Fugacity and Activity Coefficients Questions and Answers

Answer: A

The logarithmic pressure term goes to minus infinity as pressure falls, which makes chemical potential awkward to work with numerically. Fugacity carries the same information in a quantity with the units and the finite behaviour of a pressure.

Answer: B

Correct answer: its fugacity divided by its partial pressure

\[ \hat{\phi}_i = \frac{\hat{f}_i}{y_iP}. \] It is a dimensionless measure of how far the component departs from ideal gas behaviour, and it goes to unity as the pressure falls, since fugacity and partial pressure coincide in the ideal gas limit. That is the definition to keep separate from the activity coefficient, which does the analogous job for a liquid.

Answer: C

The fugacity coefficient is one throughout, so fugacity and partial pressure coincide. That identity is the reason fugacity is often described as a corrected pressure. Any departure from that equality measures non-ideality.

Answer: D

Correct answer: A-2, B-4, C-1, D-3

Four correction factors for four different departures. The fugacity coefficient measures a gas against the ideal gas. The activity coefficient measures a liquid against the ideal solution. The compressibility factor measures PVT behaviour against the ideal gas law. And the Poynting factor corrects a liquid fugacity from its saturation pressure to the system pressure. Each is unity when the corresponding idealisation holds.

Answer: A

Because the definition involves a ratio to a chosen standard state, an activity has no meaning until that state is named. The Lewis-Randall and Henry references are the two conventional choices. Each is suited to a different concentration range.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the cause. Activity is \( a_i = \hat{f}_i/f_i^{\circ} \), a ratio to the fugacity in a chosen standard state, so the same solution has different activity coefficients under the Lewis–Randall convention and under Henry’s law. A quoted value is therefore meaningless without the convention, which is why tabulated data always state it.

Answer: C

This is the convention in which the activity coefficient tends to one as the mole fraction tends to one. The Henry convention instead makes it tend to one at infinite dilution, which suits a solute. Naming the convention is part of quoting the number.

Answer: D

The first two are correct. The third is wrong in its final clause, because negative deviations from Raoult's law give activity coefficients smaller than one, as in acetone and chloroform mixtures. Such systems release heat when they are mixed.

Answer: A

Correct answer: the pressure effect on a condensed phase fugacity

\[ \exp\left[\int_{P^{sat}}^{P}\frac{V^{L}}{RT}\,\mathrm{d}P\right] \] corrects the fugacity of a liquid from its saturation pressure up to the system pressure. Because the liquid molar volume is small, the factor is very close to unity at moderate pressures and is often neglected - and it becomes significant only at high pressure or well below the normal boiling point.

Answer: B

The exponent is small because the liquid molar volume is small, so the factor differs from one by well under a per cent. At high pressure, as in reservoir calculations, it becomes significant. The exponent grows in direct proportion to the pressure.