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Chapter 1. Introduction – Thermodynamics for Process and Product Design Problem 1. What fits best? Match each sentence (system or condition) of column A in table 1.7 with the correct/expected answer indicated in column B, as shown for example in the case of n-pentane/n-hexane. Table 1.7. What fits best? A n-pentane/n-hexane B 1 (ideal solution) CHCl3/acetone Water/n-hexane Methanol/n-pentane n-pentanol/n-hexanol Polyethylene/n-hexane y1 x1 Compound A is “similar to” compound B i 1 ˆi 1 Almost ideal solution Strong negative deviations from Raoult’s law Ideal gas Azeotrope Negative deviations from Raoult’s law of order of several thousands 1 Ideal liquid solution of order of 20-50 Problem 2. Ideal solutions Figure 1.7. (Left): Pxy diagram of the methanol – ethanol mixture at 50 oC. Experimental data are taken from G.C. Schmidt, Z. Phys. Chem. (Leipzig), 1926, 121, 221. (Right): Txy diagram for the same mixture at 1 bar. Experimental data are taken from Amer et al., Ind. Eng. Chem., 1956, 48, 142. The lines are guide to the eye. Figure 1.7 shows the phase diagram of an ideal solution. i. Show that for ideal binary solutions, the pressure is given by the equation: P x1 ( P1sat P2sat ) P2sat 1.14 1 ii. What is the vapour pressure of methanol and of ethanol at 50 oC? iii. What is the normal boiling temperature of methanol and of ethanol? iv. Are the P-xy or the T-xy diagrams most useful in distillation studies and why? Problem 3. Relative volatilities The relative volatility is defined as the ratio of the equilibrium factors as: aij Ki Kj 1.15 y Ki i xi Show that the relative volatility of a binary mixture is given by the following expressions: P1sat i. a12 sat if all components obey the Dalton-Raoult law P2 1 P1sat ii. a12 if all components obey the modified Raoult’s law 2 P2sat iii. Prove that for any binary mixture, the mole fractions in the vapour and liquid phase are related to the relative volatility via the equation: y1 a12 x1 1 (a12 1) x1 1.16 iv. Distillations are often preferred at low pressures. Why? Problem 4. Multiple choice questions Fill in table 1.8. Only one answer is correct for each question. Table 1.8. Multiple choice questions. 1. Negative deviations from Raoult’s law exist when… a. The activity coefficients are negative b. The activity coefficients have values between 1 and 2 c. Azeotropes are present d. The pressure of the solution is below the value given by Raoult’s law 2. An ideal liquid solution … a. Implies that forces between “like” and “unlike” molecules and size/shape of molecules are similar b. Exists for all mixtures with hydrocarbons 2 c. d. Exists for polymer solutions if the repeating unit of the polymer is functionally similar to the solvent Is always the case when we have aqueous solutions 3. Raoult’s law is valid for... a. Ideal gases b. Ideal liquid solutions at low pressures c. Mixtures of hydrocarbons d. Mixtures of alcohols 4. Cubic equations of state are … a. Cubic with respect to volume b. Cubic with respect to pressure c. Cubic with respect to temperature d. Called “cubic” for no special reason 5. Only ONE of the following laws/equations does NOT indicate some form of “ideality” in thermodynamics. Which one? a. PV nRT b. Raoult’s law c. Lewis-Randall law d. Soave-Redlich-Kwong equation of state 6. ˆi designates (in thermodynamics) … a. The activity coefficient of compound i b. The fugacity coefficient of pure compound i c. The fugacity of compound i in a mixture d. The fugacity coefficient of compound i in a mixture 7. Polymers in mixtures with low molecular weight chemicals typically form in the liquid state… a. Non-ideal solutions if the molecular weight of the polymer is above 50000 g/mole b. Non-ideal solutions due to the large size (molecular weight) difference c. Ideal solutions if the repeating unit of the polymer and the chemical have similar structures d. Non-ideal solutions due to pronounced energy differences 8. The concept of activity coefficients is introduced in thermodynamics basically because… a. The framework of Gibbs using the chemical potential is not general enough b. Fugacity coefficients cannot be used for liquids c. It is easier to use than the fugacity coefficients d. Many traditional models like cubic equations of state do not represent satisfactorily both the vapour and liquid phases 3