Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
8th Edition
ISBN: 9781305079373
Author: William L. Masterton, Cecile N. Hurley
Publisher: Cengage Learning
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Chapter 13, Problem 51QAP

Barbituric acid, HC4H3N2O3, is used to prepare barbiturates, a class of drugs used as sedatives. Its Ka is 9.8 × 10 5 . Calculate [H+] in solutions prepared by adding enough water to the following to make 1.45 L.

(a) 0.344 mol

(b) 28.9 g

Expert Solution
Check Mark
Interpretation Introduction

(a)

Interpretation:

The concentration of hydrogen ion in the given solution should be calculated.

Concept introduction:

The dissociation reaction of a weak acid is represented as follows:

HBH++B

The expression for the acid dissociation constant will be as follows:

Ka=[H+][B][HB]

Here, [H+] is equilibrium concentration of hydrogen ion, [B] is equilibrium concentration of conjugate base and [HB] is the equilibrium concentration of weak acid.

Answer to Problem 51QAP

4.84×103 M

Explanation of Solution

The acid dissociation constant of barbituric acid is 9.8×105. The volume of solution is 1.45 L and number of moles of the acid is 0.344 mol.

The molarity of HC4H3N2O3 can be calculated as follows:

M=nV(L)

Putting the values,

M=0.344 mol1.45 L=0.24 M

Thus, the concentration of HC4H3N2O3 is 0.24 M.

The concentration all the species can be calculated using the ICE table as follows:

      HC4H3N2O3C4H3N2O3+H+I     0.24                    -               -C     -x                      x             xE     0.24-x                x             x

The expression for Ka is as follows:

Ka=[C4H3N2O3][H+][HC4H3N2O3]

Putting the values,

9.8×105=(x)(x)(0.24x)

On rearranging,

9.8×105(0.24)9.8×105x=x22.352×1059.8×105x=x2

Or,

x2+9.8×105x2.352×105=0

Comparing this with the general quadratic equation as follows:

ax2+bxc=0

Solving the quadratic equation,

x=b±b24ac2a

Putting the values,

x=9.8×105±(9.8×105)24(1)(2.352×105)2(1)=1.2×105±9.604×109+9.41×1052(1)=1.2×105±9.7×1032

x=4.84×103,4.856×103

Since, the value of x cannot be negative thus, the value of x will be 4.84×103.

From the ICE table, it is equal to the concentration of hydrogen ion thus,

[H+]=4.84×103

Therefore, the concentration of hydrogen ion is 4.84×103 M.

Expert Solution
Check Mark
Interpretation Introduction

(b)

Interpretation:

The concentration of hydrogen ion in the given solution should be calculated.

Concept introduction:

The dissociation reaction of a weak acid is represented as follows:

HBH++B

The expression for the acid dissociation constant will be as follows:

Ka=[H+][B][HB]

Here, [H+] is equilibrium concentration of hydrogen ion, [B] is equilibrium concentration of conjugate base and [HB] is the equilibrium concentration of weak acid.

Answer to Problem 51QAP

3.86×103 M

Explanation of Solution

The mass of barbituric acid is given as 28.9 g. The molecular formula of the barbituric acid is HC4H3N2O3 thus, its molar mass is 128.1 g/mol.

Now, from mass and molar mass of the HC4H3N2O3, its number of moles can be calculated as follows:

n=mM=28.9 g128.1 g/mol=0.2256 mol

Now, the molarity of HC4H3N2O3 can be calculated as follows:

M=nV(L)

Putting the values,

M=0.2256 mol1.45 L=0.156 M

Thus, the concentration of HC4H3N2O3 is 0.156 M.

The concentration all the species can be calculated using the ICE table as follows:

      HC4H3N2O3C4H3N2O3+H+I     0.156                    -               -C     -x                        x             xE     0.156-x                x            x

The expression for Ka is as follows:

Ka=[C4H3N2O3][H+][HC4H3N2O3]

Putting the values,

Ka=(x)(x)(0.156x)=9.8×105

On rearranging,

9.8×105(0.156)9.8×105x=x21.53×1059.8×105x=x2

Or,

x2+9.8×105x1.53×105=0

Comparing this with the general quadratic equation as follows:

ax2+bxc=0

Solving the quadratic equation,

x=b±b24ac2a

Putting the values,

x=9.8×105±(9.8×105)24(1)(1.53×105)2(1)=9.8×105±9.604×109+6.12×1052(1)=9.8×105±7.82×1032

x=3.86×103,3.96×103

Since, the value of x cannot be negative thus, the value of x will be 3.86×103.

From the ICE table, it is equal to the concentration of hydrogen ion thus,

[H+]=3.86×103

Therefore, the concentration of hydrogen ion is 3.86×103 M.

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Chapter 13 Solutions

Chemistry: Principles and Reactions

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