JEE Main 2026 — Jan 21, Shift 1 — Chemistry solution

JEE Main2026Jan 21, Shift 1Chemistry

The pH and conductance of a weak acid (HX) was found to be 5 and $4 \times 1 0^{- 5}$ S, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of 1 cm $^{2}$ were at a distance of 15 cm apart. The value of the limiting molar conductivity is ________ S m $^{2}$ mol $^{- 1}$ . (nearest integer) (Given: degree of dissociation of the weak acid $α ≪ 1$ )

Your answer

Solution

$[H^{+}] = 1 0^{- 5} = [H X] \cdot α = [H X] \cdot Λ_{m} / Λ_{m}^{\infty}$ .

Cell constant $G^{*} = l / A = 15/1 = 15$ cm $^{- 1}$ ; conductivity $κ = G \cdot G^{*} = 4 \times 1 0^{- 5} \times 15 = 6 \times 1 0^{- 4}$ S cm $^{- 1}$ .

$Λ_{m} = κ \times 1000/ [H X]$ and combining: $[H^{+}] = 1 0^{- 5} = [H X] \cdot 6 \times 1 0^{- 4} \times 1000/ (Λ_{m}^{\infty} \cdot [H X])$ .

$Λ_{m}^{\infty} = 60000$ S cm $^{2}$ mol $^{- 1} = 6$ S m $^{2}$ mol $^{- 1}$ .

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