Question 2.10 The conductivity of sodium chloride at 298 K has been determined at different concentrations and the results are given below:

Calculate Λ m for all concentrations and draw a plot between Λ m and c 1 / 2 . Find the value of Λ m 0 .
Answer:
Given,
κ = 1.237 × 10 − 2 S m − 1 , c = 0.001 M
Then, κ = 1.237 × 10 − 4 S cm − 1 , c 1 / 2 = 0.0316 M 1 / 2
∴ Λ m = k c = 1.237 × 10 − 4 Scm − 1 0.001 molL − 1 × 1000 cm 3 L = 123.7 S cm 2 mol − 1
Given,
κ = 11.85 × 10 − 2 S m − 1 , c = 0.010 M
Then, κ = 11.85 × 10 − 4 S cm − 1 , c 1 / 2 = 0.1 M 1 / 2
∴ Λ m = k c = 11.85 × 10 − 4 Scm − 1 0.010 mol L − 1 × 1000 cm 3 L = 118.5 S cm 2 mol − 1
Given,
κ = 23.15 × 10 − 2 S m − 1 , c = 0.020 M
Then, κ = 23.15 × 10 − 4 S cm − 1 , c 1 / 2 = 0.1414 M 1 / 2
∴ Λ m − k c = 23.15 × 10 − 4 Scm − 1 0.020 mol L − 1 × 1000 cm 3 L = 115.8 S cm 2 mol − 1
Given,
κ = 55.53 × 10 − 2 S m − 1 , c = 0.050 M Then, κ = 55.53 × 10 − 4 S cm − 1 , c 1 / 2 = 0.2236 M 1 / 2 ∴ k = k c = 55.53 × 10 − 4 Scm − 1 0.050 mol L − 1 × 1000 cm 3 L = 111.11 S cm 2 mol − 1
Given,
κ = 106.74 × 10 − 2 S m − 1 , c = 0.100 M
Then, κ = 106.74 × 10 − 4 S cm − 1 , c 1 / 2 = 0.3162 M 1 / 2
∴ Λ m = k c = 106.74 × 10 − 4 S cm − 1 0.100 mol L − 1 × 1000 cm 3 L = 106.74 S cm 2 mol − 1
Now, we have the following data:
c 1 / 2 / m 1 / 2 | 0.0316 | 0.1 | 0.1414 | 0.2236 | 0.3162 |
Λ m ( Scm 2 mol − 1 ) | 123.7 | 118.5 | 115.8 | 111.1 | 106.74 |

Since the line interrupts Λ m at 124.0 S cm 2 mol − 1 , Λ ∘ m = 124.0 S cm 2 mol − 1 .
Question 2.11 Conductivity of 0.00241 M acetic acid is 7.896×10−5Scm−1 . Calculate its molar conductivity. If Δm0 for acetic acid is 390.5Scm2mol−1 , what is its dissociation constant?
Answer:
Molar conductivity of a solution is given by :-
Λ M = κ C
So, = 7.896 × 10 − 5 0.00241 × 1000
or = 32.76 S c m 2 m o l − 1
Also, it is given that Λ m ∘ = 390.5 S c m 2 m o l − 1 .
α = Λ m Λ m ∘
or α = 32.76 390.5
α = 0.084
For dissociation constant we have,
K d = c α 2 ( 1 − α )
so, = 0.00241 × 0.084 2 ( 1 − 0.084 )
or = 1.86 × 10 − 5 m o l L − 1