Main_ISM_ch07 - Chapter 7: The Properties of Real Gases...

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7-1 Chapter 7: The Properties of Real Gases Problem numbers in italics indicate that the solution is included in the Student’s Solutions Manual. Questions on Concepts Q7.1) Explain why the oscillations in the two-phase coexistence region using the Redlich-Kwong and van der Waals equations of state (see Figure 7.4) do not correspond to reality. The oscillations predict that as V increases, P will increase. No real gas exhibits this behavior. Q7.2) Explain the significance of the Boyle temperature. The Boyle temperature provides a way to classify the way in which z varies with P at low values of P for different gases. If T > T B , z increases with increasing P ; if T < T B , z decreases with increasing P . Q7.3) The value of the Boyle temperature increases with the strength of the attractive interactions between molecules. Arrange the Boyle temperatures of the gases Ar, CH 4 , and C 6 H 6 in increasing order. Ar < CH 4 < C 6 H 6 Q7.4) Will the fugacity coefficient of a gas above the Boyle temperature be less than one at low pressures? No. The integral 0 1 P z dP P is always greater than zero for this case. Therefore, γ > 1 for all P . Q7.5) Using the concept of the intermolecular potential, explain why two gases in corresponding states can be expected to have the same value for z . Two different gases will have different values for the depth of the intermolecular potential and for the distance at which the potential becomes positive. By normalizing P , T , and V to their critical values, the differences in the intermolecular potential are to a significant extent also normalized. Q7.6) By looking at the a and b values for the van der Waals equation of state, decide whether 1 mole of O 2 or H 2 O has the higher pressure at the same value of T and V .
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Chapter 7/The Properties of Real Gases 7-2 A is significantly larger for H 2 O. Therefore, the attractive forces between H 2 O molecules are greater than between O 2 molecules. Consequently, O 2 will have a higher pressure. Q7.7) Consider the comparison made between accurate results and those based on calculations using the van der Waals and Redlich-Kwong equations of state in Figures 7.1 and 7.5. Is it clear that one of these equations of state is better than the other under all conditions? The Redlich-Kwong gives more accurate results for almost all of the values of pressure shown in these figures. However, it is not better under all conditions. Q7.8) Why is the standard state of fugacity, f º, equal to the standard state of pressure, P º? If this were not the case the fugacity would not become equal to the pressure in the limit of low pressures. Q7.9) For a given set of conditions, the fugacity of a gas is greater than the pressure. What does this tell you about the interaction between the molecules of the gas?
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Main_ISM_ch07 - Chapter 7: The Properties of Real Gases...

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