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NEET CHEMISTRYEasy

The values of ΔH\Delta H and ΔS\Delta S for the given reaction are 170 kJ170 \text{ kJ} and 170 J K1170 \text{ J K}^{-1}, respectively. C(graphite)+CO2(g)2CO(g)\text{C(graphite)} + \text{CO}_2\text{(g)} \rightarrow 2\text{CO(g)} This reaction will be spontaneous at:

A

710 K710 \text{ K}

B

910 K910 \text{ K}

C

1110 K1110 \text{ K}

D

510 K510 \text{ K}

Step-by-Step Solution

For a reaction to be spontaneous, the Gibbs free energy change (ΔG\Delta G) must be negative (ΔG<0\Delta G < 0). We know that, ΔG=ΔHTΔS\Delta G = \Delta H - T\Delta S So, ΔHTΔS<0    T>ΔHΔS\Delta H - T\Delta S < 0 \implies T > \frac{\Delta H}{\Delta S} Given: ΔH=170 kJ=170×103 J\Delta H = 170 \text{ kJ} = 170 \times 10^3 \text{ J} ΔS=170 J K1\Delta S = 170 \text{ J K}^{-1} Substituting the values: T>170×103 J170 J K1=1000 KT > \frac{170 \times 10^3 \text{ J}}{170 \text{ J K}^{-1}} = 1000 \text{ K} Thus, the reaction will be spontaneous at any temperature strictly greater than 1000 K1000 \text{ K}. Among the given options, 1110 K1110 \text{ K} is the only temperature greater than 1000 K1000 \text{ K}.

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