Question

A steady current of $5$ amps is maintained for $45$ mins. During this time it deposits $4.572$gms of zinc at the cathode of a voltmeter. E.C.E of zinc is
A. $3.387\times {{10}^{-4}}$gm/C
B.$3.387\times {{10}^{-4}}$ C/gm
C. $3.384\times {{10}^{-3}}$gm/C
D. $3.394\times {{10}^{-3}}$C/gm

Answer 1

Hint: Faraday’s first law of electrolysis states that the amount of chemical change produced by electricity at an electrode is directly proportional to the quantity of electricity passed. E.C.E or the electrochemical equivalent of any element is the amount of weight of substance transported by unit coulomb current.

Formula used: Faraday’s first law of electrolysis,
$m=Z\times i\times t$
m = Mass of substance
i = Amount of current
t = Time in seconds
Z = electrochemical equivalent or E.C.E

Complete Step by Step Answer:
According to Faraday’s first law of electrolysis, the mass of any substance ( $m$) liberated at an electrode is directly proportional to the amount of current ($i$) passed in a given time$(t)$ .
i.e, $m$$\alpha$$i\times t$
or, $m=Z\times i\times t$
or, $Z=\dfrac{m}{i\times t}$
Here $Z$ is constant and this is also called electrochemical equivalent or E.C.E

When unit ampere current is passed at the unit time the mass of the substance is equal to the electrochemical equivalent.
i.e, $i=1amp$,$t=1\sec$then $m=Z$
The electrochemical equivalent is defined by the amount of mass liberated at a unit time by passing a unit current through the electrochemical cell. A voltmeter is a device for measuring the quantity of current passing through an electrolytic solution.

Now putting the given data in the formula we can calculate E.C.E or electrochemical equivalent.
Here $m=4.572$gms, $i=5$amps, $t=45$min$=(45\times 60)$ sec
$Z=\dfrac{4.572}{5\times 45\times 60}$
Or, $Z=3.386\times {{10}^{-4}}$ C/gm
Therefore, E.C.E of zinc is $3.386\times {{10}^{-4}}$C/gm
Thus, option (A) is correct.

Note: We need to supply energy from outside for driving the electrolysis process. Otherwise the whole process is nonspontaneous. To approach this question we should remember the formula of Faraday’s law of electrolysis and also time has to be taken in seconds, not in minutes.