Question

Buffer solution $A$ of a weak monoprotic acid and its sodium salt in the concentration ratio $x:y$ has $pH=\left(pH\right)$,. Buffer solution $B$ of the same acid and its sodium salt in the concentration ratio $y:x$ has $pH=(pH{)}_2$. If $(pH{)}_2-(pH{)}_1=1$ unit and $(pH{)}_1+(pH{)}_2=9.5units$, then:

• A. $p{K}_a=4.75$
• B. $\frac{x}{y}=2.36$
• C. $\frac{x}{y}=3.162$
• D. $p{K}_a=5.25$

Answer 1

The correct option is A $p{K}_a=4.75$

$(pH{)}_1=p{K}_a+\log \frac{y}{x}$

$\Rightarrow (pH{)}_2=p{K}_a+\log \frac{x}{y}$

$\Rightarrow (pH{)}_2-(pH{)}_1=1=\log \frac{x}{y}-\log \frac{y}{x}=2\log \frac{x}{y}$

$\therefore \log \frac{x}{y}=\frac{1}{2}\Rightarrow \frac{x}{y}=3.162$

$(pH{)}_1+(pH{)}_2=9.5=2p{K}_a+\log \frac{y}{x}\times \frac{x}{y}=2p{K}_a+0$

$\therefore p{K}_a=4.75$