Fugacity and Activity Coefficients Questions and Answers

Answer: A

The calculation is iterative because the activity coefficients depend on the temperature being sought. Recognising which quantities are known at the outset is what makes the loop converge quickly. A poor initial guess merely costs a few more iterations.

Answer: B

The dilute end is where deviations are largest, so a measurement there constrains a model strongly. Several experimental techniques exist specifically to obtain these limiting values. Gas chromatography is one of the more convenient of them.

Answer: C

The excess Gibbs energy is the gas constant times temperature times the mole-fraction weighted sum of the logarithms, which is about four tenths of point four one plus six tenths of point one eight. Multiplying by twenty-five hundred gives roughly six hundred and eighty.

Answer: D

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

Both are true and the reason gives the basis. The Gibbs–Duhem equation relates the activity coefficients of the components at constant temperature and pressure, so they cannot vary independently. Data that violate it are internally inconsistent and must contain experimental error, which the area test and the point test detect - and which is why published data are screened before being correlated.

Answer: A

At a few bar the vapour is close enough to ideal that the correction is negligible, which reduces the gamma-phi expression to a modified Raoult's law. That simplification underlies most introductory distillation calculations.

Answer: B

Correct answer: True

Fugacity was introduced as a corrected pressure - the quantity that plays the role pressure would play if the substance behaved ideally - so it carries the units of pressure and is usually quoted in bar or in pascals. It is the *coefficients*, fugacity and activity alike, that are dimensionless, being ratios of fugacities.

Answer: C

The first two are correct. The third is false, and importantly so: the convention changes the numbers in the intermediate quantities but the physical equilibrium it predicts must be the same. Thermodynamics cannot depend on a bookkeeping choice.