Question

In the process of electroplating, $'m'g$ of silver is deposited when $4ampere$ of current flows for 2 minutes. The amount (in $g$ ) of silver deposited by $6ampere$of current flowing for 40 seconds will be:
A. $4m$
B. $\dfrac{m}{2}$
C. $\dfrac{{4m}}{3}$
D. $3m$

Answer 1

Hint:
Electroplating is a general name for processes that create a metal coating on a solid substrate through the reduction of cations of that metal by means of a direct electric current. The part to be coated acts as the cathode (negative electrode) of an electrolytic cell; the electrolyte is a solution of a salt of the metal to be coated; and the anode (positive electrode) is usually either a block of that metal, or of some inert conductive material.

Complete step by step answer:
Faraday's law states that the extent of chemical reaction (i.e., mass of electroplating metal, m) caused by the flow of current is proportional to the amount of electric charge (Q, in Coulombs) passed through the electrochemical cell. Mathematically, this can be written as:
$m \propto Q$ …. (i)
Where, $m = $ mass of the substance deposited
$Q = I \times t$ …. (ii)
Where, $Q = $ Charge transferred through the electrochemical cell which is equal to the product of the electric current and the time duration for which the current is passed in the electrolytic solution.
Now, from equation (i), we have:
$\dfrac{{{m_1}}}{{{m_2}}} = \dfrac{{{Q_1}}}{{{Q_2}}} = \dfrac{{{I_1} \times {t_1}}}{{{I_2} \times {t_2}}}$ …. (iii)
As per the question, ${m_1} = m$
${m_2} = ?$= Mass of silver deposited by a current of $6ampere$ flowing for $40\sec $ .
${I_1} = 4A$
${I_2} = 6A$
${t_1} = 2\min = (2 \times 60)\sec $
${t_2} = 40\sec $
Substituting the values in the equation (iii), we have:
 \[ \Rightarrow \dfrac{m}{{{m_2}}} = \dfrac{{4 \times 2 \times 60}}{{6 \times 40}}\]
Thus, on solving the above equation, we have:
${m_2} = \dfrac{m}{2}$
Thus, the correct option is B. $\dfrac{m}{2}$ .

So, the correct answer is “Option B”.

Note:
Electroplating is widely used in industry and decorative arts to improve the surface qualities of objects such as resistance to abrasion and corrosion, lubricity, reflectivity, electrical conductivity, or appearance. It may also be used to build up thickness on undersized or worn-out parts, or to manufacture metal plates with complex shape, a process called electroforming.