Chapter 17, Problem 17.59SP

Interpretation Introduction

Interpretation:

The concentration of the salt of weak acid strong base in a buffer solution.

Concept introduction:

• Buffer solution:Aqueous solution of a salt of strong acid and strong base e.g. sodium chloride (NaCl), and salt of weak acid and a weak base e.g. ammonium chloride( $N{H}_{4}Cl$ ), both have a $P^H$ of 7. But the addition of 1 cm³ of 0.1MHCl to 1 dm³ of the solutions alters the $P^H$ to 4 in the case of former, while it hardly affects the $P^H$ of the latter. The addition of an equivalent quantity of NaOH would like wise change the $P^H$ of the NaCl solution from 7 to 10, but it would not appreciably alter that $N{H}_{4}Cl$ solution. The solution of $N{H}_{4}Cl$ thus has the property of resisting the change of $P^H$
  
  when an acid or alkali is added to it and this property of solution is known as buffer action.
  
  In general, a buffer solution is one which is resistant to change of $P^H$ upon the addition of a small amount of acid or base. The buffer solutions usually contain relatively larger amount of a weak acid and salt of its conjugate base. The $P^H$ of the buffer solution is expressed by Henderson-Hasselbalch equation: $P^H=P^{K_a}+\log \frac{[salt]}{[acid]}$

Given:

The $P^H$ of a solution of $H{N}_3$ and $Na{N}_3$ is 4.86.
The acid dissociation constant of $H{N}_3$ is $1.9\times {10}^{-5}$ and the concentration is 0.016M.

To determine:

The molarity of $Na{N}_3$ in the mixture of $H{N}_3$ and $Na{N}_3$.