Question

The atomic mass number of zinc is 66 and its valency is 2, the mass of zinc liberated by 9.65 A of current in 10 sec will be
A. $33\mu g$
B. $30mg$
C. $33g$
D. $33kg$

Answer 1

Hint- For solving this problem; Faraday's first law of electrolysis will be used which says that the mass of the substance (m) deposited or liberated at any electrode is directly proportional to the quantity of electricity or charge (Q) passed.

Complete step-by-step answer:
The mathematical form;
This law can be represented as follows:
$m \propto Q$
Removing the proportionality sign gives
m = ZQ, where m is the mass in grams (g),
Q is measured in Coulombs (C),
And Z is the proportionality constant in \[g/C\] (in grams per coulomb) and is also known as the electrochemical equivalent, which is the mass of a substance produced at the electrode during electrolysis by one Coulomb of charge.
Given
The atomic mass number of zinc is Z=66.
The valency of Zinc is V = 2.
The current is I = 9.65A.
Time t=10 s
The current is rate of flow of charge, hence if Q is the charge flowing in circuit then
$I = \dfrac{Q}{t}$
\[
  Q = It \\
   = 9.65 \times 10 \\
   = 96.5C \\
 \]
Now, the mass of zinc liberated by 96500 charge (i.e. 1F charge) is
$\dfrac{Z}{V} = \dfrac{{66}}{2}$​
 =33g
Hence, the mass of zinc liberated by charge q is
$
  m = \dfrac{{33 \times 96.5}}{{96500}} \\
  m = 33mg \\
 $
Hence, the correct option is B.

Note- During electrolysis, there are substances that are produced at the anode and at the cathode. This lesson, with the help of Faraday's laws of electrolysis, will guide you towards calculating amounts of substances formed during electrolysis. And it states that when the same quantity of electricity is passed through more than one electrolyte, the mass of the substances deposited are proportional to their respective equivalent weight.