Question 19.2: Predicting the Sign of the Entropy Change of a Reaction a. T...
Predicting the Sign of the Entropy Change of a Reaction
a. The following equation represents the essential change that takes place during the fermentation of glucose (grape sugar) to ethanol (ethyl alcohol).
\underset{\text { glucose }}{\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)} \longrightarrow \underset{\substack{\text { ethanol }}}{2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)}+2 \mathrm{CO}_{2}(g)
Is S^{\circ} positive or negative? Explain.
b. Do you expect the entropy to increase or decrease in the preparation of urea from \mathrm{NH}_{3} and \mathrm{CO}_{2} ?
2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)
Explain.
c. What is the sign of \Delta S^{\circ} for the following reaction?
\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)
PROBLEM STRATEGY
Compare the reactants and products in each reaction. Look for the following: molecules breaking into smaller parts or aggregrating into larger parts, moles of gas increasing or decreasing, and changes of state. Then apply the three rules preceding this example.
a. A molecule (glucose) breaks into smaller molecules \left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right. and \left.\mathrm{CO}_{2}\right). Moreover, this results in a gas being released. You predict that \Delta S^{\circ} for this reaction is positive. That is, the entropy increases.
b. In this reaction, the moles of gas decrease (by 3 \mathrm{~mol} ), which would decrease the entropy. You predict that the entropy should decrease. That is, \Delta S^{\circ} is negative.
c. Because there is no change in the number of moles of gas, you cannot predict the sign of \Delta S^{\circ} from the rules given.