Question

the time required to liberate one gram equivalent of an element by passing one ampere current through its solution

A. 6.7 hrs
B. 13.4 hrs
C. 19.9 hrs
D. 26.8 hrs

Answer 1

Answer: D. 26.8 hrs

Explanation:

1 electron carry charge=$1.6\times 10^{-19}C$

1 mole of electrons contain=$6.023\times 10^{23}$ electrons

Thus  1 mole of electrons carry charge=$\frac{1.6\times 10^{-19}}{1}\times 6.023\times 10^{23}=96500C=1 Faraday$

$A^{n+}+ne^-\rightarrow A$

If n electrons are involved in the reaction, the passage of n Faradays i.e $(n\times 96500C)$ of electricity will liberate 1 mole or molecular mass of the substance.

1 Faraday or 96500 C of electricity will liberate=$\frac{\text {Molecular mass}}{n}$=Equivalent mass of the substance.

$Q=I\times t$

where Q= quantity of electricity in coloumbs

I = current in amperes = 1A

t= time in seconds = ?

$96500C=1A\times t$

$t=96500sec=26.8hrs$     (1hour=3600sec)

Thus the time required to liberate one gram equivalent of an element by passing one ampere current through its solution is 26.8 hours.