Question

Two buffer solutions, A and B each made with acetic acid and sodium acetate differ in their $pH$ by one unit. A has salt : acid = $x:y$, B has salt: acid = $y:x$. If $x>y$, then the value of $x:y$ is:

• A. $10,000$
• B. $3.17$
• C. $6.61$
• D. $2.10$

Answer 1

The correct option is B $3.17$

Given, two buffer solutions, A and B each made with acetic acid and sodium acetate differ in their $pH$ by one unit. A has salt : acid = $x:y$, B has salt: acid = $y:x$.

The pH of a buffer solution is given as follows:

$pH=p{K}_a+log\frac{\left[salt\right]}{\left[acid\right]}$

As given, $pH=p{K}_a+log\frac{x}{y}$

$pH-1=p{K}_a+log\frac{y}{x}$ as $x>y$

Simplifying, $1=log\frac{x}{y}-log\frac{y}{x}$

$1=log\frac{x}{y}+log\frac{x}{y}=2log\frac{x}{y}$

$\frac{1}{2}=log\frac{x}{y}$

$\frac{x}{y}=3.17$