For a strongly polar or hydrogen bonding mixture such as water and ethanol, a plain cubic equation of state
Answer: A
The attraction term averages over molecular interactions that are strongly directional in such systems, so the physical picture behind it breaks down. Gamma-phi methods using an activity coefficient model handle the liquid phase instead.
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Consider the following statements about the parameters a and b.
1. Both are determined from the critical temperature and pressure.
2. The parameter b is roughly related to the molecular size.
3. Both are independent of the substance concerned.
Answer: B
The first two are correct. The third is plainly wrong, since the whole purpose of the parameters is to distinguish one substance from another within a single equation form. Their values are tabulated or computed from critical data.
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Volume translation applied to a cubic equation of state
Answer: C
A constant shift corrects the liquid root without altering the phase equilibrium calculation, since the same shift applies on both sides. It is a cheap and widely used repair. Peng-Robinson with translation is a common simulator default.
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State whether the following is true or false.
An equation of state can supply enthalpy and entropy departures as well as volumes.
Answer: D
Differentiating it with respect to temperature at constant volume gives exactly the derivatives the residual property integrals need. That is why one equation can serve for the whole thermodynamic package in a simulator.
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At high temperature and low density the van der Waals equation should reduce to the ideal gas law. This happens because
Answer: A
Correct answer: both the a and b corrections become negligible
Van der Waals writes \[ \left(P + \frac{a}{V^{2}}\right)(V-b) = RT. \] At low density \( V \) is large, so \( a/V^{2} \) becomes negligible beside \( P \) and \( b \) becomes negligible beside \( V \); at high temperature the attractive term matters less still relative to the thermal energy. With both corrections vanishing the equation collapses to \( PV = RT \) - as any equation of state must in that limit.
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The reduced form of the van der Waals equation is notable because
Answer: B
Writing pressure, volume and temperature as fractions of their critical values eliminates a and b entirely, which is the theoretical basis of two-parameter corresponding states. Its inaccuracy is the inaccuracy of that principle.
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Iterative solution of a cubic equation of state for the vapour root is usually started from
Answer: C
The vapour root lies close to the ideal value at moderate pressure, so the iteration converges in a few steps. Starting from b, which is near the liquid volume, is the standard way to converge on the liquid root instead.
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Consider the following statements about choosing a thermodynamic model.
1. Peng-Robinson is a common default for hydrocarbon systems.
2. Activity coefficient models suit strongly non-ideal liquid mixtures.
3. The choice of model rarely affects the calculated results.
Answer: D
The first two are correct and describe standard practice. The third is dangerously wrong: model choice can shift a predicted separation enough to change the design of a column completely. Selecting the model is part of the engineering, not a detail.
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