Q. When electric current is passed through acidified water for 1930 s, 1120mL of $H_{2}$ gas is collected (at STP) at the cathode. What is the current passed in amperes?

A) 0.05
B) 0.50
C) 5.0
D) 50
Explanation

(c)
Electrolysis of water takes place as follows
$H_{2}O\ \ \ \ \ \rightleftharpoons \ {\ \ \ \ \ \ \ \ \ H}^{+}\ \ \ \ \ \ + \ \ \ \ \ \ {OH}^{-}$
Cathode anode
At anod
${OH}^{-}\ \ \ \overset{oxidation\ \ \ \ }{\rightarrow}\ OH + \ e^{-}$
$4OH\ \longrightarrow \ {2H}_{2}O\ + \ O_{2}$
At cathode
${2H}^{+} + \ {2e}^{-}\ \overset{Reduction\ \ \ \ }{\rightarrow}\ H_{2}$
Given, time, $t\ = \ 1930s$
Number of moles of hydrogen collected
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ \frac{1120\ \times \ 10^{- 3}}{22.4}\ moles$
= 0.05 moles
∵ 1 mole of hydrogen is deposited by = 2 moles of electrons
∵ 0.05 moles of hydrogen will be deposited by
$= \ 2\ \times \ 0.05$
= 0.10 mole of electrons
Charge$\mathcal{,\ Q\ = \ }nF\$
$= \ 0.1\ \times \ 96500$
Charge,$\mathcal{\ Q\ = \ }it$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1\ \times \ 96500\ = \ i\ \times \ 1930\$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ i = \ \frac{0.1\ \times 96500}{1930}$
= 5.0 A

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.