For the equilibrium $2 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{OH}^{-}$, the value of $\Delta \mathrm{G}^{0}$ at 298 K is approximately:

(C) $80 \mathrm{~kJ} \mathrm{~mol}^{-1}$

(A) $100 \mathrm{~kJ} \mathrm{~mol}^{-1}$

(B) $-80 \mathrm{~kJ} \mathrm{~mol}^{-1}$

(D) $-100 \mathrm{~kJ} \mathrm{~mol}^{-1}$

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Chemical Thermodynamics

For the equilibrium

2 H_{2} O ⇌ H_{3} O^{+} + OH^{-}

, the value of

Δ G^{0}

at 298 K is approximately:

Answer: (C)

For the autoionisation of water

K_{w} = 1 0^{- 14}

298

K. Using

Δ G^{\circ} = - 2.303 R T lo g K

Δ G^{\circ} = - 2.303 \times 8.314 \times 298 \times lo g (1 0^{- 14}) = - 2.303 \times 8.314 \times 298 \times (- 14) \approx 79900

J/mol, about

80

kJ/mol. The positive value shows the autoionisation is non-spontaneous under standard conditions.

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option