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5.18: Untitled Page 115

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  • Chapter 5

    Figure 5.10c. Pinch Point for a cascade of equilibrium stages The sequential analysis and the graphical analysis of continuous equilibrium stage processes provide a relatively clear illustration of the physical processes involved; however, more complex systems are routinely encountered in industrial practice. In those cases, powerful numerical methods are extremely useful.

    5.7 Problems

    Note: Problems marked with the symbol  will be difficult to solve without the use of computer software.

    Section 5.1

    5‐1. Show that the mole fraction in an ideal gas mixture can be expressed as y p

    p .



    5‐2. Demonstrate that the volume percent of a mixture is the same as the mole percent for an ideal gas mixture.

    Two‐Phase Systems & Equilibrium Stages 211

    5‐3. Assuming ideal gas behavior, determine the average molecular mass of a mixture made of equal amounts of mass of chlorine, argon, and ammonia.

    Section 5.2

    5‐4. A liquid mixture of hydrocarbons has 40% by weight of cyclohexane, 40% of benzene, and 20% toluene. Assuming that volumes are additive compute the following:

    (a) species densities of the components in the mixture.

    (b) overall density of the mixture

    (c) concentrations of the components in mol/m3

    (d) mole fractions of the components in the mixture.

    Section 5.3

    5‐5. Determine the vapor pressure, in Pascal, of ethyl ether at 25 C and at 30 C.

    Estimate the heat of vaporization of ethyl ether using these two vapor pressures and the Clausius‐Clapeyron equation.

    5‐6. Determine the vapor pressure of methanol at 25 C and compare it to that of ethanol at the same temperature. Consider the ethanol‐methanol system to be an ideal solution in the liquid phase and an ideal gas mixture in the vapor phase.

    Determine the mole fraction of methanol in the vapor phase when the liquid phase mole fraction is 0.50. If the liquid phase is allowed to slowly evaporate, will it become richer in methanol or ethanol? Here you are asked to provide an intuitive answer concerning the composition of the liquid phase during the process of distillation. In Chapter 8 a precise analysis of the process will be presented.

    5‐7. Determine the vapor‐liquid equilibrium curve of a binary mixture of cyclohexane and acetone. Plot the mole fraction of acetone in the vapor phase versus the mole fraction of acetone in the liquid phase at one atmosphere (760

    mm Hg).

    5‐8. Use Eqs. 5‐26 and 5‐27 order to derive 5‐28.

    5‐9. Demonstrate that Eq. 5‐31 is valid for an ideal system containing three components when an appropriate constraint is imposed.