### Video Transcript

Which of the following sets of features guarantee that a reaction is nonspontaneous? (A) Positive ΔH, positive ΔS. (B) Positive ΔH, negative ΔS. (C) Negative ΔH, negative ΔS. (D) Negative ΔH, positive ΔS. Or (E) None of the answers are correct.

In chemistry, we can look at changes in the Gibbs free energy for a reaction or process to determine if that reaction or process will be spontaneous or not. If the change in Gibbs free energy for a reaction is negative or less than zero, the reaction will occur spontaneously. But if the change in the Gibbs free energy is positive or greater than zero, the reaction will not be spontaneous. This question is asking us to determine which features will correspond to a reaction being nonspontaneous. So, we need to identify which features go along with the change in Gibbs free energy being positive.

We’re given different combinations of signs for the change in enthalpy and the change in entropy for a reaction. So let’s figure out which one will correspond to the change in Gibbs free energy being positive. Remember that the temperature in the expression for the Gibbs free energy will be in units of kelvin, so it will always be a positive number.

Our first answer choice is a positive change in enthalpy and a positive change in entropy. This would give us a positive number minus a positive number. So depending on the magnitude of these positive numbers, we could end up with a positive or a negative value for the change in Gibbs free energy. We’re looking for a set of features that will guarantee that the reaction will be nonspontaneous. And we can’t guarantee anything about these set of conditions. So this isn’t the answer choice that we’re looking for.

Our next set of conditions as a positive change in enthalpy and a negative change in entropy. This would give us a positive number minus a negative number, which would result in a positive value for the change in the Gibbs free energy. Since we’re looking for the conditions that will guarantee that a reaction will be nonspontaneous, which corresponds to a positive value for the change in Gibbs free energy, this is the answer choice that we’re looking for. But let’s review the other sets of conditions so we understand when the changes in Gibbs free energy will be positive versus negative.

The next set of conditions is a negative change in enthalpy and a negative change in entropy. This would result in a negative number minus a negative number. So this is another set of conditions where, depending on the magnitude of the change in enthalpy and the change in entropy, we can end up with a positive or a negative value for the change in the Gibbs free energy.

The final set of conditions is a negative change in enthalpy and a positive change in entropy. This would result in a negative number minus a positive number. So the change in Gibbs free energy under these conditions would have to be negative. So when the change in enthalpy is negative and the change in entropy is positive, that guarantees that the reaction will occur spontaneously since the change in Gibbs free energy is negative. Plus, we discussed earlier, we’re looking for a set of features that will guarantee that the reaction will occur nonspontaneously, which will happen when we have a positive change in enthalpy and a negative change in entropy.