The molar conductivity of 0.00241 M acetic acid is $32.87 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$. If the...

To find the dissociation constant $ K_a $ for acetic acid, we start with the relation for molar conductivity:$ \alpha = \frac{\Lambda_m}{\Lambda_m^{\circ}} $For a weak electrolyte like acetic acid, the dissociation constant can be derived from the expression:$ K_a = \frac{c \alpha^2}{1-\alpha} $Substituting the molar conductivity terms into this expression:$ K_a = \frac{c \Lambda_m^2}{\Lambda_m^{\circ} \left(\Lambda_m^{\circ} - \Lambda_m\right)} $Given:$ c = 2.41 \times 10^{-3} \, \text{M} $$ \Lambda_m = 32.87 \, \text{Scm}^2 \, \text{mol}^{-1} $$ \Lambda_m^{\circ} = 390.5 \, \text{Scm}^2 \, \text{mol}^{-1} $Substituting these values into the equation gives:$ K_a = \frac{2.41 \times 10^{-3} \times (32.87)^2}{390.5 \times (390.5 - 32.87)} $Upon calculation, this results in:$ K_a = 1.86 \times 10^{-5} \, \text{mol} \, \text{L}^{-1} $

Ionic Equilibrium - IAT-IISER Chemistry PYQs

To find the dissociation constant

K_a

for acetic acid, we start with the relation for molar conductivity:

%5Calpha%20%3D%20%5Cfrac%7B%5CLambda_m%7D%7B%5CLambda_m%5E%7B%5Ccirc%7D%7D

For a weak electrolyte like acetic acid, the dissociation constant can be derived from the expression:

K_a%20%3D%20%5Cfrac%7Bc%20%5Calpha%5E2%7D%7B1-%5Calpha%7D

Substituting the molar conductivity terms into this expression:

K_a%20%3D%20%5Cfrac%7Bc%20%5CLambda_m%5E2%7D%7B%5CLambda_m%5E%7B%5Ccirc%7D%20%5Cleft(%5CLambda_m%5E%7B%5Ccirc%7D%20-%20%5CLambda_m%5Cright)%7D

Given:

c%20%3D%202.41%20%5Ctimes%2010%5E%7B-3%7D%20%5C%2C%20%5Ctext%7BM%7D

%5CLambda_m%20%3D%2032.87%20%5C%2C%20%5Ctext%7BScm%7D%5E2%20%5C%2C%20%5Ctext%7Bmol%7D%5E%7B-1%7D

%5CLambda_m%5E%7B%5Ccirc%7D%20%3D%20390.5%20%5C%2C%20%5Ctext%7BScm%7D%5E2%20%5C%2C%20%5Ctext%7Bmol%7D%5E%7B-1%7D

Substituting these values into the equation gives:

K_a%20%3D%20%5Cfrac%7B2.41%20%5Ctimes%2010%5E%7B-3%7D%20%5Ctimes%20(32.87)%5E2%7D%7B390.5%20%5Ctimes%20(390.5%20-%2032.87)%7D

Upon calculation, this results in:

K_a%20%3D%201.86%20%5Ctimes%2010%5E%7B-5%7D%20%5C%2C%20%5Ctext%7Bmol%7D%20%5C%2C%20%5Ctext%7BL%7D%5E%7B-1%7D

Ionic Equilibrium

High-Yield Trend

Questions
1 MCQs

Official Solution

Ionic Equilibrium

High-Yield Trend

Questions 1 MCQs

Official Solution

Questions
1 MCQs