   Chapter 17, Problem 13PS

Chapter
Section
Textbook Problem

What must the ratio of acetic acid to acetate ion be to have a buffer with a pH value of 5.00?

Interpretation Introduction

Interpretation:

The ratio of concentration of acetic acid to its conjugate base has to be determined for the buffer solution has pH value 5.0

Concept introduction:

The Henderson-Hasselbalch equation relates pH of a buffer with pKa of acid, concentration of conjugate base and concentration of acid. The expression is written as,

pH=pKa+log[conjugatebase][acid] (1)

This equation shows that pH of buffer solution is controlled by two major factors. First, strength of the acid can be expressed on terms of pKa and second, the relative concentration of acid and its conjugate base at equilibrium.

Explanation

The calculation of the ratio of concentration of acid to conjugate base is done by using Henderson-Hasselbalch equation. The equilibrium between acetic acid and its conjugate base acetate is written as,

CH3COOH(aq)+H2O(l)H3O+(aq)+CH3COO(aq)  (acid)                                                     (conjugate base)

Therefore, acid is CH3COOH and its conjugate base is CH3COO.

Given:

Refer to table 16.2 in the textbook for the value of Ka.

The value of Ka for CH3COOH is 1.8×105.

Negative logarithm of the Ka value gives the pKa value of the acid.

pKa=log(Ka)=log(1.8×105)=4.74

Therefore, pKa value for the CH3COOH is 4.74.

The value of pH for the buffer solution to be prepared is 5.0.

Calculate the ratio of acid to conjugate base by using Henderson-Hasselbalch equation.

pH=pKa+log[conjugatebase][acid]

Substitute 4.74 for pKa and 5.0 for pH, [CH3COOH] for [acid] and [CH3COO] for [conjugatebase],

5.0=4.74+log[CH3COO][CH3COOH]

Rearrange for, log[CH3COO][CH3COOH]

log[CH3COO][CH3COOH]=5

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