Question

For a given reaction, \[\Delta H = {\text{ }}35.5kJmo{l^{ - 1}}\] and\[\;\Delta S{\text{ }} = 83.6kJmo{l^{ - 1}}\] . The reaction is spontaneous at: (Assume that DH and DS do not vary with temperature)
T > 425 K
All temperatures
T > 298 K
T < 425 K

Answer 1

Hint: We need to know about the dependency of a spontaneity of a reaction and what do the terms DH and DS mean. A spontaneous reaction means that the reaction favours the formation of products under the conditions at which the reaction is occurring. Reactions which are spontaneous release the extra energy that is available to do work. In thermodynamic terms, this free energy is known as Gibbs Free Energy which determines the spontaneity of a reaction.

Complete step by step answer:
We have to know that the Gibbs Free Energy is represented as $\Delta G$ and the factors that contribute to this energy are enthalpy and entropy. When a substance changes at constant pressure, enthalpy, $\Delta H$ determines the amount of heat and work which was added or removed from the substance. On the other hand, S is the entropy which measures the randomness of the system. As $\Delta H$ and $\Delta S$ changes while a reaction occurs, the free energy changes and is known as Gibbs free energy change, $\Delta G$ and is given as \[\Delta G = \Delta H - T\Delta S\] , where T is the temperature at which the reaction occurs. A spontaneous reaction is one that releases free energy, and so the sign of $\Delta G$ must be negative.
We know that,
\[\Delta G = \Delta H - T\Delta S\]
For the reaction to be spontaneous, $\Delta G$ must be negative,i.e
$\Delta G < 0$
Or,
$\Delta H - \Delta T < 0$
\[ \Rightarrow T > \dfrac{{\Delta H}}{{\Delta S}}\]
Given that
\[\Delta H = 35.5KJ/mol\]
\[ = 35500J/mol\]
\[\Delta S{\text{ }} = 83.6kJmo{l^{ - 1}}\]
Now we can substitute the known values in the formula we get,
$T > \dfrac{{35500}}{{83.6}} = 424.6411 \simeq 425$
On simplification we get,
\[T > 425K\]
Hence,the correct option is option (A).

Note:
We must be noted that Since $\Delta H$ and $\Delta S$ can be either positive or negative, depending on the characteristics of the particular reaction.A negative value of $\Delta H$ indicates that the reaction is exothermic and a positive value of $\Delta H$ means the reaction is endothermic. A positive $\Delta S$ means the entropy is increasing and the system is becoming more disordered and a negative $\Delta S$ means that entropy is decreasing and the system is becoming more ordered.