Question

What would be the magnitude of the EMF of the following cell:

At $25^{\circ }C$ ? The ionization constant of acetic acid, $K_a\sim 10^{-5}$, while that of formic acid, $K_a\sim 10^{-4}$

• A. $0.0295V$
• B. $0.059V$
• C. $-0.059$
• D. $-0.0295V$

Answer 1

Answer: (B)

At anode:
$0.1M$ acetic acid $+0.1M$ sodium acetate $\Rightarrow$ Acidic buffer
$\therefore p{H}_a=p{K}_a+\log \left[\frac{\text{ Salt }}{\text{ Acid }}\right]\left(p{K}_{a\left(C{H}_{3}COOH\right)}=5\right)$
$=5+\log \frac{0.1}{0.1}=5$
At cathode:
$0.1M$ formic acid $+0.1M$ sodium formate $\Rightarrow$
Acidic buffer
$\therefore p{H}_c=p{K}_a+\log \left(\frac{0.1}{0.1}\right)\left[p{K}_{a(HCOOH)}=4\right]$
$p{H}_c=4$
$E_{\text{cell }}=-0.059\left(p{H}_c-p{H}_a\right)=-0.059(4-5)$
$=0.059V$