Question

A current is passed for a time $t$ through a number of voltmeters. If $m$is the mass of a substance deposited on an electrode and $Z$is its electrochemical equivalent, then
A. $\dfrac{ZIt}{m}=$Constant
B. $\dfrac{Z}{mIt}=$Constant
C. $\dfrac{I}{Zmt}=$Constant
D. $\dfrac{It}{Zm}=$Constant

Answer 1

Hint: Micheal Faraday introduced a quantitative relation between the amount of current and the mass of the substance deposited at a specific electrode at a particular time. This relation is popularly known as Faraday’s law of electrolysis. Here we can use this law for solving the given problem.

Complete Step by Step Answer:
 Faraday’s first law of electrolysis: The mass of a substance liberated is directly proportional to the number of charges flowing through an electrolyte.
Given current ($I$) is passed for a time, t through a number of voltmeters. Mass of the substance is $m$, deposited and the electrochemical equivalent is z.
Let the amount of charge be$q$
According to Faraday’s first law of electrolysis, $m$$\alpha $$q$
Or, $m=z\times q$
Here $z$ is proportionality constant and is also known as electrochemical equivalent.
Again charge($q$) is defined as the amount of charge from a current ($I$) flowing per unit time $(t)$.
$q=I\times t$
Therefore $m=I\times t\times z$
Or, $\dfrac{zIt}{m}=1$
Or, $\dfrac{zIt}{m}=$ Constant
Thus, option (A) is correct.
Additional information:
Faraday’s second law of electrolysis states that when same amount of current is passed through different electrolytes, the mass of different ions deposited at the electrodes are directly proportional to chemical equivalents of elements.Therefore this law is very useful for the calculation of chemical equivalents of different electrolysis.

Note: Voltameter is a kind of electrolytic cell that determines the quantity of charge flowing through it by a resulting chemical action. Charges are generally in coulombs that’s why voltmeter is also known as coulometer. The voltmeter should not be confused with a voltmeter as voltmeter only determines the electrical difference.