Consider the following reaction : 2 A (g) + B (g) → 2 D (g) Δ U ⊖ = − 10 kJ mol − 1 and Δ S ⊖ = − 44 J K − 1 at 298 K. Identify the correct option with Δ G ⊖ for the reaction and spontaneity of the re

Question

Consider the following reaction : 2 A (g) + B (g) → 2 D (g) Δ U ⊖ = − 10 kJ mol − 1 and Δ S ⊖ = − 44 J K − 1 at 298 K. Identify the correct option with Δ G ⊖ for the reaction and spontaneity of the reaction at 298 K. (Given : R = 8.31 J mol − 1 K − 1 )NEET 2026 (Cancelled)

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The change in the number of moles of gaseous species is:

$Δ n_{g} = n_{p} - n_{r} = 2 - (2 + 1) = - 1$

The standard enthalpy change $Δ H^{⊖}$ is given by:

$Δ H^{⊖} = Δ U^{⊖} + Δ n_{g} RT$

Substituting the given values:

$Δ H^{⊖} = - 10 + (- 1) \times (8.31 \times 1 0^{- 3}) \times 298$

$Δ H^{⊖} = - 10 - 2.47638 = - 12.47638 kJ mol^{- 1}$

The standard Gibbs free energy change $Δ G^{⊖}$ is:

$Δ G^{⊖} = Δ H^{⊖} - T Δ S^{⊖}$

$Δ G^{⊖} = - 12.47638 - 298 \times (- 44 \times 1 0^{- 3})$

$Δ G^{⊖} = - 12.47638 + 13.112 = + 0.63562 kJ mol^{- 1}$

Since $Δ G^{⊖} > 0$ , the reaction is non-spontaneous.

Answer: $+ 0.63568$ kJ mol $^{- 1}$ , non-spontaneous

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