JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Chemical Thermodynamics

The incorrect expression among the following is:

Answer: (A)

Solution

From

Δ G^{\circ} = - R T ln K

and

Δ G^{\circ} = Δ H^{\circ} - T Δ S^{\circ}

, it follows that

- R T ln K = Δ H^{\circ} - T Δ S^{\circ}

, so

ln K = - \frac{Δ H ^{\circ} - T Δ S ^{\circ}}{R T}

, carrying a negative sign. For isothermal reversible expansion

w = - n R T ln (V_{f} / V_{i})

, and

K = e^{- Δ G^{\circ} / R T}

follows directly from

Δ G^{\circ} = - R T ln K

; at constant pressure

Δ G_{system} = - T Δ S_{total}

, giving

Δ G_{system} /Δ S_{total} = - T

. The expression

ln K = \frac{Δ H ^{\circ} - T Δ S ^{\circ}}{R T}

omits the negative sign and is incorrect.

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Single correct option