Consider a reaction that involves the conversion of solid calcium carbonate to solid calcium oxide and carbon dioxide gas:
Which statement accurately describes the spontaneity of the reaction?
The spontaneity of the reaction is constant and it occurs spontaneously at all temperatures.
At any temperature is the reaction spontaneous.
The spontaneity of the reaction is temperature-dependent, where it becomes spontaneous at lower temperatures but non-spontaneous at higher temperatures.
The spontaneity of the reaction changes with temperature, where the reaction becomes spontaneous at high temperatures and nonspontaneous at low temperatures.
In order to determine the spontaneity of a reaction, we can use the concept of Gibbs free energy change, . For any general process, the change in Gibbs free energy can be defined as
. For a reaction to be spontaneous,
must be negative. Since the reaction in question involves an increase in entropy
we can say that the spontaneity of the reaction depends on the sign of
.
In this case, we know that the reaction involves the conversion of a solid to another solid and a gas, which suggests that the reaction is endothermic we can say that the spontaneity of the reaction depends on the sign of
.
In this case, we know that the reaction involves the conversion of a solid to another solid and a gas, which suggests that the reaction is endothermic Therefore, if
is greater than
then the reaction will be spontaneous at low temperatures and nonspontaneous at high temperatures. On the other hand, if
is less than
, then the reaction will be nonspontaneous at low temperatures and spontaneous at high temperatures.
Since the reaction involves the conversion of a solid to another solid and a gas, we can assume that the entropy change is positive. Therefore, we can conclude that the reaction is spontaneous at low temperatures and nonspontaneous at high temperatures. Hence, option 3 is correct.
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