Question

When $X$ amperes of current is passed through molten $AlC{l_3}$ for $96.5$ seconds, $0.09$ grams of aluminium is deposited. What is the value of $X$ ?
A. 10
B. 20
C. 30
D. 40

Answer 1

Hint:To find the current passed through the molten compound Faraday’s laws of electrolysis is used which shows relationship between molar mass, oxidation number, time, current and Faraday’s constant.

Complete step by step answer:
This question will be solved by the formula of Faraday’s Law of electrolysis. Faraday’s laws are quantitative relationships based on the electrochemical research published by Michael Faraday in 1833. He reported that the mass of elements deposited at an electrode in gram is directly proportional to the charge in Columbus.
Electric current is a stream of charged particles like electrons or ions moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge past a region. The SI unit of electric current is the ampere or amp which is the flow of electric charge across a surface at the rate of one coulomb per second.
Given below are the values provided in the question,
The molar mass is given as, $m = 0.09g$
The Oxidation number of the compound is given as, $Oxidation\,Number = 3$
The time of the reaction is, $time = 96.5\sec $
Now, we have to find the current used in the reaction in amperes which is shown by the symbol $i$ and according to the question its symbol is $X$ . Therefore $X$ is equal to $i$ ,
$X = i = ?$
Now, according to the Faraday’s law of electrolysis, the formula to find current is given as below,
$M = \dfrac{E}{F}it$
$M = \dfrac{E}{F}Xt$
Here, $M$ is the molar mass of the compound, $E$ is the equivalent weight of the compound, $F$ is Faraday's constant, $X$ or $i$ is the current in amperes and $t$ time taken to complete the reaction. Now, substituting the values given in the question in the equation.
$0.09 = \dfrac{{27 \times 96.5 \times X}}{{3 \times 96500}}$
Now, finding the value of $X$ ,
$X = \dfrac{{0.9 \times 3 \times 1000}}{{27}} = 10A$

Therefore, the current passed through molten $AlC{l_3}$ is $10A$ and the correct answer is option A.

Note:
Faraday has two laws for electrolysis, First and the Second. Both laws state the relationship between the current, molar mass, oxidation number, time, equivalent weight, Avogadro’s constant and Faraday’s constant.