Verified Solution • 2025–26 Session moderate

QJEEM21Ch3484: JEE Main 2021 Chemistry - Class 12 JEEM21Ch3484 Solution: The conductivity of a weak acid HA of concentration 0.001 mol L …

The conductivity of a weak acid HA of concentration 0.001 mol L −- 1 is 2.0 ×\times 10 −- 5 S cm −- 1. If Λmo\Lambda _m^o (HA) = 190 S cm2 mol −- 1, the ionization constant (Ka) of HA is equal to ______________ ×\times 10 −- 6. (Round off to the Nearest Integer)

Step-by-Step Verified Solution

Λm=1000×κM\Lambda _m^{} = 1000 \times {\kappa \over M}

=1000×2×10−50.001=20= 1000 \times {{2 \times {{10}^{ - 5}}} \over {0.001}} = 20 S cm2 mol −- 1

⇒α=ΛmΛm∞=20190=(219)\Rightarrow \alpha = {{\Lambda _m^{}} \over {\Lambda _m^\infty }} = {{20} \over {190}} = \left( {{2 \over {19}}} \right)

HA ⇌\rightleftharpoons H+ + A −-

0.001(1−α)0.001α0.001α0.001(1 - \alpha )0.001\alpha 0.001\alpha

⇒ka=0.001(α21−α)=0.001×(219)21−(219)\Rightarrow {k_a} = 0.001\left( {{{{\alpha ^2}} \over {1 - \alpha }}} \right) = {{0.001 \times {{\left( {{2 \over {19}}} \right)}^2}} \over {1 - \left( {{2 \over {19}}} \right)}}

=12.3×10−6= 12.3 \times {10^{ - 6}}

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