In conversion of lime-stone to lime- CaCO3s- CaOs - CO2g- the values of -0H and - S0 are -179-1 kJ mol-1 and 160-2 J-Kmol respectively at 298 K and 1 bar- Assuming that - Ho and - So do not change with temperature- temperature above which conversion of limestone to lime will be spontaneous is-

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Standard XII

Chemistry

Second Law of Thermodynamics

In conversion...

Question

In conversion of lime-stone to lime, $C a C O_{3} (s) \to C a O (s) + C O_{2} (g)$ , the values of $Δ^{0} H$ and $Δ S^{0}$ are $+ 179.1 k J m o l^{- 1}$ and $160.2 J / K m o l$ respectively at $298 K$ and $1$ bar. Assuming that $Δ H^{o}$ and $Δ S^{o}$ do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is:

1008 K

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1200 K

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845 K

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1118 K

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Solution

The correct option is D $1118 K$
Gibbs free energy, G is the measure of the spontaneity of a chemical process. The negative G indicates that a reaction is spontaneous under the given conditions.

We know, $Δ G = Δ H - T Δ S$ , if $G < 0$ then, $Δ H < T Δ S$ .

Therefore, $T = \frac{Δ H}{Δ S} = \frac{(179.1 \times 1000)}{160.2} = 1118 K$

Thus, above 1118K, $Δ G$ will be negative and the reaction will be spontaneous.

Hence, the correct option is $D$

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