Related Formula
W = Z · I · t = (M)/(n · F) · I · t$$W = Z \cdot I \cdot t = \frac{M}{n \cdot F} \cdot I \cdot t$$
where,
W$W$ = mass deposited
Z$Z$ = electrochemical equivalent
I$I$ = current in amperes
t$t$ = time in seconds
M$M$ = molar mass
n$n$ = n-factor (electrons exchanged)
F$F$ = Faraday's constant (96500 C/mol$96500 \text{ C/mol}$)
Core Logic
The electrolysis of zinc sulphate (ZnSO₄$ZnSO_4$) involves the reduction of zinc ions at the cathode:
Zn⁺² + 2e^- arrow Zn$$Zn^{+2} + 2e^- \rightarrow Zn$$
Here, the n-factor (n$n$) is 2.
Step 1: Calculation
Given values:
I = 0.015 A$I = 0.015\text{ A}$
t = 15 minutes = 15 × 60 seconds = 900 s$t = 15\text{ minutes} = 15 \times 60\text{ seconds} = 900\text{ s}$
M = 65.4 g/mol$M = 65.4\text{ g/mol}$
F ≈ 96500 C$F \approx 96500\text{ C}$
Plugging the values into Faraday's First Law:
W = (65.4)/(2 × 96500) × 0.015 × 15 × 60$$W = \frac{65.4}{2 \times 96500} \times 0.015 \times 15 \times 60$$
W = (65.4)/(193000) × 13.5$$W = \frac{65.4}{193000} \times 13.5$$
W = 3.3886 × 10⁻⁴ × 13.5$$W = 3.3886 \times 10^{-4} \times 13.5$$
W = 45.746 × 10⁻⁴ g$$W = 45.746 \times 10^{-4}\text{ g}$$
Rounding to two decimal places (or nearest integer depending on convention), we get 45.75 × 10⁻⁴ g$45.75 \times 10^{-4}\text{ g}$.
Chapter Mix
Class 12 Chemistry: Electrochemistry