   Chapter 17, Problem 25PS

Chapter
Section
Textbook Problem

A buffer solution is prepared by adding 0.125 mol of ammonium chloride to 5.00 × 102 mL of 0.500 M solution of ammonia. (a) What is the pH of the buffer? (b) If 0.0100 mol of HCl gas is bubbled into 5.00 × 102 mL of the buffer, what is the new pH of the solution?

(a)

Interpretation Introduction

Interpretation:

For the buffer solution which is prepared by adding 0.125 mol of ammonium chloride in 5.0×102mL of 0.500 M NH3 . pH of the buffer solution has to be calculated.

Concept introduction:

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

pOH=pKb+log[conjugateacid][base] (1)

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

The pH value is calculated by expression, pH + pOH = 14.

Explanation

The calculation of pH is done by using Henderson-Hasselbalch equation.

Given:

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

The value of Kb for NH3 is 1.8×105.

The pKb value is calculated as follows;

pKb=log(Kb)

Substitute, 1.8×105 for Kb.

pKb=log(1.8×105)=4.74

Therefore, pKb value of NH3 is 4.74.

The initial concentration of NH3 is 0.500 molL1.

The initial moles of NH4Cl is 0.125 mol.

The volume of the buffer solution is 5×102mL.

Unit conversion of 5×102mL into L.

(5×102 mL)(1 L1000 mL)=0.500 L

Therefore, volume of the solution is 0.500 L.

The concentration of NH4Cl is calculated as follows;

Molarity=Number of molesvolume of solvent (2)

Substitute 0.125 mol for number of moles and 0.500 L for volume of solvent in equation (2).

Molarity=0

(b)

Interpretation Introduction

Interpretation:

For the buffer solution which is prepared by adding 0.125 mol of ammonium chloride in 5.0×102mL of 0.500 M NH3. pH of the solution when 0.0100 mol of HCl is added to 5.0×102 mL of buffer solution has to be calculated.

Concept introduction:

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

pOH=pKb+log[conjugateacid][base] (1)

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

The pH value is calculated by expression, pH + pOH = 14.

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