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Question: For a given reaction, \[\Delta H = {\text{ }}35.5kJmo{l^{ - 1}}\] and\[\;\Delta S{\text{ }} = 83.6kJ...

For a given reaction, ΔH= 35.5kJmol−1\Delta H = {\text{ }}35.5kJmo{l^{ - 1}} and  ΔS =83.6kJmol−1\;\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

Explanation

Solution

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 ΔG\Delta G and the factors that contribute to this energy are enthalpy and entropy. When a substance changes at constant pressure, enthalpy, ΔH\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 ΔH\Delta H and ΔS\Delta S changes while a reaction occurs, the free energy changes and is known as Gibbs free energy change, ΔG\Delta G and is given as ΔG=ΔH−TΔS\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 ΔG\Delta G must be negative.
We know that,
ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S
For the reaction to be spontaneous, ΔG\Delta G must be negative,i.e
ΔG<0\Delta G < 0
Or,
ΔH−ΔT<0\Delta H - \Delta T < 0
⇒T>ΔHΔS\Rightarrow T > \dfrac{{\Delta H}}{{\Delta S}}
Given that
ΔH=35.5KJ/mol\Delta H = 35.5KJ/mol
=35500J/mol= 35500J/mol
ΔS =83.6kJmol−1\Delta S{\text{ }} = 83.6kJmo{l^{ - 1}}
Now we can substitute the known values in the formula we get,
T>3550083.6=424.6411≃425T > \dfrac{{35500}}{{83.6}} = 424.6411 \simeq 425
On simplification we get,
T>425KT > 425K
Hence,the correct option is option (A).

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