Resistance of 0.2 M solution of an electrolyte is 50 Ω. The speci...
To find the molar conductivity of the 0.5 M solution of the electrolyte, we can use the formula:
Molar conductivity = (Specific conductance × 1000) / Concentration
Given that the specific conductance of the solution is 1.4 S m^-1 and the concentration is 0.2 M, we can calculate the molar conductivity as follows:
Molar conductivity = (1.4 × 1000) / 0.2 = 7000 S m^2 mol^-1
Now, we need to find the resistance of the 0.5 M solution of the same electrolyte. Given that the resistance of the 0.2 M solution is 50 Ω, we can use the formula:
Resistance = (Specific resistivity × Length) / Area
Since the length and area of the cell are the same for both solutions, we can write:
Resistance of 0.2 M solution = (Specific resistivity × Length) / Area
Resistance of 0.5 M solution = (Specific resistivity × Length) / Area
Dividing these two equations, we get:
(Resistance of 0.2 M solution) / (Resistance of 0.5 M solution) = (Specific resistivity of 0.2 M solution) / (Specific resistivity of 0.5 M solution)
Given that the resistance of the 0.2 M solution is 50 Ω and the resistance of the 0.5 M solution is 280 Ω, we can substitute these values into the equation and solve for the specific resistivity ratio:
(50) / (280) = (Specific resistivity of 0.2 M solution) / (Specific resistivity of 0.5 M solution)
Specific resistivity of 0.5 M solution = (Specific resistivity of 0.2 M solution) × (280 / 50)
Now, we know that the specific conductance is the reciprocal of specific resistivity:
Specific resistivity = 1 / Specific conductance
Substituting this into the equation, we get:
Specific resistivity of 0.5 M solution = (1 / Specific conductance of 0.2 M solution) × (280 / 50)
Given that the specific conductance of the 0.2 M solution is 1.4 S m^-1, we can substitute this value into the equation and solve for the specific resistivity of the 0.5 M solution:
Specific resistivity of 0.5 M solution = (1 / 1.4) × (280 / 50) = 4
Now, we need to find the molar conductivity of the 0.5 M solution using the specific resistivity:
Molar conductivity = (1 / Specific resistivity) × 1000 = (1 / 4) × 1000 = 250 S m^2 mol^-1
Therefore, the correct answer is option A: 5 × 10^4 S m^2 mol^-1.