hypertension Vasoconstriction Dyspnea Azotemia Headache Anxiety |
Contraindications
Pheochromocytoma Uncorrected tachyarrhythmias or ventricular fibrillation Allergy to metabisulfite |
Nursing Implications
The nurse should do the following for clients receiving dopamine intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor blood pressure frequently.
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- Monitor IV site for signs of extravasation.
- Monitor for signs and symptoms of occlusive vascular disease.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
In hypotension or shock, the client may be unconscious.
If the client receiving dopamine is alert and oriented, the client should:
- Inform the health care team if they have a change in status (better or worse) after medication administration.
- Inform the heath care team if they have pain at the IV site.
- Inform the health care team if they have a headache.
FDA Black Box Warning
Dopamine
Dopamine may cause peripheral ischemia in clients with a history of occlusive vascular disease.
Dobutamine
Dobutamine is a beta-1 adrenergic agonist that stimulates the heart to contract more forcefully and, to a lesser extent, faster. It is used for the cardiac decompensation that can occur immediately after a cardiac event.
Adverse Effects and Contraindications
Dobutamine can cause increased heart rate, increased blood pressure, ventricular ectopic activity, hypotension, and IV site reaction. It is important to note that the benefit of dobutamine in a life-threatening event outweighs the risk of adverse effects.
Contraindications to the use of dobutamine include idiopathic hypertrophic subaortic stenosis and hypersensitivity to bisulfite. Use after AMI may be contraindicated because of increased contractility. Dobutamine may cause marked increase in blood pressure or heart rate. Hypovolemia must be corrected prior to initiating dobutamine.
Clinical Tip
Dobutamine
Dobutamine should not be mixed with any other drug in the same solution because it is incompatible with many other drugs.
Table 22.12 is a drug prototype table for dobutamine. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Inotrope Mechanism of Action Directly stimulates beta-1 receptors in the heart, which increases contractility and heart rate |
Drug Dosage
For hemodynamic instability: Initiate titration at 0.5–1 mcg/kg/min; titrate based on client response, including blood pressure and urine output. |
|
Indications
Short-term inotropic support for cardiac decompensation Therapeutic Effects Increases contractility Increases heart rate |
Drug Interactions
Beta-adrenergic blockers (may reduce the effectiveness of dobutamine) Sodium bicarbonate Alkaline solutions Food Interactions No significant interactions |
|
Adverse Effects
Increased heart rate Increased blood pressure Ventricular ectopic activity Hypotension IV site reaction |
Contraindications
Idiopathic hypertrophic subaortic stenosis Hypersensitivity to bisulfite |
Nursing Implications
The nurse should do the following for clients receiving dobutamine intravenously:
- Place the client on continuous cardiac monitoring.
- Monitor blood pressure frequently.
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- Ensure that dobutamine is not mixed with any other drug in the same solution.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client receiving dobutamine should:
-
Inform the health care team if any of these occur:
- They have a change in status (better or worse) after medication administration.
- They notice chest pain; dyspnea; or numbness, tingling, or burning in their extremities.
- They have discomfort or pain at the IV site.
General Nursing Implications for Cardiac Emergencies and Anaphylaxis
In the emergency department and critical care unit, nurses are current in cardiopulmonary resuscitation (CPR), advanced cardiac life support (ACLS), advanced trauma life support (ATLS), and other emergency certifications. Many nurses undergo certified emergency nurse (CEN) or certified critical care nurse (CCRN) certification. Advanced training for cardiac and other emergencies is helpful in a fast-paced, stressful environment.
Case Study
Read the following clinical scenario to answer the questions that follow.
James Ryan is a 72-year-old client whose wife brought him to the emergency department because of chest pain and difficulty breathing. He said he was shoveling snow from the sidewalk when he started having pain in his left arm and chest. He also had difficulty catching his breath. After a few minutes, James went inside and sat down, but the pain in his arm and chest continued. He started to feel lightheaded, and even though he was sitting down, he still found it hard to breathe. James wanted to lie down on the couch, but his wife insisted that he go to the emergency department.
History
Hypertension
Current Medications
Losartan 50 mg daily
Hydrochlorothiazide 25 mg daily
| Vital Signs | Physical Examination | |
|---|---|---|
| Temperature: | 98.1°F |
|
| Blood pressure: | 160/92 mm Hg | |
| Heart rate: | 86 beats/min | |
| Respiratory rate: | 20 breaths/min | |
| Oxygen saturation: | 96% on room air | |
| Height: | 5'11" | |
| Weight: | 240 lb |
In the emergency department, James underwent an ECG and bloodwork, which revealed he was in the midst of an AMI.
The nurse receives orders to administer nitroglycerin sublingually. Which parameter will the nurse monitor to determine the effectiveness of nitroglycerin?
- Answer
-
Chest pain
The health care provider orders aspirin for James. Which action should the nurse take?
- Answer
-
Ask James if he has a history of asthma.


9.1: Ordinary Points
If \(x_{0}\) is an ordinary point of \(Equation \ref{9.1}\) , then it is possible to determine two power series (i.e., Taylor series) solutions for \(y=y(x)\) centered at \(x=x_{0}\) . We illustrate the method of solution by solving two examples, with \(x_{0}=0\) .
Example: Find the general solution of \(y^{\prime \prime}+y=0\) .
By now, you should know that the general solution is \(y(x)=a_{0} \cos x+a_{1} \sin x\) , with \(a_{0}\) and \(a_{1}\) constants. To find a power series solution about the point \(x_{0}=0\) , we write
\[y(x)=\sum_{n=0}^{\infty} a_{n} x^{n} \nonumber \]
and upon differentiating term-by-term
\[y^{\prime}(x)=\sum_{n=1}^{\infty} n a_{n} x^{n-1}, \nonumber \]
and
\[y^{\prime \prime}(x)=\sum_{n=2}^{\infty} n(n-1) a_{n} x^{n-2} \nonumber \]
Substituting the power series for \(y\) and its derivatives into the differential equation to be solved, we obtain
\[\sum_{n=2}^{\infty} n(n-1) a_{n} x^{n-2}+\sum_{n=0}^{\infty} a_{n} x^{n}=0 \nonumber \]
The power-series solution method requires combining the two sums on the lefthand-side of Equation \ref{9.2} into a single power series in \(x\) . To shift the exponent of \(x^{n-2}\) in the first sum upward by two to obtain \(x^{n}\) , we need to shift the summation index downward by two; that is,
\[\sum_{n=2}^{\infty} n(n-1) a_{n} x^{n-2}=\sum_{n=0}^{\infty}(n+2)(n+1) a_{n+2} x^{n} . \nonumber \]
We can then combine the two sums in Equation \ref{9.2} to obtain
\[\sum_{n=0}^{\infty}\left((n+2)(n+1) a_{n+2}+a_{n}\right) x^{n}=0 . \nonumber \]
For Equation \ref{9.3} to be satisfied, the coefficient of each power of \(x\) must vanish separately. (This can be proved by setting \(x=0\) after successive differentiation.) We therefore obtain the recurrence relation
\[a_{n+2}=-\frac{a_{n}}{(n+2)(n+1)}, \quad n=0,1,2, \ldots \nonumber \]
We observe that even and odd coefficients decouple. We thus obtain two independent sequences starting with first term \(a_{0}\) or \(a_{1}\) . Developing these sequences, we have for the sequence beginning with \(a_{0}\) :
\[\begin{aligned} &a_{0} \\ &a_{2}=-\frac{1}{2} a_{0} \\ &a_{4}=-\frac{1}{4 \cdot 3} a_{2}=\frac{1}{4 \cdot 3 \cdot 2} a_{0} \\ &a_{6}=-\frac{1}{6 \cdot 5} a_{4}=-\frac{1}{6 !} a_{0} \end{aligned} \nonumber \]
and the general coefficient in this sequence for \(n=0,1,2, \ldots\) is
\[a_{2 n}=\frac{(-1)^{n}}{(2 n) !} a_{0} . \nonumber \]
Also, for the sequence beginning with \(a_{1}\) :
\[\begin{aligned} &a_{1} \\ &a_{3}=-\frac{1}{3 \cdot 2} a_{1} \\ &a_{5}=-\frac{1}{5 \cdot 4} a_{3}=\frac{1}{5 \cdot 4 \cdot 3 \cdot 2} a_{1}, \\ &a_{7}=-\frac{1}{7 \cdot 6} a_{5}=-\frac{1}{7 !} a_{1} \end{aligned} \nonumber \]
and the general coefficient in this sequence for \(n=0,1,2, \ldots\) is
\[a_{2 n+1}=\frac{(-1)^{n}}{(2 n+1) !} a_{1} . \nonumber \]
Using the principle of superposition, the general solution is therefore
\[\begin{aligned} y(x) &=a_{0} \sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n) !} x^{2 n}+a_{1} \sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n+1) !} x^{2 n+1} \\ &=a_{0}\left(1-\frac{x^{2}}{2 !}+\frac{x^{4}}{4 !}-\ldots\right)+a_{1}\left(x-\frac{x^{3}}{3 !}+\frac{x^{5}}{5 !}-\ldots\right) \\ &=a_{0} \cos x+a_{1} \sin x \end{aligned} \nonumber \]
as expected.
In our next example, we will solve the Airy’s Equation. This differential equation arises in the study of optics, fluid mechanics, and quantum mechanics.
Example: Find the general solution of \(y^{\prime \prime}-x y=0\) .
With
\[y(x)=\sum_{n=0}^{\infty} a_{n} x^{n} \nonumber \]
the differential equation becomes
\[\sum_{n=2}^{\infty} n(n-1) a_{n} x^{n-2}-\sum_{n=0}^{\infty} a_{n} x^{n+1}=0 \nonumber \]
We shift the first sum to \(x^{n+1}\) by shifting the exponent up by three, i.e.,
\[\sum_{n=2}^{\infty} n(n-1) a_{n} x^{n-2}=\sum_{n=-1}^{\infty}(n+3)(n+2) a_{n+3} x^{n+1} \nonumber \]
When combining the two sums in Equation \ref{9.4}, we separate out the extra \(n=-1\) term in the first sum given by \(2 a_{2}\) . Therefore, \(Equation \ref{9.4}\) becomes
\[2 a_{2}+\sum_{n=0}^{\infty}\left((n+3)(n+2) a_{n+3}-a_{n}\right) x^{n+1}=0 . \nonumber \]
Setting coefficients of powers of \(x\) to zero, we first find \(a_{2}=0\) , and then obtain the recursion relation
\[a_{n+3}=\frac{1}{(n+3)(n+2)} a_{n} \nonumber \]
Three sequences of coefficients-those starting with either \(a_{0}, a_{1}\) or \(a_{2}\) -decouple. In particular the three sequences are
\[\begin{aligned} &a_{0}, a_{3}, a_{6}, a_{9}, \ldots \\ &a_{1}, a_{4}, a_{7}, a_{10}, \ldots \\ &a_{2}, a_{5}, a_{8}, a_{11} \ldots \end{aligned} \nonumber \]
Since \(a_{2}=0\) , we find immediately for the last sequence
\[a_{2}=a_{5}=a_{8}=a_{11}=\cdots=0 . \nonumber \]
We compute the first four nonzero terms in the power series with coefficients corresponding to the first two sequences. Starting with \(a_{0}\) , we have
\[\begin{aligned} &a_{0} \\ &a_{3}=\frac{1}{3 \cdot 2} a_{0} \\ &a_{6}=\frac{1}{6 \cdot 5 \cdot 3 \cdot 2} a_{0} \\ &a_{9}=\frac{1}{9 \cdot 8 \cdot 6 \cdot 5 \cdot 3 \cdot 2} a_{0} \end{aligned} \nonumber \]
and starting with \(a_{1}\) ,
\[\begin{aligned} a_{1} \\ a_{4} &=\frac{1}{4 \cdot 3} a_{1} \\ a_{7} &=\frac{1}{7 \cdot 6 \cdot 4 \cdot 3} a_{1} \\ a_{10} &=\frac{1}{10 \cdot 9 \cdot 7 \cdot 6 \cdot 4 \cdot 3} a_{1} \end{aligned} \nonumber \]
The general solution for \(y=y(x)\) , can therefore be written as
\[\begin{aligned} y(x) &=a_{0}\left(1+\frac{x^{3}}{6}+\frac{x^{6}}{180}+\frac{x^{9}}{12960}+\ldots\right)+a_{1}\left(x+\frac{x^{4}}{12}+\frac{x^{7}}{504}+\frac{x^{10}}{45360}+\ldots\right) \\ &=a_{0} y_{0}(x)+a_{1} y_{1}(x) \end{aligned} \nonumber \]
Suppose we would like to graph the solutions \(y=y_{0}(x)\) and \(y=y_{1}(x)\) versus \(x\) by solving the differential equation \(y^{\prime \prime}-x y=0\) numerically. What initial conditions should we use? Clearly, \(y=y_{0}(x)\) solves the ode with initial values \(y(0)=1\) and \(y^{\prime}(0)=0\) , while \(y=y_{1}(x)\) solves the ode with initial values \(y(0)=0\) and \(y^{\prime}(0)=1\) .
The numerical solutions, obtained using MATLAB, are shown in Fig. 9.1. Note that the solutions oscillate for negative \(x\) and grow exponentially for positive \(x\) . This can be understood by recalling that \(y^{\prime \prime}+y=0\) has oscillatory sine and cosine solutions and \(y^{\prime \prime}-y=0\) has exponential hyperbolic sine and cosine solutions.


16.1: Scientific Method
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Learning Objectives
- B rief discussion of the most important principles of the scientific method
This section contains a brief discussion of the most important principles of the scientific method. A thorough treatment of the philosophy of science is beyond the scope of this work.
One of the hallmarks of the scientific method is that it depends on empirical data. To be a proper scientific investigation the data must be collected systematically. However, scientific investigation does not necessarily require experimentation in the sense of manipulating variables and observing the results. Observational studies in the fields of astronomy, developmental psychology, and ethology are common and provide valuable scientific information.
Theories and explanations are very important in science. Theories in science can never be proved since one can never be 100% certain that a new empirical finding inconsistent with the theory will never be found.
Scientific theories must be potentially disconfirmable. If a theory can accommodate all possible results then it is not a scientific theory. Therefore, a scientific theory should lead to testable hypotheses. If a hypothesis is disconfirmed, then the theory from which the hypothesis was deduced is incorrect. For example, the secondary reinforcement theory of attachment states that an infant becomes attached to its parent by means of a pairing of the parent with a primary reinforcer (food). It is through this "secondary reinforcement" that the child-parent bond forms. The secondary reinforcement theory has been disconfirmed by numerous experiments.  The infant monkeys formed no attachment to the wire monkeys and frequently clung to the cloth surrogate mothers.
History of Attachment Theory
If a hypothesis derived from a theory is confirmed then the theory has survived a test and it becomes more useful and better thought of by the researchers in the field. A theory is not confirmed when correct hypotheses are derived from it.
A key difference between scientific explanations and faith-based explanations is simply that faith-based explanations are based on faith and do not need to be testable. This does not mean that an explanation that cannot be tested is incorrect in some cosmic sense. It just means that it is not a scientific explanation.
The method of investigation in which a hypothesis is developed from a theory and then confirmed or disconfirmed involves deductive reasoning. However, deductive reasoning does not explain where the theory came from in the first place. In general, a theory is developed by a scientist who is aware of many empirical findings on a topic of interest. Then, through a generally poorly understood process called "induction" the scientist develops a way to explain all or most of the findings within a relatively simple framework or theory.
An important attribute of a good scientific theory is that it is parsimonious. That is, that it is simple in the sense that it uses relatively few constructs to explain many empirical findings. A theory that it so complex that it has as many assumptions as it has predictions is not very valuable.
Although strictly speaking, disconfirming an hypothesis deduced from a theory disconfirms the theory, it rarely leads to the abandonment of the theory. Instead, the theory will probably be modified to accommodate the inconsistent finding. If the theory has to be modified over and over to accommodate new findings, the theory generally becomes less and less parsimonious. This can lead to discontent with the theory and the search for a new theory. If a new theory is developed that can explain the same facts in a more parsimonious way, then the new theory will eventually supercede the old theory.


6.1: Elementary Formulas
We first consider integration from 0 to \(h\) , with \(h\) small, to serve as the building blocks for integration over larger domains. We here define \(I_{h}\) as the following integral:
\[I_{h}=\int_{0}^{h} f(x) d x . \nonumber \]
To perform this integral, we consider a Taylor series expansion of \(f(x)\) about the value \(x=h / 2\) :
\[\begin{aligned} f(x)=f(h / 2)+(x-h / 2) f^{\prime} &(h / 2)+\frac{(x-h / 2)^{2}}{2} f^{\prime \prime}(h / 2) \\ &+\frac{(x-h / 2)^{3}}{6} f^{\prime \prime \prime}(h / 2)+\frac{(x-h / 2)^{4}}{24} f^{\prime \prime \prime \prime}(h / 2)+\ldots \end{aligned} \nonumber \]
6.1.1. Midpoint rule
The midpoint rule makes use of only the first term in the Taylor series expansion. Here, we will determine the error in this approximation. Integrating,
\[\begin{aligned} I_{h}=h f(h / 2)+\int_{0}^{h}(&(x-h / 2) f^{\prime}(h / 2)+\frac{(x-h / 2)^{2}}{2} f^{\prime \prime}(h / 2) \\ &\left.+\frac{(x-h / 2)^{3}}{6} f^{\prime \prime \prime}(h / 2)+\frac{(x-h / 2)^{4}}{24} f^{\prime \prime \prime \prime}(h / 2)+\ldots\right) d x . \end{aligned} \nonumber \]
Changing variables by letting \(y=x-h / 2\) and \(d y=d x\) , and simplifying the integral depending on whether the integrand is even or odd, we have
\[\begin{aligned} I_{h}=& h f(h / 2) \\ &+\int_{-h / 2}^{h / 2}\left(y f^{\prime}(h / 2)+\frac{y^{2}}{2} f^{\prime \prime}(h / 2)+\frac{y^{3}}{6} f^{\prime \prime \prime}(h / 2)+\frac{y^{4}}{24} f^{\prime \prime \prime \prime}(h / 2)+\ldots\right) d y \\ =& h f(h / 2)+\int_{0}^{h / 2}\left(y^{2} f^{\prime \prime}(h / 2)+\frac{y^{4}}{12} f^{\prime \prime \prime \prime}(h / 2)+\ldots\right) d y \end{aligned} \nonumber \]
The integrals that we need here are
\[\int_{0}^{\frac{h}{2}} y^{2} d y=\frac{h^{3}}{24}, \quad \int_{0}^{\frac{h}{2}} y^{4} d y=\frac{h^{5}}{160} \nonumber \]
Therefore,
\[I_{h}=h f(h / 2)+\frac{h^{3}}{24} f^{\prime \prime}(h / 2)+\frac{h^{5}}{1920} f^{\prime \prime \prime \prime}(h / 2)+\ldots \nonumber \]
6.1.2. Trapezoidal rule
From the Taylor series expansion of \(f(x)\) about \(x=h / 2\) , we have
\[f(0)=f(h / 2)-\frac{h}{2} f^{\prime}(h / 2)+\frac{h^{2}}{8} f^{\prime \prime}(h / 2)-\frac{h^{3}}{48} f^{\prime \prime \prime}(h / 2)+\frac{h^{4}}{384} f^{\prime \prime \prime \prime}(h / 2)+\ldots, \nonumber \]
and
\[f(h)=f(h / 2)+\frac{h}{2} f^{\prime}(h / 2)+\frac{h^{2}}{8} f^{\prime \prime}(h / 2)+\frac{h^{3}}{48} f^{\prime \prime \prime}(h / 2)+\frac{h^{4}}{384} f^{\prime \prime \prime \prime}(h / 2)+\ldots \ldots \nonumber \]
Adding and multiplying by \(h / 2\) we obtain
\[\frac{h}{2}(f(0)+f(h))=h f(h / 2)+\frac{h^{3}}{8} f^{\prime \prime}(h / 2)+\frac{h^{5}}{384} f^{\prime \prime \prime \prime}(h / 2)+\ldots . \nonumber \]
We now substitute for the first term on the right-hand-side using the midpoint rule formula:
\[\begin{array}{r} \frac{h}{2}(f(0)+f(h))=\left(I_{h}-\frac{h^{3}}{24} f^{\prime \prime}(h / 2)-\frac{h^{5}}{1920} f^{\prime \prime \prime \prime}(h / 2)\right) \\ +\frac{h^{3}}{8} f^{\prime \prime}(h / 2)+\frac{h^{5}}{384} f^{\prime \prime \prime \prime}(h / 2)+\ldots, \end{array} \nonumber \]
and solving for \(I_{h}\) , we find
\[I_{h}=\frac{h}{2}(f(0)+f(h))-\frac{h^{3}}{12} f^{\prime \prime}(h / 2)-\frac{h^{5}}{480} f^{\prime \prime \prime \prime}(h / 2)+\ldots \nonumber \]
6.1.3. Simpson’s rule
To obtain Simpson’s rule, we combine the midpoint and trapezoidal rule to eliminate the error term proportional to \(h^{3}\) . Multiplying (6.3) by two and adding to (6.4), we obtain
\[3 I_{h}=h\left(2 f(h / 2)+\frac{1}{2}(f(0)+f(h))\right)+h^{5}\left(\frac{2}{1920}-\frac{1}{480}\right) f^{\prime \prime \prime \prime}(h / 2)+\ldots, \nonumber \]
or
\[I_{h}=\frac{h}{6}(f(0)+4 f(h / 2)+f(h))-\frac{h^{5}}{2880} f^{\prime \prime \prime \prime}(h / 2)+\ldots . \nonumber \]
Usually, Simpson’s rule is written by considering the three consecutive points \(0, h\) and \(2 h\) . Substituting \(h \rightarrow 2 h\) , we obtain the standard result
\[I_{2 h}=\frac{h}{3}(f(0)+4 f(h)+f(2 h))-\frac{h^{5}}{90} f^{\prime \prime \prime \prime}(h)+\ldots \nonumber \]


5: Thermochemistry
Useful forms of energy are also available from a variety of chemical reactions other than combustion. For example, the energy produced by the batteries in a cell phone, car, or flashlight results from chemical reactions. This chapter introduces many of the basic ideas necessary to explore the relationships between chemical changes and energy, with a focus on thermal energy.
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- 5.1: Prelude to Thermochemistry
- Useful forms of energy are also available from a variety of chemical reactions other than combustion. For example, the energy produced by the batteries in a cell phone, car, or flashlight results from chemical reactions. This chapter introduces many of the basic ideas necessary to explore the relationships between chemical changes and energy, with a focus on thermal energy.
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- 5.2: Energy Basics
- Energy is the capacity to do work (applying a force to move matter). Heat is energy that is transferred between objects at different temperatures; it flows from a high to a low temperature. Chemical and physical processes can absorb heat (endothermic) or release heat (exothermic). The SI unit of energy, heat, and work is the joule (J). Specific heat and heat capacity are measures of the energy needed to change the temperature of a substance or object.
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- 5.3: Calorimetry
- Calorimetry is used to measure the amount of thermal energy transferred in a chemical or physical process. This requires careful measurement of the temperature change that occurs during the process and the masses of the system and surroundings. These measured quantities are then used to compute the amount of heat produced or consumed in the process using known mathematical relations. Calorimeters are designed to minimize energy exchange between the system and its surroundings.
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- 5.4: Enthalpy
- 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 ΔH. Examples of enthalpy changes include enthalpy of combustion, enthalpy of fusion, enthalpy of vaporization, and standard enthalpy of formation. If the enthalpies of formation are available for the reactants and products of a reaction, the enthalpy change can be calculated using Hess’s law.
Thumbnail: Flames of charcoal. (CC BY-SA 3.0; Oscar via Wikipedia )


11.1: Use the Rectangular Coordinate System (Part 1)
- Plot points on a rectangular coordinate system
- Identify points on a graph
- Verify solutions to an equation in two variables
- Complete a table of solutions to a linear equation
- Find solutions to linear equations in two variables
Before you get started, take this readiness quiz.
- Evaluate: x + 3 when x = −1. If you missed this problem, review Example 3.4.10 .
- Evaluate: 2x − 5y when x = 3, y = −2. If you missed this problem, review Example 3.8.106 .
- Solve for y: 40 − 4y = 20. If you missed this problem, review Example 8.4.1 .
Plot Points on a Rectangular Coordinate System
Many maps, such as the Campus Map shown in Figure \(\PageIndex{1}\), use a grid system to identify locations. Do you see the numbers 1, 2, 3, and 4 across the top and bottom of the map and the letters A, B, C, and D along the sides? Every location on the map can be identified by a number and a letter.
For example, the Student Center is in section 2B. It is located in the grid section above the number 2 and next to the letter B. In which grid section is the Stadium? The Stadium is in section 4D.
Figure \(\PageIndex{1}\)
Use the map in Figure \(\PageIndex{1}\). (a) Find the grid section of the Residence Halls. (b) What is located in grid section 4C?
Solution
(a) Read the number below the Residence Halls, 4, and the letter to the side, A. So the Residence Halls are in grid section 4A.
(b) Find 4 across the bottom of the map and C along the side. Look below the 4 and next to the C. Tiger Field is in grid section 4C.
Use the map in Figure \(\PageIndex{1}\). (a) Find the grid section of Taylor Hall. (b) What is located in section 3B?
- Answer a
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1C
- Answer b
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Engineering Building
Use the map in Figure \(\PageIndex{1}\). (a) Find the grid section of the Parking Garage. (b) What is located in section 2C?
- Answer a
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1A
- Answer b
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Library
Just as maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a rectangular coordinate system. To create a rectangular coordinate system, start with a horizontal number line. Show both positive and negative numbers as you did before, using a convenient scale unit. This horizontal number line is called the x-axis .
Now, make a vertical number line passing through the x-axis at 0. Put the positive numbers above 0 and the negative numbers below 0. See Figure \(\PageIndex{2}\). This vertical line is called the y-axis .
Vertical grid lines pass through the integers marked on the x-axis. Horizontal grid lines pass through the integers marked on the y-axis. The resulting grid is the rectangular coordinate system.
The rectangular coordinate system is also called the x-y plane, the coordinate plane, or the Cartesian coordinate system (since it was developed by a mathematician named René Descartes.)
Figure \(\PageIndex{2}\) - The rectangular coordinate system.
The x-axis and the y-axis form the rectangular coordinate system. These axes divide a plane into four areas, called quadrants . The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See Figure \(\PageIndex{3}\).
Figure \(\PageIndex{3}\) - The four quadrants of the rectangular coordinate system.
In the rectangular coordinate system, every point is represented by an ordered pair . The first number in the ordered pair is the x-coordinate of the point, and the second number is the y-coordinate of the point.
An ordered pair, (x, y) gives the coordinates of a point in a rectangular coordinate system. The first number is the x-coordinate. The second number is the y-coordinate.
So how do the coordinates of a point help you locate a point on the x-y plane?
Let’s try locating the point (2, 5) . In this ordered pair, the x -coordinate is 2 and the y -coordinate is 5 .
We start by locating the x value, 2, on the x-axis. Then we lightly sketch a vertical line through x = 2, as shown in Figure \(\PageIndex{4}\)
Figure \(\PageIndex{4}\)
Now we locate the y value, 5, on the y -axis and sketch a horizontal line through y = 5. The point where these two lines meet is the point with coordinates (2, 5). We plot the point there, as shown in Figure \(\PageIndex{5}\).
Figure \(\PageIndex{5}\)
Plot (1, 3) and (3, 1) in the same rectangular coordinate system.
Solution
The coordinate values are the same for both points, but the x and y values are reversed. Let’s begin with point (1, 3). The x-coordinate is 1 so find 1 on the x-axis and sketch a vertical line through x = 1. The y-coordinate is 3 so we find 3 on the y-axis and sketch a horizontal line through y = 3. Where the two lines meet, we plot the point (1, 3).
To plot the point (3, 1), we start by locating 3 on the x-axis and sketch a vertical line through x = 3. Then we find 1 on the y-axis and sketch a horizontal line through y = 1. Where the two lines meet, we plot the point (3, 1).
Notice that the order of the coordinates does matter, so, (1, 3) is not the same point as (3, 1).
Plot each point on the same rectangular coordinate system: (2, 5), (5, 2).
- Answer
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Plot each point on the same rectangular coordinate system: (4, 2), (2, 4).
- Answer
Plot each point in the rectangular coordinate system and identify the quadrant in which the point is located: (a) (−1, 3) (b) (−3, −4) (c) (2, −3) (d) \(\left(3, \dfrac{5}{2}\right)\)
Solution
The first number of the coordinate pair is the x-coordinate, and the second number is the y-coordinate.
- Since x = −1, y = 3, the point (−1, 3) is in Quadrant II.
- Since x = −3, y = −4, the point (−3, −4) is in Quadrant III.
- Since x = 2, y = −1, the point (2, −1) is in Quadrant lV.
- Since x = 3, y = \(\dfrac{5}{2}\), the point \(\left(3, \dfrac{5}{2}\right)\) is in Quadrant I. It may be helpful to write \(\dfrac{5}{2}\) as the mixed number, \(2 \dfrac{1}{2}\), or decimal, 2.5. Then we know that the point is halfway between 2 and 3 on the y-axis.
Plot each point in the rectangular coordinate system and identify the quadrant in which the point is located: (a) (−2, 1) (b) (−3, −1) (c) (4, −4) (d) \(\left(-4, \dfrac{3}{2}\right)\)
- Answer
Plot each point in the rectangular coordinate system and identify the quadrant in which the point is located: (a) (−4, 1) (b) (−2, 3) (c) (2, −5) (d) \(\left(-3, \dfrac{5}{2}\right)\)
- Answer
How do the signs affect the location of the points?
Plot each point: (a) (−5, 2) (b) (−5, −2) (c) (5, 2) (d) (5, −2)
Solution
As we locate the x-coordinate and the y-coordinate, we must be careful with the signs.
Plot each point: (a) (4, −3) (b) (4, 3) (c) (−4, −3) (d) (−4, 3)
- Answer
Plot each point: (a) (−1, 4) (b) (1, 4) (c) (1, −4) (d) (−1, −4)
- Answer
You may have noticed some patterns as you graphed the points in the two previous examples.
For each point in Quadrant IV, what do you notice about the signs of the coordinates?
What about the signs of the coordinates of the points in the third quadrant? The second quadrant? The first quadrant?
Can you tell just by looking at the coordinates in which quadrant the point (−2, 5) is located? In which quadrant is (2, −5) located?
We can summarize sign patterns of the quadrants as follows. Also see Figure \(\PageIndex{6}\).
| Quadrant I | Quadrant II | Quadrant III | Quadrant IV |
|---|---|---|---|
| (x,y) | (x,y) | (x,y) | (x,y) |
| (+,+) | (-,+) | (-,-) | (+,-) |
Figure \(\PageIndex{6}\)
What if one coordinate is zero? Where is the point (0, 4) located? Where is the point (−2, 0) located? The point (0, 4) is on the y-axis and the point ( − 2, 0) is on the x-axis.
Points with a y-coordinate equal to 0 are on the x-axis, and have coordinates (a, 0).
Points with an x-coordinate equal to 0 are on the y-axis, and have coordinates (0, b).
What is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is (0, 0). The point has a special name. It is called the origin .
The point (0, 0) is called the origin. It is the point where the x-axis and y-axis intersect.
Plot each point on a coordinate grid: (a) (0, 5) (b) (4, 0) (c) (−3, 0) (d) (0, 0) (e) (0, −1)
Solution
- Since x = 0, the point whose coordinates are (0, 5) is on the y-axis.
- Since y = 0, the point whose coordinates are (4, 0) is on the x-axis.
- Since y = 0, the point whose coordinates are (−3, 0) is on the x-axis.
- Since x = 0 and y = 0, the point whose coordinates are (0, 0) is the origin.
- Since x = 0, the point whose coordinates are (0, −1) is on the y-axis.
Plot each point on a coordinate grid: (a) (4, 0) (b) (−2, 0) (c) (0, 0) (d) (0, 2) (e) (0, −3)
- Answer
Plot each point on a coordinate grid: (a) (−5, 0) (b) (3, 0) (c) (0, 0) (d) (0, −1) (e) (0, 4)
- Answer
Identify Points on a Graph
In algebra, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the x-coordinate of a point on a graph, read the number on the x-axis directly above or below the point. To identify the y-coordinate of a point, read the number on the y-axis directly to the left or right of the point. Remember, to write the ordered pair using the correct order (x, y).
Name the ordered pair of each point shown:
Solution
Point A is above −3 on the x-axis, so the x-coordinate of the point is −3. The point is to the left of 3 on the y-axis, so the y-coordinate of the point is 3. The coordinates of the point are (−3, 3).
Point B is below −1 on the x-axis, so the x-coordinate of the point is −1. The point is to the left of −3 on the y-axis, so the y-coordinate of the point is −3. The coordinates of the point are (−1, −3).
Point C is above 2 on the x-axis, so the x-coordinate of the point is 2. The point is to the right of 4 on the y-axis, so the y-coordinate of the point is 4. The coordinates of the point are (2, 4).
Point D is below 4 on the x - axis, so the x-coordinate of the point is 4. The point is to the right of −4 on the y-axis, so the y-coordinate of the point is −4. The coordinates of the point are (4, −4)
Name the ordered pair of each point shown:
- Answer
- A: (5,1), B: (−2,4), C: (−5,−1), D: (3,−2)
Name the ordered pair of each point shown:
- Answer
- A: (4,2), B: (−2,3), C: (−4,−4), D: (3,−5)
Name the ordered pair of each point shown:
Solution
| Point A is on the x-axis at x = − 4. | The coordinates of point A are (− 4, 0). |
| Point B is on the y-axis at y = − 2. | The coordinates of point B are (0, − 2). |
| Point C is on the x-axis at x = 3. | The coordinates of point C are (3, 0). |
| Point D is on the y-axis at y = 1. | The coordinates of point D are (0, 1). |
Name the ordered pair of each point shown:
- Answer
- A: (4,0), B: (0,3), C: (−3,0), D: (0,−5)
Name the ordered pair of each point shown:
- Answer
- A: (−3,0), B: (0,−3), C: (5,0), D: (0,2)
Contributors and Attributions
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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>."


1.4: Gaia - Bioregulation of the Environment
The Gaia Hypothesis
The physical conditions under which life as we know it can exist encompass a relatively narrow range of temperature, pH, osmotic pressure, and ultraviolet radiation intensity. It seems remarkable enough that life was able to get started at all; it is even more remarkable that it has continued to thrive in the face of all the perils that have, or could have occurred, during the past 3 billion years or so.
During the time that life has been evolving, the sun has also been going through the process of evolution characteristic of a typical star; one consequence of this is an increase in its energy output by about 30 percent during this time. If the sun’s output should suddenly drop to what it was 3 billion years ago, the oceans would freeze. How is it that the earth was not in a frozen state for the first 1.5 billion years of life’s existence? Alternatively, if conditions were somehow suitable 3 billion years ago, why have the oceans not long since boiled away?
A rather non-traditional answer to this kind of question is that the biosphere is far from playing a passive role in which it is continually at the mercy of environmental conditions. Instead, the earth’s atmosphere, and to a lesser extent the hydrosphere, may be actively maintained and regulated by the biosphere. This view has been championed by the British geochemist J.E. Lovelock, and is known as the Gaia hypothesis .
Gaia is another name for the Greek earth-goddess Ge , from which root the sciences of geography, geometry, and geology derive their names. Lovelock's book Gaia: a new look at life on Earth (Oxford, 1979) is a short and highly readable discussion of the hypothesis.
Evidence in support of this hypothesis is entirely circumstantial, but nevertheless points to important questions that must be answered: how have the climatic and chemical conditions on the earth remained optimal for life during all this time; how can the chemical composition of the atmosphere remain in a state that is tens of orders of magnitude from equilibrium?
Note
Although the Gaia hypothesis has received considerable publicity in the popular press, it has never been very well received by the scientific community, many of whom feel that there is no justification for proposing a special hypothesis to describe a set of connections which can be quite adequately explained by conventional geochemical processes. More recently, even Lovelock has backed away from the teleological interpretation of these relations, so that the Gaia hypothesis should now be more properly described as a set of loosely connected effects, rather than as a hypothesis. Nevertheless, these effects and the mechanisms that might act to connect them are sufficiently interesting that it seems worthwhile to provide an overview of the major observations that led to the development of the hypothesis.
Teleology is the doctrine that natural processes operate with a purpose. See No longer willful, Gaia becomes respectable. 1988: Science 240 393-395.
Bioregulation of the Atmosphere
The increase in the oxygen content of the atmosphere as a result of the development of the eucaryotic cell was discussed above. Why has the oxygen content leveled off at 21 percent? It is interesting to note that if the oxygen concentration in the atmosphere were only four percent higher, even damp vegetation, once ignited by lightning, would continue to burn, enveloping vast areas of the earth in a firestorm. Evidence for such a worldwide firestorm that may be related to the extinction of the dinosaurs has recently been discovered. The charcoal layers found in widely distributed sediments laid down about 65 million years ago are coincident with the iridium anomaly believed to be due to the collision of a large meteor with the earth.
- Oxygen : Regulation of the oxygen partial pressure is probably achieved by a balance between its production through photosynthesis and its consumption during oxidation of organic matter; the present steady state requires the burial of about 0.1% the carbon that is fixed annually, leaving one O 2 molecule in the air for each atom of carbon removed from the photosynthetic cycle. The large quantities of microbially-produced methane and N 2 O also constitute important oxygen sinks; if methanogenic bacteria should suddenly cease to exist, the O 2 concentration would rise by 1% in about 12,000 years. This type of regulation implies a negative feedback mechanism, in which an increase in atmospheric oxygen would increase the activity of organisms capable of generating metabolic products that react with it.
- Nitrous oxide : Nitrous oxide, in addition to serving as an oxygen sink, might also be a factor in the regulation of the intensity of the ultraviolet component of sunlight. N 2 O acts as a catalytic intermediate in the decomposition of stratospheric ozone, which shields the earth from excessive ultraviolet radiation.
- Ammonia : Ammonia, another atmospheric gas, is produced by the biosphere in approximately the same quantities as methane, 10 9 tons per year, and at the expense of a considerable amount of metabolic energy. The function of NH 3 could well be to regulate the pH of the environment; in the absence of ammonia, the large amounts of SO 2 and HCl produced by volcanic action would reduce the pH of rain to about 3. The fact that the atmospheric concentration of ammonia is only 10 –8 times that of N 2 should not imply that this “trace” component plays a less significant role in the overall nitrogen cycle than does than N 2 . In fact, the annual rates of production of the two gases are roughly the same; the much lower steady-state concentration of NH 3 is due to its faster turnover time.
- Nitrogen : As stable as the triply-bonded N 2 molecule is, there is a still more stable form of nitrogen: the hydrated nitrate ion. How is this stability consistent with the predominance of nitrogen in the atmosphere? The answer is that it is not: if it were not for nitrogen-fixing bacteria (powered directly or indirectly by the free energy of ATP captured from sunlight), the nitrogen content of the atmosphere would disappear to almost zero. This would raise the oxygen fraction to disastrously high levels, and the additional NO 3 – concentration would increase the ionic strength and osmotic pressure of seawater to levels inconsistent with most forms of life.
Bioregulation of the Oceans
The input of salts into the sea from streams and rivers is about 5.4 x 10 8 tons per year, into a total volume of about 1.2 x 10 9 km 3 yr –1 . Upwelling of juvenile water and hydrothermal action at oceanic ridges provide additional inputs of salts. With a few bizarre exceptions such as the brine shrimp and halophilic bacteria, 6 percent is about the maximum salinity level that organisms can tolerate. The internal salinities of cells must be maintained at much lower levels (around 1%) to prevent denaturation of proteins and other macromolecules whose conformations are dependent on electrostatic forces. At higher levels than this, the electrostatic interaction between the salt ions and the cell membrane destroys the integrity of the latter so that it can no longer pump out salt ions that leak in along the osmotic gradient. At the present rate of salt input, the oceans would have reached their present levels of salinity millions of years ago, and would by now have an ionic strength far to high to support life, as is presently the case in the landlocked Dead Sea.
The present average salinity of seawater is 3.4 percent. The salinity of blood, and of many other intra- and intercellular fluids in animals, is about 0.8 percent. If we assume that the first organisms were approximately in osmotic equilibrium with seawater, then our body fluids might represent “fossilized” seawater as it existed at the time our predecessors moved out of the sea and onto the land.
By what processes is salt removed from the oceans in order to maintain a steady-state salinity? This remains one of the major open questions of chemical oceanography. There are a number of answers, mostly based on strictly inorganic processes, but none is adequately supported by available evidence. For example, Na + and Mg 2 + ions could adsorb to particulate debris as it drops to the seafloor, and become incorporated into sediments. The requirement for charge conservation might be met by the involvement of negatively charged silicate and hydroxyaluminum ions. Another possible mechanism might be the burial of salt beds formed by evaporation in shallow, isolated arms of the sea, such as the Persian Gulf. Extensive underground salt deposits are certainly found on most continents, but it is difficult to see how this very slow mechanism could have led to an unfluctuating salinity over shorter periods of highly variable climatic conditions.
The possibility of biological control of oceanic salinity starts with the observation that about half of the earth’s biomass resides in the sea, and that a significant fraction of this consists of diatoms and other organisms that build skeletons of silica. When these organism die, they sink to the bottom of the sea and add about 300 million tons of silica to sedimentary rocks annually. It is for this reason that the upper levels of the sea are undersaturated in silica, and that the ratio of silica to salt in dead salt lakes is much higher than in the ocean.
These facts could constitute a basis for a biological control of the silica content of seawater; any link between silica and salt could lead to the control of the latter substance as well. For example, the salt ions might adsorb onto the silica skeletons, and be carried down with them; if the growth of these silica-containing organisms is itself dependent on salinity, we would have our negative feedback mechanism.
The continual buildup of biogenic sedimentary deposits on the ocean floor might possibly deform the thin oceanic crust by its weight, and cause local heating by its insulating properties. This could conceivably lead to volcanic action and the formation of new land mass, thus linking the lithosphere into Gaia.
Contributors and Attributions
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Stephen Lower, Professor Emeritus ( Simon Fraser U. ) Chem1 Virtual Textbook