Fugacity and Activity Coefficients Questions and Answers

Answer: C

The exponent is the volume times the pressure difference divided by the gas constant and temperature, which is one ten-thousandth times one million pascals over about twenty-five hundred. That gives about four hundredths, so the factor itself is close to unity.

Answer: D

Correct answer: the number of components in the mixture

The fugacity of a pure liquid component is its vapour pressure, corrected by the fugacity coefficient at saturation for vapour non-ideality and by the Poynting factor for the pressure difference. All three of those appear in the expression; the number of components does not. Mixture effects enter through the activity coefficient, which multiplies this quantity rather than altering it.

Answer: A

It treats each phase with the model that suits it, which is why it handles strongly non-ideal liquids well. The alternative phi-phi approach uses one equation of state for both phases and suits high pressure hydrocarbon systems.

Answer: B

Both are true and the reason gives the motivation: the liquid phase is where the difficulty lies, so an activity coefficient model fitted to real data is used there while the vapour is handled by a simple equation of state.

Answer: C

Correct answer: an empirical expansion of excess Gibbs energy

Margules writes the excess Gibbs energy as a polynomial in composition and obtains the activity coefficients by differentiation. It is a correlation with adjustable constants rather than a theory - it fits binary data well and predicts nothing about a system it has not been fitted to, which is what distinguishes it from the models based on local composition.

Answer: D

Correct answer: the Peng-Robinson equation

Peng–Robinson is a cubic equation of state: it describes PVT behaviour and is used for fugacity coefficients in the vapour phase. Wilson, NRTL and UNIQUAC are all activity coefficient models for the liquid phase, based on the idea of local composition. The distinction matters because the two approaches meet different halves of a vapour–liquid equilibrium calculation.

Answer: A

Its mathematical form simply cannot produce two liquid phases, which is why NRTL was developed for partially miscible systems. It extends to multicomponent mixtures from binary parameters well. Its two parameters are regressed from binary data.

Answer: B

The first two are correct and are why it is widely used for aqueous organic systems. The third is wrong, since its parameters are regressed from binary equilibrium data. No activity coefficient model is genuinely predictive.

Answer: C

By treating a molecule as a collection of groups it can predict behaviour for a binary that has never been measured, which is invaluable in early design. Its accuracy is lower than a model fitted to real data for the actual pair.

Answer: D

It gives an estimate that is usually good enough to screen options, but a design decision resting on a close separation still needs measured data. Treating a prediction as a measurement is a real hazard in process design.