Question

$wg$ of copper is deposited in a copper voltameter when an electric current of $2$ ampere is passed for $2$ hours. If one ampere of electric current is passed for $4$ hours in the same voltameter, copper deposited will be:

• A. $w$
• B. $w/2$
• C. $w/4$
• D. $2w$

Answer 1

The correct option is A $w$

Given Data: 1) $I_1$ = $2$ $amp$

2) $t_1$ = $2$ $hrs$ = $2\times 3600$ =$7200$ $secs$

3) $I_2$= $1$ $amp$

4) $t_2$ = $4$ $hrs$ = $4\times 3600$ =$14400$ $secs$

Now let us write the cathode reaction for the following,

$Cu$${}^2$${}^{+}$ + $2e$${}^{-}$ $\to$ $Cu$

For $I_1$ = $2$ $amp$ and $t_1$ = $7200$ $secs$ we have,

$Q_1$ = $I_1{t}_1$ = $2\times 7200$ $C$ = $14400$ $C$

$14400$ $C$ will deposit = $\frac{63.5\times 2\times 7200}{2\times 96500}$

= $1.00513$ $g$

= $W$ $g$ of $Cu$ .........................(suppose)

Now,

For $I_2$ = $1$ $amp$ and $t_2$ =$14400$$secs$ we have,

$Q_2$ = $1$ $\times 14400$ = $14400$ $C$

$14400$ $C$ will deposit = $\frac{63.5\times 14400}{2\times 96500}$

=$1.00153$ $g$

= $W$ $g$

Hence the correct option is 'A'.