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

Hint: 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.