Question

For an exothermic reaction to be spontaneous ($\Delta {{S}}$ = negative):
A. The temperature must be high
B. The temperature must be zero
C. The temperature may have any magnitude
D. The temperature must be low

Answer 1

A reaction is called spontaneous if it can continue the formation of products under the given conditions, without any external support from the surrounding. And in an exothermic reaction the enthalpy/or energy is released by the system, therefore the value of $ \Delta {{H = }} - {{ve}}.

Complete Step by step answer:
We can use the concept of Gibbs free energy o determine whether or not the reaction is spontaneous,
If the value of ${{\Delta G}}$ = -ve, then the reaction is spontaneous. And if the value of
${{\Delta G}}$ = +ve, then the reaction is not spontaneous or nonspontaneous.
As mentioned in the hint for an exothermic reaction the value of enthalpy is;
$\Delta {{H = }} - {{ve}}$
It is also given in the question that the value of $\Delta {{S}}$ is negative.
$\Rightarrow {{\Delta G}} = {{\Delta H}} - {{T}}\Delta {{S}}$
$\Rightarrow$ ${{\Delta G}}$ = ( $-$ ${{\Delta H}}$ ) $-$ T( $-$ $\Delta {{S}}$ )
$\Rightarrow$ ${{\Delta G}}$ = ( $-$ ${{\Delta H}}$ ) + T( $\Delta {{S}}$ )
If the temperature is high (assuming higher than the value of ${{\Delta H}}$ ) and if the value of ${{T}}$ it can be of any magnitude, that means it could also be –ve, which will result in the overall value of ${{\Delta G}}$ as +ve. Hence, we can conclude options (A) and (C) as wrong.
Therefore, for the overall value ${{\Delta G}}$ to be negative and the reaction to be spontaneous, we need the value ${{T}}$ to be, low or the temperature can also be zero.

Hence, the correct answers are options (B) and (D).

Note: For an endothermic reaction to be spontaneous, the temperature of the system must is very high, or the change in entropy (degree of randomness) should be high to counteract the +ve value of enthalpy (${{\Delta H}}$). Therefore, the conditions of the spontaneity of a reaction depend on all three factors equally i.e., enthalpy, temperature and entropy.