(a) Since the standard enthalpy change, H¢X, is negative, it means that the reactants have a higher enthalpy than the products. This suggests that the reaction releases energy and becomes more stable. Entropy, on the other hand, is a measure of disorder or randomness in a system. Generally, when a reaction becomes more stable, it tends to have a decrease in entropy because the products are more orderly than the reactants. Therefore, based on the given information, we can predict that the sign of the standard entropy change, S¢X, for the reaction is negative.
(b) According to thermodynamic principles, the spontaneity of a reaction at a given temperature can be determined by the change in Gibbs free energy, G¢X. The equation relating the change in Gibbs free energy, temperature, and the change in enthalpy is:
ΔG = ΔH - TΔS
Since the forward reaction is spontaneous at 298 K, it means that ΔG is negative. When the temperature is increased, the ΔS term (change in entropy) has a negative sign due to part (a) and the equation becomes:
ΔG = ΔH - TΔS
If ΔH and ΔS remain constant, an increase in temperature (T) would make the negative (-TΔS) term larger. As a result, ΔG would become less negative or even positive, indicating that the reaction would become less spontaneous or even non-spontaneous.
(c) The equilibrium constant, Keq, is related to the change in Gibbs free energy by the equation:
ΔG = -RT*ln(Keq)
where R is the gas constant and T is the temperature.
As we saw in part (b), an increase in temperature would cause the value of ΔG to become less negative or even positive. Since ΔG is in the denominator of the equation, a smaller (less negative) ΔG would make the right side of the equation (the natural logarithm term) larger. This means that the value of Keq would decrease. Therefore, an increase in temperature would cause a decrease in the value of the equilibrium constant, Keq.
(d) The absolute temperature at which the forward reaction becomes non-spontaneous can be predicted using the equation:
ΔG = ΔH - TΔS
To find the temperature, we can set ΔG equal to zero. This gives us:
0 = ΔH - TΔS
Rearranging the equation, we get:
T = ΔH/ΔS
This equation can only provide an approximate value for the temperature because it assumes that ΔH and ΔS remain constant over the entire temperature range, which might not always be true. Additionally, this equation does not account for other factors such as changes in heat capacity with temperature. Nevertheless, it gives us a rough estimate of the temperature at which the forward reaction becomes non-spontaneous.