Question

In an electroplating experiment, $m$ grams of silver are deposited when 4 A of current flows for 2 minutes. The amount of silver deposited by 6 A of current when it flows for 40 seconds will be:
A) $2m$
B) $m/4$
C) $m/2$
D) $4m$

Answer 1

In this solution, we will apply the concepts of electrochemical equivalent $(Z)$. We will calculate the deposition of mass due to the flow of current for both the situations and then take the ratio of the two equations.

Formula used: In this solution, we will use the following formula:
Mass deposited due to flow of current $m = ZIt$ where $I$ is the amount of current flowing in the circuit and $t$ is the time for which the current flows and $Z$ is the electrochemical equivalent.

Complete step by step answer:
The relation of mass deposited when current is passed through it is given by
$m = ZIt$
For the first case, the mass deposited in 2 minutes of 120 seconds can be calculated as
$m = Z(4)(120)$
Then in the second case, the mass deposited can be calculated as
${m_2} = Z(6)40$
Taking the ratio of the above two equations, we can write
$\dfrac{m}{{{m_2}}} = \dfrac{{4 \times 120}}{{6 \times 40}}$
Which on simplifying becomes
${m_2} = \dfrac{m}{2}$
Hence, the mass deposited when 6 A of current when it flows for 40 seconds will be $m/2$ so the correct choice is option (C).

Note: The mass deposited is derived from Faraday’s law of electrolysis. It states that the amount of mass deposited at any electrode when current is passed through it is proportional to the quantity of electricity passing through the electrolyte which implies:
$m \propto q$
We can write an equal relation by placing a proportionality constant $Z$ as
$m = Zq$
Since the current is the product of current and the time the current flows for, we get
$m = ZIt$ which is the relation of mass with that we used in the solution.