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Resistance of a conductivity cell (cell constant 129 m–1) filled with 74.5 ppm solution of KCl is 100  Ω (labeled as solution 1). When the same cell is filled with KCl solution of 149 ppm, the resistance is 50  Ω (labeled as solution 2). The ratio of molar conductivity of solution 1 and solution 2 is i.e.  ∧1∧2  =  x × 10−3. The value of x is______. (Nearest integer)Given, molar mass of KCl is 74.5 g mol–1.

Question

Resistance of a conductivity cell (cell constant 129 m–1) filled with 74.5 ppm solution of KCl is 100  Ω (labeled as solution 1). When the same cell is filled with KCl solution of 149 ppm, the resistance is 50  Ω (labeled as solution 2). The ratio of molar conductivity of solution 1 and solution 2 is i.e.  ∧1∧2  =  x × 10−3. The value of x is______. (Nearest integer)Given, molar mass of KCl is 74.5 g mol–1.

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Solution

The molar conductivity (Λ) is given by the equation Λ = K/R, where K is the cell constant and R is the resistance.

For solution 1, we have: Λ1 = K/R1 = 129 m^-1 / 100 Ω = 1.29 m^-1 Ω^-1

For solution 2, we have: Λ2 = K/R2 = 129 m^-1 / 50 Ω = 2.58 m^-1 Ω^-1

The ratio of molar conductivity of solution 1 to solution 2 is therefore: Λ1/Λ2 = 1.29 m^-1 Ω^-1 / 2.58 m^-1 Ω^-1 = 0.5

So, the value of x is 0.5 × 10^3 = 500.

Therefore, the nearest integer value of x is 500.

This problem has been solved

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