As shown in the figure, a current is passed through an electrolyte of $\text{AgCl}$ . It is observed that $2.68 \text{ g}$ of silver is deposited on the cathode in $10$ minutes. Determine the heat developed in the $20 \text{ }\Omega$ resistor during this period. The atomic weight of silver is $107.9 \text{ g mol}^{-1}$ .

Question

As shown in the figure, a current is passed through an electrolyte of

\text{AgCl}

. It is observed that

2.68 \text{ g}

of silver is deposited on the cathode in

10

minutes. Determine the heat developed in the

20 \text{ }\Omega

resistor during this period. The atomic weight of silver is

107.9 \text{ g mol}^{-1}

.

Quantrex Academy · Accepted Answer

Correct answer: D. 1.9 × 10^5 J

According to Faraday's first law of electrolysis, the mass of the substance deposited is given by:

m = ZIt = \dfrac{M}{nF}It

Substituting the given values (

m = 2.68 \text{ g}

,

M = 107.9 \text{ g mol}^{-1}

,

n = 1

,

F = 96500 \text{ C mol}^{-1}

,

t = 600 \text{ s}

):

2.68 = \dfrac{107.9}{1 \times 96500} \times I \times 600

I = \dfrac{2.68 \times 96500}{107.9 \times 600} \approx 4 \text{ A}

The heat developed in the resistor is given by Joule's law of heating:

H = I^2Rt

Using

R = 20 \text{ }\Omega

and

t = 600 \text{ s}

:

H = (4)^2 \times 20 \times 600

H = 16 \times 12000 = 192000 \text{ J}

H = 1.92 \times 10^5 \text{ J} \approx 1.9 \times 10^5 \text{ J}

As shown in the figure, a current is passed through an electrolyte...