"For a chemical reaction A + B ⇌ C + D(${\Delta _r}{H^\Theta }$ = 80 kJ mol$-$1) the entropy change ${\Delta _r}{S^\Theta }$ depends on the temperature T (in K) as ${\Delta _r}{S^\Theta }$ = 2T (J K$-$1mol$-$1).Minimum temperature at which it will become spontaneous is ___________ K. (Integer)"

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Accepted Answer

"We know, $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$

For a reaction to be spontaneous
$\Delta G^\circ < 0$

$\Rightarrow$ $\Delta H^\circ - T\Delta S^\circ < 0$

$\Rightarrow$ $T > {{\Delta H^\circ } \over {\Delta S^\circ }}$

$\Rightarrow$ $T > {{80000} \over {2T}}$

$\Rightarrow$ 2T² > 80000

$\Rightarrow$ T² > 40000

$\Rightarrow$ T > 200

The minimum temperature to make it spontaneous is 200 K."

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For a chemical reaction A + B ⇌ C + D(${\Delta _r}{H^\Theta }$ = 80 kJ mol$-$1) the entropy change ${\Delta _r}{S^\Theta }$ depends on the temperature T (in K) as ${\Delta _r}{S^\Theta }$ = 2T (J K$-$1mol$-$1).Minimum temperature at which it will become spontaneous is ___________ K. (Integer)

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