JEE MAIN - Chemistry (2021 - 26th February Morning Shift - No. 16)
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)
($${\Delta _r}{H^\Theta }$$ = 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)
Answer
200
Explanation
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.
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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