Answer: The reaction is spontaneous at low temperatures
Explanation:
Let's first remember the definition of certain terms;
Enthalpy (H) in thermodynamics is defined as the heat content of a reaction. While Entropy (S) in thermodynamics is termed as the quantification of disorder or randomness of a reaction.
Gibb’s free energy change helps to determine the direction of the reaction.
Using the Gibbs free energy equation to solve this question.
∆G = ∆H - T∆S
Where;
∆G = Gibbs free energy
∆H = change in enthalpy
T= temperature of the reaction
∆S = change in entropy.
The question states that it is an exothermic reaction with negative entropy. This means that the change in both enthalpy and entropy will be negative. That is;
∆H = >0 ( it's positive)
∆S = < 0 (negative)
Let's remember that an exothermic reaction generally releases energy to it surroundings. This energy is usually released in the form of heat. Therefore, the change in enthalpy H of an exothermic reaction will always be negative. A negative change in entropy S indicates that there is a decrease in disorder, with respect to the reaction.
Using Gibb’s free energy equation at constant temperature and pressure, we have;
∆G = ∆H - T∆S
Now, the change in enthalpy and change in entropy can be written as follows;
∆H = >0 ( it's positive)
∆S = < 0 (negative)
Substitute these values in the above equation;
∆G = ∆H - T - (∆S)
∆G = ∆H + T∆S
According to the sign convention seen in the equation above,
Change in ∆G will be negative <0 when the value ∆H is greater than T∆S.
This change can occur only at low temperatures. Thus, this reaction is spontaneous at low temperatures.
