Question

1. Define molar conductivity of a substance and describe how for weak and strong electrolytes, molar conductivity changes with concentration of solute. How is such change explained?
2. A voltaic cell is set up at 25°C with the following half cells:
   Ag+ (0.001 M) | Ag and Cu2+ (0.10 M) | Cu

What would be the voltage of this cell? (Eo cell = 0.46 V)

Answer 1

(a.) Molar conductivity is the conductivity of a solution, which contains a given number of moles of solute in 1L. The symbol for molar conductivity is lambda and the SI unit is Sm²mol⁻¹. It behaves differently for both weak and strong electrolytes.

Strong : Molar conductivity increases linearly with the square root of the concentration. But eventually reaches a limiting value ( limiting molar conductivity) at very high concentration.

Weak : Molar conductivity increases but it is less significant as compared to strong electrolyte. At lower concentration the increase in conductivity is linear and significant.

(b.) Ecell = E°cell - $\frac{0.059}{n}$ log $\frac{[Cu 2^{+}]}{[Ag^{+}]^{2}}$

According to the question, Ecell = 0.46V, n=2, [Cu2+] = 0.1M, [Ag+] = 0.001M

Substituting the values,

$E_{cell}=0.46 - \frac{0.0591}{2} \text{ } log \frac{0.1}{(10^{-3})^{2}}$
$E_{cell}=0.46 - \frac{0.0591}{2} \text{ } log 10^{5}$
$E_{cell}=0.46 - \frac{0.0591}{2} \times 5log 10$
$E_{cell}=0.46 - 0.14775$
$E_{cell}=0.312V$