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9B Degradation of Amino Acids—The Fate of the Carbon Skeleton

9B Degradation of Amino Acids—The Fate of the Carbon Skeleton

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770



CARBOHYDRATE, LIPID, AND PROTEIN METABOLISM



Some amino acids such as alanine (Section 24.9A) are catabolized to pyruvate. Since pyruvate is an

intermediate in both glycolysis and gluconeogenesis, pyruvate can be broken down for energy or used

to synthesize glucose. In considering catabolism, amino acids are often divided into two groups.

• Glucogenic amino acids are catabolized to pyruvate or an intermediate in the citric acid

cycle. Since these catabolic products can be used for gluconeogenesis, glucogenic

amino acids can be used to synthesize glucose.

• Ketogenic amino acids are converted to acetyl CoA, or the related thioester

acetoacetyl CoA, CH3COCH2COSCoA. These catabolic products cannot be used to

synthesize glucose, but they can be converted to ketone bodies and yield energy by this

path.



We will not examine the specific pathways that convert the carbon skeletons of individual amino

acids into other products. Figure 24.10 illustrates where each amino acid feeds into the metabolic

pathways we have already discussed.



PROBLEM 24.32



What metabolic intermediate is produced from the carbon atoms of each amino acid?

a. cysteine



b. aspartic acid



c. valine



d. threonine



CHAPTER HIGHLIGHTS

KEY TERMS

Acyl CoA (24.7)

Cori cycle (24.6)

Decarboxylation (24.2)

Fermentation (24.4)

Glucogenic amino acid (24.9)

Gluconeogenesis (24.6)



Glycolysis (24.3)

Isomerase (24.2)

Ketogenesis (24.8)

Ketogenic amino acid (24.9)

Ketone bodies (24.8)

Ketosis (24.8)



Kinase (24.2)

β-Oxidation (24.7)

Oxidative deamination (24.9)

Transamination (24.9)

Urea cycle (24.9)



KEY CONCEPTS

❶ What are the main elements that provide clues to the

outcome of a biochemical reaction? (24.2)

• To understand the course of a biochemical reaction,

examine the functional groups that are added or removed,

the reagents (coenzymes or other materials), and the

enzyme. The name of an enzyme is often a clue as to the

type of reaction.

❷ What are the main aspects of glycolysis? (24.3)

• Glycolysis is a linear, 10-step pathway that converts glucose

to two three-carbon pyruvate molecules. In the energyinvestment phase, steps [1]–[5], the energy from two ATP

molecules is used for phosphorylation and two three-carbon

products are formed. In the energy-generating phase, steps

[6]–[10], the following species are generated: two pyruvate

molecules (CH3COCO2–), 2 NADHs, and 4 ATPs.

• The net result of glycolysis, considering both phases,

is 2 CH3COCO2–, 2 NADHs, and 2 ATPs.



smi26573_ch24.indd 770



❸ What are the major pathways for pyruvate metabolism?

(24.4)

• When oxygen is plentiful, pyruvate is converted to acetyl

CoA, which can enter the citric acid cycle.

• When the oxygen level is low, the anaerobic metabolism of

pyruvate forms lactate and NAD+.

• In yeast and other microorganisms, pyruvate is converted to

ethanol and CO2 by fermentation.

❹ How much ATP is formed by the complete catabolism of

glucose? (24.5)

• To calculate the amount of ATP formed in the catabolism

of glucose, we must take into account the ATP yield from

glycolysis, the oxidation of two molecules of pyruvate to

two molecules of acetyl CoA, the citric acid cycle, and

oxidative phosphorylation.

• As shown in Figure 24.6, the complete catabolism of

glucose forms six CO2 molecules and 32 molecules of ATP.



12/19/08 2:35:49 PM



PROBLEMS



771



coenzymes produced during β-oxidation, and the ATP that

results from the catabolism of each acetyl CoA.

• As an example, the complete catabolism of stearic acid,

C18H36O2, yields 120 ATPs.



❺ What are the main features of gluconeogenesis? (24.6)

• Gluconeogenesis is the synthesis of glucose from

noncarbohydrate sources—lactate, amino acids, or glycerol.

Gluconeogenesis converts two molecules of pyruvate to

glucose. Conceptually, gluconeogenesis is the reverse

of glycolysis, but three steps in gluconeogenesis require

different enzymes.

• Gluconeogenesis occurs when the body has depleted its

supplies of glucose and stored glycogen, and occurs during

sustained physical exercise and fasting.



❽ What are ketone bodies and how do they play a role in

metabolism? (24.8)

• Ketone bodies—acetoacetate, β-hydroxybutyrate, and

acetone—are formed when acetyl CoA levels exceed the

capacity of the citric acid cycle. Ketone bodies can be reconverted to acetyl CoA and metabolized for energy. When

the level of ketone bodies is high, the pH of the blood can

be lowered, causing ketoacidosis.



❻ Describe the main features of the 𝛃-oxidation of fatty

acids. (24.7)

• β-Oxidation is a spiral metabolic pathway that sequentially

cleaves two-carbon acetyl CoA units from an acyl CoA

derived from a fatty acid. Each cycle of β-oxidation

consists of a four-step sequence that forms one molecule

each of acetyl CoA, NADH, and FADH2.



❾ What are the main features of amino acid catabolism?

(24.9)

• The catabolism of amino acids involves two parts. First,

the amino group is removed by transamination followed

by oxidative deamination. The NH4+ ion formed enters

the urea cycle where it is converted to urea and eliminated

in urine. The carbon skeletons of the amino acids are

catabolized by a variety of pathways to yield pyruvate,

acetyl CoA, or an intermediate in the citric acid cycle.



❼ How much ATP is formed from complete fatty acid

oxidation? (24.7)

• To determine the ATP yield from the complete catabolism

of a fatty acid, we must consider the ATP used up in

the synthesis of the acyl CoA, the ATP generated from



PROBLEMS

Selected in-chapter and end-of-chapter problems have brief answers provided in Appendix B.



Analyzing Biochemical Reactions

24.33



Analyze each reaction by considering the functional groups that change, the coenzyme or other reactant, and the name of

the enzyme.

OH



a.



CH3



CH



NAD+



O

CH2



C



SCoA



b.

24.34



−O CCH

2

2



CO2−



C



C



O

CH2



C



SCoA



PO32−



GDP



phosphoenolpyruvate

carboxykinase



CH2



O



O



C



C



O−



+



CO2



Analyze each reaction by considering the functional groups that change, the coenzyme or other reactant, and the name of

the enzyme.

PO32−



a.



O



OH



CH2



ATP



O



CH



C



O



ATP



CH3



C



CO2







+



PO32−



phosphoglycerate

kinase



O



b.



ADP



O−



3-phosphoglycerate



smi26573_ch24.indd 771



O



CH3



β-hydroxyacyl CoA

dehydrogenase



GTP



O



NADH + H+



CO2



OH



O



CH2 CH C O PO32−

1,3-bisphosphoglycerate



ADP + HPO42−



O

−O



pyruvate carboxylase



2CCH2



C



CO2−



12/19/08 2:35:50 PM



772



CARBOHYDRATE, LIPID, AND PROTEIN METABOLISM



24.35



In the conversion of glucose to stored glycogen, glucose

6-phosphate is converted to glucose 1-phosphate by the

enzyme phosphoglucomutase. Suggest a reason for the

name of this enzyme.

When mannose is metabolized to an intermediate in

glycolysis, mannose 6-phosphate is converted to fructose

6-phosphate by phosphomannose isomerase. (a) Why is

an isomerase enzyme used for this reaction? (b) What

type of isomers do mannose 6-phosphate and fructose

6-phosphate represent?



24.36



CH2OPO3

O

H

OH



H

H



CH2



OH



HO



OH



24.46

24.47

24.48



OPO32−



2−



H



24.45



phosphomannose

isomerase



H



mannose 6-phosphate



H



CH2OH



O



24.49



HO



H



OH

OH



H



fructose 6-phosphate



24.50



Glucose Metabolism

24.37



24.38



24.39



24.40



24.41



24.42

24.43



24.44



Compare the energy-investment phase and the energygenerating phase of glycolysis with regards to each of

the following: (a) the reactant that begins the phase and

the final product formed; (b) the amount of ATP used or

formed; (c) the number of reduced coenzymes used or

formed.

Compare glycolysis and gluconeogenesis with regards

to the reactant that begins the pathway and the product

formed at the end of the pathway.

Considering the individual steps in glycolysis:

a. Which steps form ATP?

b. Which steps use ATP?

c. Which steps form a reduced coenzyme?

d. Which step breaks a C C bond?

Explain the role of the coenzymes NAD+ and NADH in

each reaction.

a. pyruvate → acetyl CoA

b. pyruvate → lactate

c. pyruvate → ethanol

Glucose is completely metabolized to six molecules of

CO2. What specific reactions generate each molecule

of CO2?

Why is glycolysis described as an anaerobic process?

Write the overall equation with key coenzymes for each

process.

a. glucose → pyruvate

b. glucose → ethanol

c. pyruvate → lactate

Write the overall equation with key coenzymes for each

process.

a. glucose → lactate

b. pyruvate → ethanol

c. pyruvate → acetyl CoA



smi26573_ch24.indd 772



24.51

24.52

24.53



24.54



24.55

24.56

24.57

24.58



Consider the aerobic and anaerobic avenues of pyruvate

metabolism in the human body.

a. Where do the carbon atoms of pyruvate end up in each

pathway?

b. What coenzymes are used and formed?

What is the main purpose for the conversion of pyruvate

to lactate under anaerobic conditions?

What is the difference between glycolysis and

gluconeogenesis?

Why is it incorrect to say that gluconeogenesis is simply

the reverse of glycolysis?

What effect is observed on the rate of glycolysis under

each of the following conditions?

a. low ATP concentration

c. high carbohydrate diet

b. low ADP concentration

d. low carbohydrate diet

What effect is observed on the rate of gluconeogenesis

under each of the following conditions?

a. low ATP concentration

c. high carbohydrate diet

b. low ADP concentration

d. low carbohydrate diet

Describe the steps in the Cori cycle. In what organs do

key reactions of the cycle occur?

How does a defect in monosaccharide metabolism result

in galactosemia?

What metabolic products are formed from pyruvate

in each case: (a) anaerobic conditions in the body;

(b) anaerobic conditions in yeast; (c) aerobic conditions?

Why must the NADH produced in glycolysis be

re-oxidized to NAD+? How is this accomplished

aerobically? How is this accomplished anaerobically?

Explain in detail how 32 ATP molecules are generated

during the complete catabolism of glucose to CO2.

What are the starting material and product of each step of

gluconeogenesis: (a) step [2]; (b) step [5]; (c) step [8]?

In fermentation, where do the six carbon atoms of

glucose end up?

In what ways is alcohol fermentation similar to lactate

production in muscle?



Triacylglycerol Metabolism

24.59

24.60

24.61



How much ATP is used or formed when a fatty acid is

converted to an acyl CoA? Explain your reasoning.

How much ATP is ultimately generated from each cycle

of β-oxidation of a fatty acid?

For each carboxylic acid: [1] How many molecules of

acetyl CoA are formed from complete β-oxidation?

[2] How many cycles of β-oxidation are needed for

complete oxidation?

a. hexanoic acid, CH3(CH2)4CO2H

b. myristic acid, C13H27CO2H



12/19/08 2:35:50 PM



PROBLEMS



24.62



24.63

24.64

24.65



24.66



24.67



24.68



24.69



24.70



24.71



24.72



For each carboxylic acid: [1] How many molecules of

acetyl CoA are formed from complete β-oxidation?

[2] How many cycles of β-oxidation are needed for

complete oxidation?

a. octanoic acid, CH3(CH2)6CO2H

b. oleic acid, C17H33CO2H

How much ATP is generated by the complete catabolism

of the carboxylic acids in Problem 24.61?

How much ATP is generated by the complete catabolism

of the carboxylic acids in Problem 24.62?

Draw the structure of the acyl CoA formed from palmitic

acid, C15H31CO2H. Use this acyl CoA to write out the

four steps of β-oxidation.

Draw the structure of the acyl CoA formed from hexanoic

acid, C5H11CO2H. Use this acyl CoA to write out the four

steps of β-oxidation.

Why is step [1] of β-oxidation considered an oxidation

reaction even though the product has no additional C O

bonds?

Why is the enzyme for step [2] of β-oxidation called

a hydratase? What type of reaction does this enzyme

catalyze?

Consider decanoic acid, C9H19CO2H.

a. Label the α and β carbons.

b. Draw the acyl CoA derived from this fatty acid.

c. How many acetyl CoA molecules are formed by

complete β-oxidation?

d. How many cycles of β-oxidation are needed for

complete oxidation?

e. How many molecules of ATP are formed from the

complete catabolism of this fatty acid?

Consider docosanoic acid, C21H43CO2H.

a. Label the α and β carbons.

b. Draw the acyl CoA derived from this fatty acid.

c. How many acetyl CoA molecules are formed by

complete β-oxidation?

d. How many cycles of β-oxidation are needed for

complete oxidation?

e. How many molecules of ATP are formed from the

complete catabolism of this fatty acid?

How many moles of ATP per gram of fatty acid are

formed from the complete catabolism of decanoic acid

(molar mass 172 g/mol) in Problem 24.69?

How many moles of ATP per gram of fatty acid are

formed from the complete catabolism of docosanoic acid

(molar mass 341 g/mol) in Problem 24.70?



Ketone Bodies

24.73

24.74



smi26573_ch24.indd 773



What is the difference between ketosis and ketogenesis?

How is the production of ketone bodies related to

ketoacidosis?



773



24.75

24.76



Why are more ketone bodies produced in an individual

whose diabetes is poorly managed?

Why do some individuals use test strips to measure the

presence of ketone bodies in their urine?



Amino Acid Metabolism

24.77

24.78

24.79



24.80



24.81



What is the difference between ketogenic and glucogenic

amino acids?

What is the difference between transamination and

oxidative deamination?

Draw the structure of the α-keto acid formed by

the transamination of each amino acid: (a) glycine;

(b) phenylalanine.

Draw the structure of the α-keto acid formed by

the transamination of each amino acid: (a) tyrosine;

(b) asparagine.

Draw the products formed in each transamination

reaction.

+



NH3



a.



CH3



C



O





+



CO2



−O CCH

2

2



C



CO2−



H

+



NH3



b.



(CH3)2CHCH2



C



O





CO2



+



−O



2CCH2



C



CO2−



H



24.82



Draw the products formed in each transamination

reaction.

+



NH3



a.



(CH3)2CH



C



O





CO2



+



−O CCH

2

2



C



CO2−



H

+



NH3



b.



CH3CH2CH(CH3)



C



O

CO2−



+



−O



2CCH2CH2



C



CO2−



H



24.83



24.84



24.85



24.86



What products are formed when each amino acid

undergoes oxidative deamination with NAD+ and a

dehydrogenase enzyme: (a) leucine; (b) phenylalanine?

What products are formed when each amino acid

undergoes oxidative deamination with NAD+ and a

dehydrogenase enzyme: (a) tyrosine; (b) tryptophan?

What metabolic intermediate is formed from the carbon

skeleton of each amino acid?

a. phenylalanine

c. asparagine

b. glutamic acid

d. glycine

What metabolic intermediate is formed from the carbon

skeleton of each amino acid?

a. lysine

c. methionine

b. tryptophan

d. serine



12/19/08 2:35:50 PM



774



24.87

24.88



CARBOHYDRATE, LIPID, AND PROTEIN METABOLISM



Can an amino acid be considered both glucogenic and

ketogenic? Explain your choice.

Which amino acids are classified as only glucogenic?



24.97



O



a.



General Questions and Applications

24.89

24.90

24.91

24.92

24.93

24.94

24.95

24.96



What is the difference between a spiral and a cyclic

metabolic pathway? Give an example of each.

What is the cause of the pain and cramping in a runner’s

muscles?

Explain the reaction that occurs during the baking of

bread that causes the bread to rise.

Why is the concentration of ethanol in wine typically

12% or less?

How might pyruvate be metabolized in the cornea, tissue

that has little blood supply?

How is pyruvate metabolized in red blood cells, which

contain no mitochondria?

Why is the Atkins low carbohydrate diet called a

ketogenic diet?

What metabolic conditions induce ketogenesis?



What type of enzyme would catalyze the conversion of

hydroxyacetone (CH3COCH2OH) to each compound?

CH3



C



CH2OPO32−



O



b.



CH3



C



CHO

O



c.

24.98



HO2CCH2



C



CH2OH



What coenzyme would convert 6-hydroxy-2-hexanone

(CH3COCH2CH2CH2CH2OH) to each compound?

OH



a.



CH3



CH(CH2)4OH

O



b.



CH3



C



(CH2)3CHO



O



c.



CH3



C



CH



CHCH2CH2OH



CHALLENGE QUESTIONS

24.99



How much ATP is produced from the complete

catabolism of one molecule of glycerol,

HOCH2CH(OH)CH2OH?



smi26573_ch24.indd 774



24.100 How much ATP is produced from the complete



catabolism of one molecule of the given triacylglycerol?

O

CH2



O



C

O



(CH2)4CH3



CH



O



C

O



(CH2)4CH3



CH2



O



C



(CH2)4CH3



12/19/08 2:35:51 PM



Appendix A

Useful Mathematical Concepts

Three common mathematical concepts are needed to solve many problems in chemistry:

• Using scientific notation

• Determining the number of significant figures

• Using a scientific calculator



SCIENTIFIC NOTATION

To write numbers that contain many leading zeros (at the beginning) or trailing zeros (at the end),

scientists use scientific notation.

• In scientific notation, a number is written as y × 10x, where y (the coefficient) is a

number between 1 and 10, and x is an exponent, which can be any positive or

negative whole number.



To convert a standard number to scientific notation:

1. Move the decimal point to give a number between 1 and 10.

2. Multiply the result by 10x, where x is the number of places the decimal point was moved.

• If the decimal point is moved to the left, x is positive.

• If the decimal point is moved to the right, x is negative.

2822.



=



2.822 × 103



the number of places the decimal

point was moved to the left



Move the decimal point three places to the left.

0.000 004 5



=



4.5 × 10−6



the number of places the decimal

point was moved to the right



Move the decimal point six places to the right.



To convert a number in scientific notation to a standard number, use the value of x in 10x to indicate the number of places to move the decimal point in the coefficient.

• Move the decimal point to the right when x is positive.

• Move the decimal point to the left when x is negative.

2.521 × 102



2.521



252.1



Move the decimal point to the right two places.

2.68 × 10−2



00268



0.0268



Move the decimal point to the left two places.



A-1



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A-2



USEFUL MATHEMATICAL CONCEPTS



Table A.1 shows how several numbers are written in scientific notation.



TABLE A.1



Numbers in Standard Form and Scientific Notation

Number



Scientific Notation



26,200



2.62 × 104



0.006 40



6.40 × 10–3



3,000,000



3 × 106



0.000 000 139



1.39 × 10–7



2,000.20



2.00020 × 103



Often, numbers written in scientific notation must be multiplied or divided.

• To multiply two numbers in scientific notation, multiply the coefficients together and

add the exponents in the powers of 10.

Add exponents.

(8 + 3)

×



(3.0 × 108)



(2.0 × 103)



=



6.0 × 1011



Multiply coefficients.

(3.0 × 2.0)



• To divide two numbers in scientific notation, divide the coefficients and subtract the

exponents in the powers of 10.

Divide coefficients.

(6.0/2.0)



6.0 × 106

2.0 × 1010



Subtract exponents.

(6 − 10)



=



3.0 × 10−4



Table A.2 shows the result of multiplying or dividing several numbers written in scientific notation.



TABLE A.2



Calculations Using Numbers Written in Scientific Notation

Calculation



Answer



(3.5 × 103) × (2.2 × 1022) =



7.7 × 1025



(3.5 × 103)/(2.2 × 1022) =



1.6 × 10–19



(3.5 × 103) × (2.2 × 10–10) =



7.7 × 10–7



(3.5 × 103)/(2.2 × 10–10) =



1.6 × 1013



SIGNIFICANT FIGURES

Whenever we measure a number, there is a degree of uncertainty associated with the result. The

last number (furthest to the right) is an estimate. Significant figures are all of the digits in a

measured number including one estimated digit. How many significant figures are contained in

a number?



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12/19/08 2:01:34 PM



SIGNIFICANT FIGURES



A-3



• All nonzero digits are always significant.

• A zero counts as a significant figure when it occurs between two nonzero digits, or at the

end of a number with a decimal point.

• A zero does not count as a significant figure when it occurs at the beginning of a

number, or at the end of a number that does not have a decimal point.



Table A.3 lists the number of significant figures in several quantities.



TABLE A.3



Examples Illustrating Significant Figures

Number of

Significant Figures



Quantity



Quantity



Number of

Significant Figures



1,267 g



Four



203 L



Three



24,345 km



Five



6.10 atm



Three



1.200 mg



Four



0.3040 g



Four



0.000 001 mL



One



1,200 m



Two



The number of significant figures must also be taken into account in calculations. To avoid reporting a value with too many digits, we must often round off the number to give the correct number

of significant figures. Two rules are used in rounding off numbers.

• If the first number that must be dropped is 4 or less, drop it and all remaining numbers.

• If the first number that must be dropped is 5 or greater, round the number up by adding

one to the last digit that will be retained.



To round 63.854 to two significant figures:

These digits must be retained.

63.854

These digits must be dropped.



first digit to be dropped

• Since the first digit to be dropped is 8 (a 5 or greater),

add 1 to the first digit to its left.

• The number 63.854 rounded to two digits is 64.



Table A.4 gives other examples of rounding off numbers.



TABLE A.4



Rounding Off Numbers



Original Number



Rounded to



Rounded Number



15.2538



Two places



15



15.2538



Three places



15.3



15.2538



Four places



15.25



15.2538



Five places



15.254



The first number to be dropped is indicated in red in each original number.



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12/19/08 2:01:34 PM



A-4



USEFUL MATHEMATICAL CONCEPTS



The number of significant figures in the answer of a problem depends on the type of mathematical calculation—multiplication (and division) or addition (and subtraction).

• In multiplication and division, the answer has the same number of significant figures as

the original number with the fewest significant figures.

five significant figures



first digit to be dropped



×

5.5067

two significant figures



2.6



=



14.31742 rounded to 14

The answer must contain only two significant figures.



• In addition and subtraction, the answer has the same number of decimal places as the

original number with the fewest decimal places.

two digits after the decimal point

+

10.17

one digit after the decimal point



=



3.5



13.67 rounded to 13.7



last significant digit



The answer can have only one digit after the decimal point.



Table A.5 lists other examples of calculations that take into account the number of significant

figures.



TABLE A.5



Calculations Using Significant Figures

Calculation



Answer



3.2 × 699 =



2,236.8 rounded to 2,200



4.66892/2.13 =



2.191981221 rounded to 2.19



25.3 + 3.668 + 29.1004 =



58.0684 rounded to 58.1



95.1 – 26.335 =



68.765 rounded to 68.8



USING A SCIENTIFIC CALCULATOR

A scientific calculator is capable of carrying out more complicated mathematical functions than

simple addition, subtraction, multiplication, and division. For example, these calculators allow

the user to convert a standard number to scientific notation, as well as readily determine the

logarithm (log) or antilogarithm (antilog) of a value. Carrying out these operations is especially

important in determining pH or hydronium ion concentration in Chapter 9.

Described in this section are the steps that can be followed in calculations with some types of

calculators. Consult your manual if these steps do not produce the stated result.



CONVERTING A NUMBER TO SCIENTIFIC NOTATION

To convert a number, such as 1,200, from its standard form to scientific notation:

• Enter 1200.

• Press 2nd and then SCI.

• The number will appear as 1.203, indicating that 1,200 = 1.2 × 103.



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12/19/08 2:01:34 PM



USING A SCIENTIFIC CALCULATOR



A-5



ENTERING A NUMBER WRITTEN IN SCIENTIFIC NOTATION

To enter a number written in scientific notation with a positive exponent, such as 1.5 ì 108:











Enter 1.5.

Press EE.

Enter 8.

The number will appear as 1.508, indicating that it is equal to 1.5 × 108.



To enter a number written in scientific notation with a negative exponent, such as 3.5 ì 104:













Enter 3.5.

Press EE.

Enter 4.

Press CHANGE SIGN (+ → –).

The number will appear as 3.5–04, indicating that it is equal to 3.5 × 10–4.



TAKING THE LOGARITHM OF A NUMBER:

CALCULATING pH FROM A KNOWN [H3O+]

Since pH = –log [H3O+], we must learn how to calculate logarithms on a calculator in order

to determine pH values. To determine the pH from a known hydronium ion concentration, say

[H3O+] = 1.8 ì 105, carry out the following steps:

Enter 1.8 × 10–5 (Enter 1.8; press EE; enter 5; press CHANGE SIGN). The number 1.8–05

will appear.

• Press LOG.

• Press CHANGE SIGN (+ → –).

• The number 4.744 727 495 will appear. Since the coefficient, 1.8, contains two significant

figures, round the logarithm to 4.74, which has two digits to the right of the decimal point.

Thus, the pH of the solution is 4.74.



TAKING THE ANTILOGARITHM OF A NUMBER:

CALCULATING [H3O+] FROM A KNOWN pH

Since [H3O+] = antilog(–pH), we must learn how to calculate an antilogarithm—that is, the

number that has a given logarithm value—using a calculator. To determine the hydronium ion

concentration from a given pH, say 3.91, carry out the following steps:











Enter 3.91.

Press CHANGE SIGN (+ → –).

Press 2nd and then LOG.

The number 0.000 123 027 will appear. To convert this number to scientific notation, press

2nd and SCI.

• The number 1.230 268 771–04 will appear, indicating that [H3O+] = 1.230 268 771 × 10–4.

Since the original pH (a logarithm) had two digits to the right of the decimal point, the

answer must have two significant figures in the coefficient in scientific notation. As a result,

[H3O+] = 1.2 × 10–4.



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A-6



USEFUL MATHEMATICAL CONCEPTS



Table A.6 lists pH values that correspond to given [H3O+] values. You can practice using a calculator to determine pH or [H3O+] by entering a value in one column, following the listed steps, and

then checking to see if you obtain the corresponding value in the other column.



TABLE A.6

[H3O+]



pH



[H3O+]



pH



1.8 × 10–10



9.74



4.0 × 10–13



12.40



–2



3.8 × 10



5.0 × 10–12

–7



4.2 × 10



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The pH of a Solution from a Given Hydronium Ion

Concentration [H3O+]



–4



3.18



11.30



2.6 × 10–9



8.59



6.38



–8



7.14



1.42



6.6 × 10



7.3 × 10



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