Question

In an electroplating experiment, m grams of silver are deposited when 4A of current flows for 2 minutes. The amount of silver deposited by 6A of current for 40sec will be:
A. 2m
B. $\dfrac{m}{4}$
C. $\dfrac{m}{2}$
D. 4m

Answer 1

We will apply the electrochemical equivalent (Z) formula to find out the mass when the larger current flows for longer time i,e., m = Zit. Forming two equations for two different conditions and then dividing them, we can get the required answer.

Complete step-by-step answer :
Now, from the question we have
Mass m, deposited in time t at electrode is given by
m = Zit, where
Z – electrochemical equivalent
I – current flowing
t – time taken
hence, as per the given condition
${m_1} = Z{I_1}{t_1}$ and ${m_2} = Z{I_2}{t_2}$
Where,
${m_1}$ = m
${I_1}$ = 4A
${I_2}$ = 6A
${t_2}$ = 2min = 120s
From above equations we can write
$\dfrac{{{m_2}}}{{{m_1}}} = \dfrac{{Z{I_1}{t_1}}}{{Z{I_2}{t_2}}}$
$\therefore {m_2} = \dfrac{{Z{I_1}{t_1}}}{{Z{I_2}{t_2}}}{m_1}$
${m_2} = \dfrac{{(6)(40)}}{{(4)(2)(60)}}m$
Therefore, ${m_2} = \dfrac{m}{2}$, which gives option C. is the correct option.

Note : Faraday’s – First Law of Electrolysis
It is one among the first laws of electrolysis. It states, during electrolysis, the number of reactions which occurs at any electrode under the influence of electricity is proportional to the quantity of electricity passed through the electrolyte.
According to first law, we have
$m \propto q$
Then, m = Zq (where Z is the electrochemical equivalent) …..(1)
We know that, $I = \dfrac{q}{t} \Rightarrow q = It$
Substituting in (1), we get
m = ZIt