How to Calculate ∆S⁰ for a Reaction at 9900 °C

What is the value of ∆S⁰ for the reaction at 9900 °C with ∆G = 0?

a) Not enough information provided
b) 0
c) Positive
d) Negative

Final Answer:

The value of ∆S⁰ for the reaction at 9900 °C with ∆G = 0 cannot be determined without knowing the value of ∆H⁰, since ∆S⁰ is calculated by dividing ∆H⁰ by temperature. Without this information, the answer is that there is not enough information provided to determine the sign of ∆S⁰.

Explanation:

To determine the value of ∆S⁰ for the reaction at 9900 °C where ∆G = 0, we can use the following relationship between Gibbs free energy (∆G⁰), enthalpy (∆H⁰), and entropy (∆S⁰):

∆G⁰ = ∆H⁰ - T∆S⁰

Given that ∆G is 0, we can rearrange the equation to solve for ∆S⁰:

0 = ∆H⁰ - T∆S⁰

∆S⁰ = ∆H⁰ / T

Since at equilibrium ∆G = 0, if the temperature (T) and ∆H⁰ are known, ∆S⁰ must be a definite, calculable value. Given that the sign of ∆H⁰ is not specified, but the temperature is positive, we know that if ∆H⁰ is positive, then ∆S⁰ will indeed be positive. If ∆H⁰ is negative, then ∆S⁰ would also be negative. However, without the value of ∆H⁰, there is not enough information to state whether ∆S⁰ is positive or negative. Therefore, the answer is (a) Not enough information provided.