The pH and conductance of a weak acid (HX) was found to be 5 and $4 \times 10^{-5} \mathrm{~S}$, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of $1 \mathrm{~cm}^{2}$ were at a distance of 15 cm apart. The value of the limiting molar conductivity is _____ $\mathrm{S} \mathrm{m}^{2} \mathrm{~mol}^{-1}$. (nearest integer) (Given: degree of dissociation of the weak acid (α) << 1)

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Redox Reactions and Electrochemistry

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)

Answer: 6

The cell constant is

G^{*} = l / A = 15/1 = 15 c m^{- 1}

, so the conductivity is

κ = G \times G^{*} = 4 \times 1 0^{- 5} \times 15 = 6 \times 1 0^{- 4} S c m^{- 1}

. For a weak acid of concentration

c

[H^{+}] = c α

with

α = Λ_{m} / Λ_{m}^{\infty}

and

Λ_{m} = \frac{1000 κ}{c}

, so

[H^{+}] = c \cdot \frac{Λ _{m}}{Λ _{m}^{\infty}} = \frac{1000 κ}{Λ _{m}^{\infty}}

. Since

pH = 5

gives

[H^{+}] = 1 0^{- 5} M

Λ_{m}^{\infty} = \frac{1000 \times 6 \times 1 0 ^{- 4}}{1 0 ^{- 5}} = 6 \times 1 0^{4} S c m^{2} mo l^{- 1}

. Converting units,

6 \times 1 0^{4} S c m^{2} mo l^{- 1} = 6 S m^{2} mo l^{- 1}

. The limiting molar conductivity is

6 S m^{2} mo l^{- 1}

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Integer answer