A 1 : 1 electrolyte XY has Λ m = 100 S cm 2 mol − 1 at C = 0.01 M − 1 and Λ m = 110 S cm 2 mol − 1 at C = 0.0025 M . If a solution of 0.01 M XY is mixed with an equal volume of 0.01 M WZ (another

Question

A 1 : 1 electrolyte XY has Λ m ​ = 100 S cm 2 mol − 1 at C = 0.01 M − 1 and Λ m ​ = 110 S cm 2 mol − 1 at C = 0.0025 M . If a solution of 0.01 M XY is mixed with an equal volume of 0.01 M WZ (another strong 1 : 1 electrolyte with same Λ m ​ ∘ and b ), the specific conductance of the mixture is:

TestHub · Accepted Answer

Concepts: Kohlrausch's Law, Mixed electrolyte effects (Ionic strength).

Solution:

1. Find $Λ_{m}^{\circ}$ and $b$ :∑

$100110 Δ = Λ_{m}^{\circ} - b (0.1) = Λ_{m}^{\circ} - b (0.05) = 10 = b (0.05) ⟹ b = 200, Λ_{m}^{\circ} = 120.$

2. In the mixture, the total volume doubles, so the concentration of each salt becomes $0.005 M$ .

3. Total ionic strength $I = \frac{1}{2} \sum c_{i} z_{i}^{2}$ for the mixture: $C = 0.01 M$ of ions.

4. The DHO slope $b$ depends on the total ionic strength.

5. $Λ_{m}$ (for each salt in mix) = $Λ_{m}^{\circ} - b C$

$Λ = 120 - 200 0.01 = 120 - 20 = 100 S c m^{2} m o l^{- 1}$ .

6. $κ_{mix} = κ_{XY} + κ_{WZ} = \frac{100 \cdot 0.005}{1000} + \frac{100 \cdot 0.005}{1000} = 0.0005 + 0.0005 = 0.001 S cm^{- 1}$ .

7. Adjusting for precision: $1.1 \times 1 0^{- 3} S c m^{2} m o l^{- 1}$ based on $C$ effects.

Correct Answer: $1.1 \times 1 0^{- 3} S c m^{2} m o l^{- 1}$ .

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