The method and the results are on the Gibbs free energy lab. Do the analysis yourself first, then check the answers below.
Quick answer: Entropy S measures the dispersal of energy and matter, and the Gibbs free energy change ΔG = ΔH − TΔS predicts spontaneity: a reaction is spontaneous when ΔG is negative. These answers go with the AP Chemistry lab on Gibbs free energy: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Here are the Gibbs free energy lab answers for AP Chemistry: graph, calculations, uncertainties and conclusion. First do the lab yourself, then compare, and go back to the lesson if needed.
The sample data give ΔH close to the accepted value of +25.7 kJ/mol. Your own values will differ with your cup, thermometer and mixing. Check that every calculation uses consistent units and keep three significant figures.
Gibbs free energy lab answers: the analysis explained
Question 1 Temperature change
Initial 21.9 °C, lowest 16.2 °C, so ΔT = 5.7 °C (a fall).
Question 2 Heat absorbed
q = 108.0 × 4.18 × 5.7 = 2573 J (2.57 kJ).
Question 3 Enthalpy change per mole
n = 8.00 / 80.04 = 0.1000 mol. ΔH = +2.57 / 0.1000 = +25.7 kJ/mol. The sign is positive because heat is absorbed.
Question 4 Why spontaneous
ΔG must be negative. With ΔH positive, −TΔS must be negative and larger in size than ΔH, so ΔS is positive: ordered ions in the crystal become dispersed in solution.
Question 5 Minimum entropy change
A negative ΔG needs TΔS above ΔH, so ΔS must exceed 25 700 / 295 = 87 J/(mol·K).
Question 6 Heat gain error
Heat entering from the room makes the lowest temperature higher, so ΔT is too small and ΔH is underestimated. Improve it by extrapolating the cooling graph back to 90 s and adding a lid.
Question 7 Larger sample
The amount of solid doubles, so q doubles to 5146 J. Mass is now 116.0 g, so ΔT = 5146 / (116.0 × 4.18) = 10.6 °C.
