Question

State Faraday’s law of electrolysis. A solution of \[{\text{CuS}}{{\text{O}}_4}\] is electrolyzed for 10 minutes and a current of \[1.5\] amperes. What is the mass of copper deposited at the cathode?

Answer 1

Hint: The above question is based upon the faraday’s first law of electrolysis. Calculate the charge passed through the solution using current and time and divide by Faraday’s constant.
Formula used:
 \[{\text{amount deposited}} = \dfrac{{{\text{Charge}}}}{{1{\text{ Faraday}}}}\] and \[{\text{charge}} = {\text{current}} \times {\text{time}}\]

Complete step by step answer:
Faraday gave two laws for electrolysis, first law of electrolysis and second law of electrolysis.
Faraday’s first law of electrolysis: It states that the amount of substance deposited during electrolysis at any electrode is directly proportional to the quantity of electrical energy passed through the electrolyte.
Faraday gave a constant known as Faraday’s constant whose value is \[96500{\text{ Cmo}}{{\text{l}}^{ - 1}}\] equals to charge carried by 1 mole of electron.
Since in \[{\text{CuS}}{{\text{O}}_4}\] copper has a charge of \[ + 2\] and hence need electricity equals to 2 moles of electron hence we have to multiply faraday constant with 2.
We will calculate the value of charge in Coulomb from the current and time using the formula. We need to convert time into a standard unit that is in seconds. \[1{\text{ min }} = 60{\text{ sec}}\] So, \[10{\text{ min }} = 600{\text{ sec}}\]
\[{\text{charge}} = {\text{current}} \times {\text{time}}\]
\[{\text{charge }} = 1.5{\text{ A }} \times {\text{ }}600{\text{ sec}} = 900{\text{ C}}\]
Substituting the values in the formula we will get:
\[{\text{amount deposited}} = \dfrac{{900{\text{ C}}}}{{2 \times 96500{\text{ Cmo}}{{\text{l}}^{ - 1}}}}\]
Dividing the above equations we will get: \[0.004663{\text{ moles}}\]
To calculate the mass we need to multiply the number of moles with molar mass of copper that is 63.5. Mass of copper deposited will be:
\[ \Rightarrow 0.004663 \times 63.5{\text{ = }}0.296{\text{ g}}\]

Note:
Electrolysis is the breaking down of an electrolyte due to the supply of electricity. In electrolysis we need to supply external energy to initiate chemical reaction which is non spontaneous in nature otherwise. The second law of Faraday states that when the same amount of energy is passed through the electrolytic solution of a number of substances then and the equivalent weight of electrolyte in each solution will be in a ratio to each other.