Question

A solution of metal salt was electrolyzed for $15$ minutes, with a current of $1.5A$. The mass of a metal deposited was $0.00783kg$. Calculate the equivalent mass of metal.

Answer 1

One Faraday $(96,487C)$ is the quantity of electricity that is capable of depositing or liberating $1$ gram equivalent weight of a substance in electrolysis.
The quantity of electricity requires is given by :
Number of coulumbs passed,
$Q\left(C\right)=I\left(A\right)\times t\left(s\right)$
Current passed $\left(I\right)=15A$
Time $\left(t\right)=15$ min
$=15\times \frac{60s}{min}$
$Q=\frac{15\left(A\right)\times 15\left(min\right)\times 60\left(s\right)}{\left(min\right)}$
$=1350C$
Hence,
Moles of electrons actually passed $=\frac{Q\left(C\right)}{96500\left(C/mol\right)}=\frac{1350\left(C\right)}{96500\left(C/mol\right)}$
$=0.014{mol}^{-1}$
Let us assume that mole ratio of metal is $1molmetal/mol$
Moles of metal formed $=$ moles of electros actually passed $\times$ mole ratio
$=0.014{mol}^{-1}\times 1molmetal/mol$
$=0.014molmetal$
Mass of metal produced $=0.00783kg=0.00783\times {10}^{3}g$
$=7.83g$
Mass of metal produced $=$ Moles of metal formed $\times$ Molar mass of metal
$7.83g=0.014mol\times$ Molar mass of metal
Molar mass of metal $=\frac{7.83g}{0.014mol}$
$=559.2g/mol$
Thus, equivalent mass of metal is $559.2g/mol$.