Predict the signs (-, +, or 0) of $\Delta$H and $\Delta$S, in that order, for the expansion of an ideal gas into a vacuum.
A) 0, -
B) 0, +
C) +, +
D) -, -
E) None of the above

Question

Quizplus · Accepted Answer

For an expansion of an ideal gas into a vacuum, the final pressure is zero. Therefore, ΔF1F1F10H and ΔF1F1F10S are positive values. From thermodynamics, we know that:
ΔG = ΔH - TΔS
At constant temperature and pressure (which is the case for an expansion into a vacuum), this becomes:
ΔG = ΔH - 0ΔS = ΔH
ΔG is negative for a spontaneous process. Therefore, if ΔH is positive, ΔG is negative when the temperature is high enough, and hence the process would be spontaneous. This means that F1F1F1S1F1F1F10S is predicted to be positive (i.e. +). On the other hand, F1F1F1S1F1F1F10H is related to the energy content of the system, and since the expansion causes the energy to spread out, the change in enthalpy is close to zero. As a result, its sign would be close to zero (i.e. 0), but not exactly zero due to slight energy changes. Therefore, the correct answer is option B (0, +).

Predict the Signs (-, +, or 0) Of Δ\DeltaΔ H And Δ\DeltaΔ

Predict the Signs (-, +, or 0) Of $\Delta$ H And $\Delta$