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.) E_cell = 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, 

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