Question

If a steady current of 4 amp maintained for 40 minutes, deposits 4.5 gm of zinc at the cathode and then the electro-chemical equivalent will be
A. \[51 \times {10^{ - 17}}gm/C\]
B. \[28 \times {10^{ - 6}}gm/C\]
C. \[32 \times {10^{ - 5}}gm/C\]
D. \[47 \times {10^{ - 5}}gm/C\]

Answer 1

Hint: We use Faraday’s first law of electrolysis which gives the relation between the mass of ion liberated during electrolysis, electric current, and the time.

Formula Used:\[m = Zit\], where m is the mass of ion liberated from an electrolyte when current I is passed through it for the time period of t and Z is the electro-chemical equivalent of the substance.

Complete answer:According to Faraday’s first law of electrolysis the mass (m) of ions liberated from an electrolyte is directly proportional to the amount of the current (i) passed through the electrolyte during the process of electrolysis and the time (t) for which the current is flowing through the electrolyte.
Mathematically, \[m \propto it\]
\[m = Zit\]where the Z is the proportionality constant and it is a characteristic property of the substance of the electrolyte used in the process of electrolysis.
If a steady current of 4 amp is maintained for 40 minutes, deposits of 4.5 gm of zinc are at the cathode, and then the electro-chemical equivalent will be
For the given question, the amount of current passing through the electrolyte is 4A.
\[i = 4A\]
The time period in which the electric current is passing is given as 40 minutes.
On changing the time in the standard unit, we get
\[t = 40\min \]
\[t = 40 \times 60s\]
\[t = 2400s\]
The mass of zinc deposited is given as 4.5 gm.
\[m = 4.5gm\]
From faraday’s first law of electrolysis,
\[m = Zit\]
\[Z = \dfrac{m}{{it}}\]
\[Z = \dfrac{{4.5gm}}{{4 \times 2400C}}\]
\[Z = 4.7 \times {10^{ - 4}}gm/C\]
\[Z = 47 \times {10^{ - 5}}gm/C\]
Hence, the electrochemical equivalent is \[47 \times {10^{ - 5}}gm/C\]
Therefore,

the correct option is (D).

Note: We should be careful while using Faraday’s first law of electrolysis. We need to change the time to seconds. The unit of the product of the electric current and time in the standard unit will be the unit of charge.