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If for a certain reaction $\Delta_rH$ is 30 kJ mol$^{-1}$ at 450 K, the value of $\Delta_rS$ (in $JK^{-1}mol^{-1}$) for which the same reaction will be spontaneous at the same temperature is
A
$-70$
B
70
C
$-33$
D
33
Detailed Solution
For spontaneity, $\Delta G=\Delta H-T\Delta S\dfrac{\Delta H}{T}=\dfrac{30000}{450}\approx66.7\ JK^{-1}mol^{-1}$. Among the given options, the value that satisfies this (making the reaction spontaneous) is $\Delta S=70\ JK^{-1}mol^{-1}$.