Question

A very thin copper plate is electroplated with gold using gold chloride in $HCl$. The current was passed for 20 min and the increase in weight if the plate was found to be 2 g. [Au = 197]. The current passed was?
(a)- 0816 amp
(b)- 1.632 amp
(c)- 2.448 amp
(d)- 3.264 amp

Answer 1

Hint: The charge required for the electrolysis can be calculated by multiplying the current with the time taken in seconds. Now calculate the current by the formula $I=\dfrac{w\text{ x 96500}}{Eq.\text{ }wt\ \text{x }t}$ where w is the weight of gold, eq. wt is the equivalent weight of gold, and t is the time taken.

Complete step by step answer:
Faraday’s first law of electrolysis:
It states that the amount of mass liberated at the electrode is always directly proportional to the quantity of the current which is passed into the solution.
\[W\text{ }=\text{ }Z\text{ x }Q\]
W = mass,
 Z = proportionality constant called electrochemical equivalent.
Q = amount of electricity.
 Faraday’s second law of Electrolysis.
It states that when electricity is passed to a solution which contains electrolyte that is connected in series, the masses produced at the electrode is directly proportional to their equivalent weight.
When electrolysis occurs, the charge carried by one mole of an electron is obtained by the product of charge present on one electron with Avogadro's number which equals to 96500coloumbs. This quantity is called one faraday.
So, by combining both the laws we can formulate:
$W=\dfrac{Q}{F}\text{ x }E$
Now when gold is deposited as the reaction:
$A{{u}^{3+}}(aq)+3{{e}^{-}}\to Au(s)$

The charge required for the electrolysis can be calculated by multiplying the current with the time taken in seconds
$Q=I\text{ x t}$
Given time is 20 minutes, and it has to be converted into seconds,
$t=20\text{ x 60 = 1200 sec}$
F = 3 faraday, because 3 electrons are involved in the reaction.
1 F = $96500\text{ }C/mol$
F = $3\text{ x 96500 C/mol}$
W = 2 g (Given)
E = Eq. wt of gold = $\dfrac{197}{3}$
So, the formula will be = $I=\dfrac{w\text{ x 96500}}{Eq.\text{ }wt\ \text{x }t}$
Now putting the values, we get,
$\Rightarrow I=\dfrac{\text{2 x 3 x 96500}}{197\ \text{x 1200}}=\dfrac{1930}{788}=2.448$
So, the current passed is 2.448 amp.
So, the correct answer is “Option C”.

Note: The actual value of the faraday is 96487 but for numerical and easier calculation 96500 is used. If the time is not given we can directly use $W=\dfrac{QM}{Fz}$ the formula. And if the time is mentioned then always take the value in seconds.