For a reaction A2(g)+2B2(g)⟶2AB2, ΔrH∘=−100kJmol−1 and ΔrS∘=−250.0JK−1mol−1. The reaction will be spontaneous

Since ΔrG∘=ΔrH∘−TΔrS 0 or −ΔrH∘>−TΔΓS∘ or T<−ΔrH∘/−ΔrS∘=100×103Jmol−1/250JK−1mol−1=400 K.

For a reaction A2(g)+2B2(g)⟶2AB2, ΔrH∘=−100kJmol−1 and ΔrS∘=−250.0JK−1mol−1. The reaction will be spontaneous

Since ΔrG∘=ΔrH∘−TΔrS 0 or −ΔrH∘>−TΔΓS∘ or T<−ΔrH∘/−ΔrS∘=100×103Jmol−1/250JK−1mol−1=400 K.

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For a reaction $A_{2} (g) + 2 B_{2} (g) ⟶ 2 {AB}_{2}, Δ_{r} H^{\circ} = - 100 kJ {mol}^{- 1} and Δ_{r} S^{\circ} = - 250.0 {JK}^{- 1} {mol}^{- 1}$ . The reaction will be spontaneous

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provided $T > 500 K$

provided $T = 400 K$

provided $T < 400 K$

provided $T > 400 K$

answer is C.

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Detailed Solution

Since $Δ_{r} G^{\circ} = Δ_{r} H^{\circ} - T Δ_{r} S < 0$ ,we have $(- Δ_{r} H^{\circ}) - (- T Δ_{r} S^{\circ}) > 0$ or $(- Δ_{r} H^{\circ}) > (- T Δ_{Γ} S^{\circ})$ or $T < (- Δ_{r} H^{\circ}) / (- Δ_{r} S^{\circ}) = (100 \times 10^{3} J {mol}^{- 1}) / (250 {JK}^{- 1} {mol}^{- 1}) = 400 K$ .