Question

The mass of copper deposited from a solution of copper sulphate by a uniform current of 0.25 ampere flowing for one hour is 0.295 g. Find the equivalent mass of copper. (1 faraday = 96500 coulomb)
A. 31.75
B. 75
C. 3175
D. 3.175

Answer 1

Hint: The deposited mass ‘w’ as a result of current ‘i’ over time ‘t’ in grams is given by:
$w=\dfrac{i\times t\times e}{96500}$, where e is the charge equivalent mass of the given element. With this relation in mind, try to find the equivalent mass of copper in the given scenario.

Complete step by step solution: It has been given that 1 faraday = 96500 Coulomb.
In the given scenario, the oxidation state of Copper is reduced from +2 to ground state as a result of the given setup. Therefore, we can safely conclude that the chemical reaction in question is as follows:

$C{{u}^{2+}}+2{{e}^{-}}\to C{{u}^{0}}$

Now, we know that each mole of any ion ${{A}^{x+}}$ requires x Faraday of charge.
Therefore, we know that 1 mole of Copper would require 2F of charge.
That implies, 63.5 grams of Copper would require 2F of Charge. (Since, the molar mass of Copper is 63.5 grams).

Thus, we obtain a relation for the deposited mass ‘w’ as a result of current ‘i’ over time ‘t’ in grams is given by:
$w=\dfrac{i\times t\times e}{96500}$, where e is the equivalent mass of the given element.
Plugging in w = 0.295 grams, I = 0.25 A and t = 3600 (Since one hour has 3600 seconds)
\[0.295g=\dfrac{0.25A\times 3600s\times e}{96500C}\]
\[e=\dfrac{0.295g\times 96500C}{0.25A\times 3600s}\]
\[e=\dfrac{284.68}{9}g\]
\[e=31.63g\]
The obtained value of e is closest to 31.75 grams in the given options. Some errors occur during calculation due to problems in rounding off and approximations.
Thus, we can conclude that the answer to this question is ‘A. 31.75g’

Note: Be extremely wary of the change in oxidation state that takes place in the given reaction as any mistake in doing so could result in the calculation of an incorrect amount of charge which is required for the given chemical reaction. Also, be very careful of the differences between the concepts of molar and equivalent masses of compounds.