Resistance of a conductivity cell filled with a solution of an electro...
Solution:
Given, the resistance of a conductivity cell filled with a solution of an electrolyte of concentration 0.1 M is 100 ohm and the conductivity of this solution is 1.29 S m-1.
Resistance of the same cell filled with 0.02 M of the same solution if the electrolyte is 520 ohm.
The molar conductivity of 0.02 M solution of electrolyte would be:
We know that the resistance of a conductivity cell is given by the equation:
R = (1/k) x [(l/A)]
where, R = Resistance of the conductivity cell, k = Conductivity of the solution, l = Distance between the electrodes, and A = Area of cross-section of the electrodes.
Let's assume that the distance between the electrodes and the area of cross-section of the electrodes are constant in both cases.
So, we can write:
R1/R2 = k2/k1
where, R1 = Resistance of the conductivity cell filled with 0.1 M solution of electrolyte and R2 = Resistance of the same cell filled with 0.02 M solution of electrolyte.
Substituting the given values, we get:
100/520 = k2/1.29
k2 = (100/520) x 1.29
k2 = 0.24867 S m-1
Now, we can use the equation for molar conductivity:
Λm = k x (1/c)
where, Λm = Molar conductivity, k = Conductivity of the solution, and c = Concentration of the solution.
Substituting the values, we get:
Λm = 0.24867 x (1/0.02)
Λm = 12.4335 S m2 mol-1
Rounding off to two significant figures, we get:
Λm = 12.4 x 104 S m2 mol-1
Therefore, the correct option is A) 124 x 104 S m2 mol-1.