# Chapter 7: Solutions and Phase Behavior (Solution)

**Problem 7.1: **n-Heptane and toluene form an ideal solution. At 373 K their vapour pressures are 106 kPa and 74 kPa respectively. Determine the composition of the liquid and the vapor in equilibrium at 373 K and 101.3 kPa.

**Problem 7.2:** The vapour pressures of benzene and toluene are given by the Antoine equation

where P is in kPa and T in K. The Antoine constants are

A | B | C | |

Benzene | 13.8858 | 2788.51 | 52.36 |

Toluene | 13.9987 | 3096.52 | 53.67 |

Determine the partial pressures and the weight composition of the vapour in equilibrium with a liquid mixture consisting of equal weights of the two components at 300 K.

**Problem 7.3:** At 300 K, the vapour pressures of two pure liquids A and B are respectively 80 kPa and 50 kPa. The concentration of A in the vapour in equilibrium with a solution of A and B is found to be 35% (mol). Determine (a) The composition of the liquid and (b) The total pressure of the vapour.

**Problem 7.4:** Air is cooled to 80 K at 101.3 kPa. Calculate the composition of the liquid and the vapour phases at this condition assuming that the mixture behaves ideally. The vapour pressure of nitrogen at 80 K = 135.74 kPa and the vapour pressure of oxygen at 80 K = 30.04 kPa.

**Problem 7.5:** A mixture of A and B conforms closely to Raoult’s law. The pure component vapour pressures P^{S}_{A} and P^{S}_{B} in kPa at temperature T in K are given by

If the bubble point of a certain mixture of A and B is 349 K at a total pressure of 80 kPa, find the composition of the first vapour that forms.

**Problem 7.6** The vapour pressures of substances A and B can be evaluated by the Antoine equations

where T is in K and P is in kPa. Assuming that the solutions formed by these are ideal, calculate the compositions of the vapour and the liquid in equilibrium at 327 K and 65 kPa.

**Problem 7.7: **A mixture of n-hexane and n-heptane containing 10% n-hexane is vaporized at a pressure of 100 kPa. Determine the following: (a) The bubble point temperature (b) The composition of the vapour. The vapour pressures are given by the Antoine equation

where P is in kPa and T in K. The Antoine constants are

Name | A | B | C |

n-heptane | 13.8587 | 2911.32 | 56.51 |

n-hexane | 13.8216 | 2697.55 | 48.78 |

**Problem 7.8:** The vapour pressures of benzene and toluene are given below.

T (K) | 353.1 | 358 | 363 | 368 | 373 | 378 | 383 | 383.6 |

P_{A}^{S} (kPa) | 101.3 | 116.9 | 135.4 | 155.7 | 179.1 | 204.2 | 233.0 | 240.0 |

P_{B}^{S} (kPa) | 39.6 | 46.0 | 54.0 | 63.3 | 74.2 | 86.0 | 99.0 | 101.3 |

Calculate the equilibrium data for the system at 101.3 kPa.

**Problem 7.9:** At 303 K the vapour pressures of benzene (A) and toluene (B) are 15.75 kPa and 4.89 kPa respectively. Determine the partial pressures and the weight composition of the vapour in equilibrium with a liquid mixture consisting of equal weights of the two components.

**Problem 7.10: **The vapour pressures of benzene (A) and chlorobenzene (B) are given below:

T (K) | 352.8 | 363.2 | 373.2 | 383.2 | 393.2 | 405.3 |

P_{A}^{S} (kPa) | 101.3 | 135.1 | 178.7 | 232.5 | 298.0 | 395.3 |

P_{B}^{S} (kPa) | 18.2 | 27.7 | 39.06 | 53.7 | 72.3 | 101.3 |

Assume that benzene and chlorobenzene form the ideal solutions. (a) Prepare the P-x-y diagram for the system at 373.2 K. (b) Using the P-x-y diagram of the part (a), determine the bubble point pressure and dew-point pressure of an equimolar mixture of benzene and chlorobenzene at 373.2 K.

**Problem 7.11: **An equimolar mixture of benzene and toluene is contained in a cylinder at 65 kPa. Determine the temperature range in which the mixture exists as two phases. The vapor pressure of benzene and toluene are given by the Antoine equation with the following constants. Pressure is in kPa and temperature in K.

Name | A | B | C |

Benzene | 13.8858 | 2788.51 | 52.36 |

Toluene | 13.9987 | 3096.52 | 53.67 |

**Problem 7.12:** A 40% (mol) solution of methanol in water boils at 348.5 K. The vapor analyzed was 72.9% methanol. How does this compare with the vapor composition given by Raoult’s law? The vapor pressures (kPa) are given by the Antoine equation with the following constants:

Name | A | B | C |

Water | 16.26205 | 3799.887 | 46.854 |

Methyl alcohol | 16.5725 | 3626.55 | 34.29 |

**Problem 7.13: **An equimolar solution of benzene and toluene is totally evaporated at a constant temperature of 363 K. At this temperature, the vapor pressures of benzene and toluene are 135.4 kPa and 54 kPa respectively. What are the pressures at the beginning and at the end of the vaporization process?

**Problem 7.14: **A liquid mixture containing 15% A, 25% B and the rest C is in equilibrium with the vapor which contains 40% B. All the percentages are on a mole basis. The equilibrium pressure and temperature are 200 kPa and 350 K. At 350 K the vapour pressure of C is 20 kPa. What is the percentage of A in the vapor?

**Problem 7.15:** A liquid mixture contains 10% A, 15% B, and the rest C, all compositions being in mole percent. At equilibrium, the pressure was 230 kPa and temperature was 340 K, and the vapor was found to contain 34% B. The vapor pressure of C at the equilibrium temperature is 3.5 kPa. Assuming ideal behavior for the gas and the liquid, calculate the vapor composition.

**Problem 7.16: **Three liquids A (MW = 40), B (MW = 60) and C (MW = 80) form an ideal solution. At 370 K, the vapor pressures are found to be 50 kPa, 25 kPa and 12.5 kPa respectively for A, B and C. A vapor analyzing 40% A, 40% B, and 20% C on a volume basis is in equilibrium with the liquid at 370 K. Determine the following: (a) The equilibrium pressure (b) The composition of the liquid in weight percent.

**Problem 7.17: **Liquids A and B form ideal solutions while liquid C is immiscible with both A and B. A mixture of A, B and C is found to boil at 240 K under a pressure of 100 kPa. What is the composition of the liquid on a C-free basis? The vapor pressures at 240 K are 15 kPa, 3 kPa and 95 kPa respectively for A, B and C.

**Problem 7.18: **Three liquids A, B and C form an ideal solution. The dew point of a vapor mixture consisting of A, B and C at a pressure of 15 kPa is found to be 323 K. The vapor pressures of pure liquids A, B and C are correlated by the Antoine equations. With vapor pressure in kPa and temperature in K, the Antoine constants are as follows:

Liquid | A | B | C |

A | 13.9 | 2800 | 52.4 |

B | 14.0 | 3100 | 53.7 |

C | 16.3 | 3800 | 46.9 |

Determine the following: (a) The composition of the vapor assuming that the vapor contains equimolar quantities of A and B. (b) The composition of the first drop of liquid formed at 323 K and 15 kPa.

**Problem 7.19:** The vapor pressures of substances A and B can be evaluated by the Antoine equations

where T is in K and P is in kPa. Assuming that the solutions formed by these are ideal, calculate the following: (a) The bubble-point temperature of a liquid containing 40% (mole) A at 65 kPa and the composition of the vapor in equilibrium with this liquid. (b) The bubble-point pressure for a liquid containing 40% (mole) A and the composition of vapour in equilibrium at 327 K.

**Problem 7.20:** The vapor pressures of substances A and B can be evaluated by the Antoine equations

where T is in K and P is in kPa. Assuming that the solutions formed by these are ideal, calculate the fraction of the system that is liquid and the composition of the liquid and the vapor in equilibrium at 327 K and 65 kPa when the overall composition of the system is 70 mole percent A.

**Problem 7.21:** A solution of methanol in water containing 0.158 mole fraction methanol boils at 357.3 K and 101.3 kPa and produces a vapor containing 0.553 mole fraction methanol. Is Raoult’s law valid? If not determine the percent deviation from it for each component. The vapor pressure of methanol may be estimated using the Antoine equation

**Problem 7.22: **Two substances A and B are known to form ideal liquid solutions. A vapor mixture containing 50 mol % A and 50 mol % B is at 311 K and 101.3 kPa. This mixture is compressed isothermally until condensation occurs. At what pressure does condensation occur and what is the composition of the liquid that forms? The vapor pressures of A and B are 142 kPa and 122 kPa respectively.

**Problem 7.23:** A liquefied fuel gas consists of 60% n-butane, 35% propane and 5% ethane. All compositions are on mole basis. The vapor pressures at 303 K are: ethane = 4.72×103 kPa, propane = 1.09×103 kPa and n-butane = 3.45×102 kPa. Calculate the following: (a) The vapor pressure of the liquid at 303 K (b) The composition of the vapor at 303 K (c) Repeat parts (a) and (b) if all ethane is removed from the liquid.

**Problem 7.24:** Hexane (A) and heptane (B) form an ideal solution. The vapor pressures of pure hexane and heptane are:

T (K) | 342 | 343 | 348 | 353 | 358 | 363 | 368 | 372.4 |

P_{A}^{S} (kPa) | 101.3 | 104 | 122 | 141.3 | 163.3 | 187.3 | 210.2 | 235.3 |

P_{B}^{S} (kPa) | 39.3 | 40.3 | 46.4 | 56.8 | 66.4 | 78.4 | 90 | 101.3 |

(a) Plot the boiling point diagram for the system at 101.3 kPa. (b) Plot the equilibrium diagram at 101.3 kPa.

**Problem 7.25: **The binary system, acetone (A)-acetonitrile (B) may be treated as an ideal solution. Using the vapor pressure data given below prepare the following: (a) A plot of P versus x and P versus y at 323 K (b) Boiling point diagram

T (K) | 311.45 | 315 | 319 | 323 | 327 | 331 | 335.33 |

P_{A}^{S} (kPa) | 53.32 | 61.09 | 70.91 | 81.97 | 94.36 | 108.2 | 124.95 |

P_{B}^{S} (kPa) | 21.25 | 24.61 | 28.90 | 33.79 | 39.35 | 45.62 | 53.32 |

**Problem 7.26: **The vapor pressures of benzene (A) and chlorobenzene (B) are given below:

T (K) | 352.8 | 363.2 | 373.2 | 383.2 | 393.2 | 405.3 |

P_{A}^{S} (kPa) | 101.3 | 135.1 | 178.7 | 232.5 | 298.0 | 395.3 |

P_{B}^{S} (kPa) | 18.2 | 27.7 | 39.06 | 53.7 | 72.3 | 101.3 |

Assume that benzene and chlorobenzene form an ideal solution. (a) What are the normal boiling points of benzene and chlorobenzene? (b) Prepare the T-x-y diagram for the system at 101.3 kPa. (c) Using the T-x-y diagram of part (b) determine the bubble point and dew point of an equimolar mixture of benzene and chlorobenzene at 101.3 kPa.

**Problem 7.27: **Assuming Raoult’s law to be valid for the system benzene (A)-ethyl benzene (B) and the vapor pressures are given by the Antoine equations:

where P is in kPa and T is in K. (a) Construct the P-x-y diagram at 370 K. (b) Construct the T-x-y diagram at 100 kPa.

**Problem 7.28:** A liquid mixture containing 65 mol % benzene and 35 mol % toluene is subjected to flash vaporization at 363 K and 101.3 kPa. The vapour pressure of benzene at this temperature is 136.09 kPa and the vapour pressure of toluene is 54.21 kPa. Flash vaporization is essentially an equilibrium stage operation. Calculate the following: (a) The exit vapour composition (b) The exit liquid composition (c) The mole percent of the feed that is vaporized.

**Problem 7.29 **A solution containing 25% benzene (MW = 78.048), 35% toluene (MW = 92.064) and 40% xylene (MW = 106.08) is in equilibrium with its vapour at 373 K. All percentages are on a weight basis. Determine the following: (a) The total pressure (b) The composition of the vapour (c) The average molecular weight of the liquid and vapour.

The vapour pressures at 373 K are: benzene = 178.7 kPa, toluene = 74.7 kPa and xylene = 28 kPa.

**Problem 7.30:** For the system n-pentane (A)-n-heptane (B) the vapour pressures are given by the Antoine equation

where P is in kPa and T is in K. The constants are as follows:

System | A | B | C |

n-pentane | 13.8183 | 2477.07 | 40.00 |

n-heptane | 13.8587 | 2911.32 | 56.56 |

Assuming that the solution formed is ideal, calculate the following: (a) The composition of the liquid and the vapour in equilibrium at 130 kPa and 335 K (b) The composition of the vapour in equilibrium with a liquid containing 30% (mol) pentane and the equilibrium temperature at P = 100 kPa (c) The total pressure and the vapour composition in equilibrium with a liquid of composition x = 0.40 at T = 335 K.

**Problem 7.31:** The vapour pressures of ethanol and water are given by the Antoine equation. The Antoine constants are:

Name | A | B | C |

Water | 16.26205 | 3799.887 | 46.854 |

Ethyl alcohol | 16.5092 | 3578.91 | 50.50 |

Compare the equilibrium data calculated using Raoult’s law with the experimental values given below:

T (K) | 373.2 | 368.7 | 359.9 | 357.3 | 355.5 | 353.9 | 351.94 | 351.61 | 351.35 | 351.61 |

x | 0 | 0.019 | 0.097 | 0.166 | 0.261 | 0.397 | 0.676 | 0.747 | 0.894 | 1 |

y | 0 | 0.17 | 0.438 | 0.509 | 0.558 | 0.612 | 0.739 | 0.782 | 0.894 | 1 |

An ethanol-water solution containing 25% by mole ethanol at 313 K is being heated in a closed container at a constant pressure of 101.3 kPa. Calculate the following using the experimental values: (a) The temperature at which vaporization begins (b) The composition of the first bubble of vapour formed (c) The composition of the residual liquid when 25 mole % is vaporized.

**Problem 7.32: **An aqueous solution of acetaldehyde contains 1% acetaldehyde by weight. The partial pressure of acetaldehyde over the solution is found to be 20.6 kPa at 367 K. What will be the partial pressure over a 0.1 molal solution at the same temperature?

**Problem 7.33: **Henry’s law constant for oxygen in water at 298 K is 4.4×10^{4} bar. Estimate the solubility of oxygen in water at 298 K for partial pressure of oxygen of 0.25 bar.

**Problem 7.34: **How many cubic metres of oxygen at 100 kPa can be dissolved in 10 kg water at 293 K if Henry’s law constant for oxygen in water at 293 K is 4.4×10^{9} N/m^{2}?

**Problem 7.35: **At 293 K, the solubility of oxygen in water is found to be 1 g in 100 g water for a partial pressure of 0.25 bar for oxygen. Estimate Henry’s law constant of oxygen in water at 293 K.

**Problem 7.36: **The partial pressure of acetone (A) and chloroform (B) were measured at 298 K and are reported below:

x_{B} | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |

p_{A} (bar) | 0.457 | 0.355 | 0.243 | 0.134 | 0.049 | 0 |

p_{B} (bar) | 0 | 0.046 | 0.108 | 0.187 | 0.288 | 0.386 |

Determine Henry’s law constants.

**Problem 7.37: **Calculate the concentration of nitrogen in water exposed to air at 298 K and 1 bar if Henry’s law constant for nitrogen in water is 8.68×10^{4} bar at this temperature. Express the result in moles of nitrogen per kg water (Hint: Air is 79 percent nitrogen by volume).

**Problem 7.38: **The partial pressure of methyl chloride in a mixture varies with its mole fraction at 298 K as detailed below:

X | 0.0005 | 0.0009 | 0.0019 | 0.0024 |

p (bar) | 0.27 | 0.48 | 0.99 | 1.24 |

Estimate Henry’s law constant of methyl chloride.

**Problem 7.39:** A solution contains 50.0% n-pentane, 30.0% n-hexane and 20.0% n-heptane. The Antoine constants for the constituents are given below:

Name | A | B | C |

n-pentane | 13.8183 | 2477.07 | 39.94 |

n-hexane | 13.8216 | 2697.55 | 48.78 |

n-heptane | 13.8587 | 2911.32 | 56.51 |

Assuming that Raoult’s law is applicable, determine the following: (a) The dew-point pressure of the mixture at 295 K (b) The dew-point temperature at 400 kPa (c) The bubble-point temperature at 400 kPa (d) The bubble-point pressure at 295 K.

**Problem 7.40: **A solution of hydrocarbons contains n-propane 5.0%, n-butane 30.0%, n-pentane 40.0% and n-hexane 25.0%. Compute the bubble point and the dew point at 350 kPa. The K-values can be taken from the De Priester nomographs.

**Problem 7.41: **A mixture of hydrocarbon vapours containing 21.8% ethane, 66.5% propane, 10.73% isobutane and 0.97% n-butane is cooled at a constant temperature of 311 K. Using the following K values determine the dew-point pressure and the liquid composition.

Component | P = 1310 kPa | P = 1380 kPa | P = 1450 kPa |

Ethane | 3.22 | 3.07 | 2.92 |

Propane | 1.005 | 0.973 | 0.92 |

Isobutane | 0.45 | 0.43 | 0.41 |

n-butane | 0.315 | 0.305 | 0.295 |

**Problem 7.42: **A solution has the following composition in mol %: ethane 0.25%, propane 25.00%, isobutane 18.5%, n-butane 56.0%, isopentane 0.25%. For a pressure of 10 bars, calculate the following: (a) The bubble point (b) The dew-point (c) The composition of the liquid and vapour when 40% of the mixture is vaporized.

**Problem 7.43:** 1000 moles of a mixture of the following composition is contained in a vessel at 2200 kPa and 355 K.

Component | Mole percent | K value |

Methane | 16.0 | 8.8 |

Ethane | 23.0 | 1.82 |

Propane | 36.0 | 0.71 |

Isobutane | 11.0 | 0.35 |

n-butane | 14.0 | 0.27 |

How many moles of liquid and vapor will be there under these conditions? Also, calculate the liquid and vapor compositions.

**Problem 7.44: **A stream of gas in a natural gasoline plant has the following composition by volume: ethane 10%, propane 14%, isobutane 19%, n-butane 54% and isopentane 3%. (a) Calculate the pressure necessary to condense this gas completely at 311 K. (b) For a condenser operating at the pressure in part (a), calculate the temperature at which condensation starts and the temperature at which 50 mol % of the vapour gets condensed. Also, calculate the composition of the first liquid to condense and the composition of the liquid and vapour phases at 50% condensation.

**Problem 7.45 **Determine the composition of the vapour in equilibrium with the liquid and the pressure of the system at 313 K for a liquid mixture of 5 mol % methane, 10 mol % ethane, 30 mol % propane, 25 mol % iso-butane, and 30 mol % n-butane. Determine the pressure and the composition of the liquid in equilibrium with a vapour mixture of the above composition.

**Problem 7.46: **Calculate the pressure at which condensation starts and the pressure at which condensation is complete when a vapour mixture of the following composition is subjected to condensation at a temperature of 300 K: 20 mol % ethylene, 20 mol % ethane, 40 mol % propane and 20 mol % n-butane.

**Problem 7.47: **A vapour mixture containing 15% ethane, 20% propane, 60% isobutane and the rest of n-butane is subjected to partial condensation so that 75% of the vapour is condensed. If the condenser temperature is 300 K, determine the pressure.

**Problem 7.48: **An equimolar mixture of propane (1) and n-butane (2) is partially condensed so that 50 mol % of the mixture is in the liquid state at 311 K. Using the De Priester nomograph, determine the following: (a) The pressure (b) The vapour and liquid compositions (c) The pressure at which condensation begins at the constant temperature of 311 K.

**Problem 7.49: **The following table gives the vapor pressures of alcohols in kPa at different temperatures (K).

T (K) | Vapor pressure (kPa) Methanol | Vapor pressure (kPa) Ethanol | Vapor pressure (kPa) n-Propanol | Vapor pressure (kPa) n-Butanol |

323 | 55.3 | 29.3 | 11.9 | 4.5 |

333 | 83.9 | 46.9 | 19.9 | 7.9 |

338 | 102.2 | 58.4 | 25.3 | 10.4 |

343 | 123.9 | 72.3 | 32.1 | 13.3 |

348 | 149.2 | 88.7 | 40.3 | 17.5 |

353 | 178.5 | 108.3 | 50.1 | 22.0 |

358 | 212.4 | 131.2 | 62.0 | 27.5 |

363 | 251.2 | 158.0 | 76.1 | 30.1 |

373 | 346.4 | 227.4 | 112.4 | 51.7 |

For an alcohol mixture of composition 30% methanol, 20% ethanol, 15% n-propanol and 35% n-butanol, calculate the following for a total pressure of 101.3 kPa: (a) The bubble-point temperature and vapour composition (b) The dew-point temperature and liquid composition.

**Problem 7.50: **Ethyl ether and water are charged into a still in the weight ratio 3:1 and allowed to boil. Ether and water are immiscible. The temperature of the contents is maintained at 303 K at which the vapour pressures of the pure liquids are 4.2 kPa for water and 80 kPa for ether. Calculate the following: (a) The pressure inside the still (b) The composition of the residual liquid when half the original mixture is vaporized.

**Problem 7.51: **A vapour mixture contains 85% (mol) benzene and 15% (mol) water at 101 kPa and 373 K. Assume that liquid benzene and water are immiscible. The vapour pressures are given by Antoine equations, the constants of which are:

Name | A | B | C |

Benzene | 13.8858 | 2788.51 | 52.36 |

Water | 16.26205 | 3799.887 | 46.854 |

(a) On cooling this vapour at constant pressure, at what temperature does condensation begin and what is the composition of the condensate? (b) If cooling is continued, at what temperature do both liquids condense together?

**Problem 7.52: **A liquid of molecular weight 150 is insoluble in water and is to be purified by steam distillation at a total pressure of 101.3 kPa. The vapour pressure of the liquid at the temperature of distillation is 3.5 kPa. How many kilograms of steam is required theoretically to distil one kilogram of the liquid?

**Problem 7.53:** A high-boiling organic liquid (MW = 185) is being steam-distilled. The vapour temperature is measured to be 374.2 K. (a) What is the pressure in the still? (b) If the vapour analysed 87% water by weight, what is the vaporization efficiency? (The vaporization efficiency may be defined as the ratio of the minimum steam required for steam distillation to the actual steam consumption.) The vapour pressure of water at 374.2 K is 105 kPa and that of the organic liquid is 2.3 kPa.

**Problem 7.54: **It is proposed to purify benzene from small amounts of non-volatile impurities by subjecting it to distillation with saturated steam at 99.3 kPa. Calculate the temperature at which distillation will proceed and the weight of steam accompanying 1 kg benzene. The vapour pressure data is given below:

T (K) | 323 | 333 | 343 | 348 | 353 | 363 | 373 |

P_{water}^{S} (kPa) | 12.40 | 19.86 | 31.06 | 37.99 | 47.32 | 70.11 | 101.3 |

P_{benzene}^{S} (kPa) | 35.85 | 51.85 | 72.91 | 85.31 | 100.50 | 135.42 | 179.14 |

**Problem 7.55: **Benzene (1) is to be purified from non-volatile impurities by subjecting it to steam distillation at a pressure of 100 kPa. It may be assumed that benzene is immiscible with water (2). The following vapour pressure data are available:

T (K) | 323 | 333 | 343 | 348 | 353 | 363 | 373 |

P_{1}^{S} (kPa) | 35.85 | 51.85 | 72.91 | 85.31 | 100.50 | 135.42 | 179.14 |

P_{2}^{S} (kPa) | 12.40 | 19.86 | 31.06 | 37.99 | 47.32 | 70.11 | 101.3 |

Determine the following: (a) The temperature of distillation (b) The mole fraction of benzene in the vapour (c) The mass of steam required to distil 1 kg benzene.

**Problem 7.56: **Ethyl aniline is purified from dissolved non-volatile impurities by steam distillation at 101.3 kPa pressure. The vapour pressure of aniline and water are as follows:

T (K) | 353.8 | 369.2 | 373.3 | 386.4 |

Aniline (kPa) | 1.33 | 2.67 | 3.04 | 5.33 |

Water (kPa) | 48.5 | 87.7 | 98.3 | 163.3 |

Calculate the following: (a) The boiling points of the mixture (b) The composition of the distillate.

**Problem 7.57: **A mixture containing chlorobenzene and water is being distilled. The liquids may be assumed immiscible. The distillation is carried out under such conditions that two liquid layers are present in the still. The vapour pressure data is as follows:

For Chlorobenzene,

\ln P^S=13.9926-\frac{3295.12}{T-55.60}For water,

\ln P^S=16.26205-\frac{3799.887}{T-46.854}Determine the temperature of distillation and the composition of the vapour if (a) The pressure is 4 kPa. (b) The pressure is 40 kPa.

**Problem 7.58 **It is desired to separate CHCl_{3} from a non-volatile insoluble impurity by steam distillation at a total pressure of 175 kPa. Saturated steam at 200 kPa is introduced directly into the liquid. Calculate: (a) The boiling point of the mixture (b) The composition of the distillate (c) The composition of the distillate if 20% more steam than the theoretical amount distils over. The vapour pressure data are as follows:

T (K) | 299.1 | 315.9 | 334.5 | 357.05 | 393.2 |

Chloroform (kPa) | 26.7 | 53.3 | 101.3 | 202.7 | 506.6 |

Water (kPa) | 3.3 | 8.5 | 21.1 | 55.3 | 198.2 |

**Problem 7.59: **A gas mixture contained 2×10^{5} kg of hexane and 5×10^{3} kg of water vapour at 373 K and 200 kPa. The mixture is cooled at constant pressure till water begins to condense. Assume that hexane and water are immiscible in the liquid phase. (a) What is the initial partial pressure of hexane in the gas? (b) What is the temperature at which condensation begins?

The vapour pressure of n-hexane is given by the Antoine equation with the following constants when pressure is in kPa and temperature in K: A = 13.8216, B = 2697.55 and C = 48.78

**Problem 7.60: **A vapour mixture contains 85 mol% CS_{2} and 15 mol% H_{2}0 at 101.3 kPa and 373 K. The liquids CS_{2} and H_{2}0 are immiscible. Vapour pressure data for the pure fluids are given as follows:

T (K) | 283.2 | 293.2 | 303.2 | 313.2 | 323.2 | 333.2 |

CS_{2} (kPa) | 26.34 | 39.69 | 57.95 | 82.35 | 114.26 | 155.15 |

Water (kPa) | 1.227 | 2.337 | 4.241 | 7.375 | 12.34 | 19.92 |

The vapour is cooled at 101.3 kPa till condensation begins. Determine the following: (a) The temperature at which condensation begins (b) The composition of the first condensate (c) The temperature at which both liquids condense together.

**Problem 7.61 **Dimethylaniline is distilled with steam at 90 kPa to free it from non-volatile impurities. Assuming it to be completely immiscible with water, determine the following: (a) The distillation temperature (b) The composition of the vapour produced. The vapour pressure data are as follows:

T (K) | 343.2 | 374.8 | 399 |

P^{S} (aniline), kPa | 1.333 | 5.332 | 13.329 |

P^{S} (water), kPa | 31.19 | 106.91 | 285.86 |

The plot of ln P^{S} versus 1/T may be assumed linear.

**Problem 7.62** A stream contains 30 mol % toluene, 40 mol % ethyl benzene and 30 mol % water. Assuming that mixtures of ethylbenzene and toluene obey Raoult’s law and they are completely immiscible in water, calculate the following for a total pressure of 101.3 kPa: (a) The bubble-point temperature and the composition of the vapour (b) The dew-point temperature and the composition of the liquid. The vapour pressure data are given below:

T (K) | 352.6 | 361.0 | 366.5 | 383.2 | 388.8 |

P^{S} (water), kPa | 46.29 | 64.33 | 79.42 | ||

P^{S} (toluene), kPa | 38.49 | 50.65 | 60.78 | 99.27 | 116.50 |

P^{S} (ethyl benzene), kPa | 16.41 | 22.79 | 27.35 | 47.61 | 56.73 |

**Problem 7.63: **n-heptane (1) and water (2) are essentially immiscible as liquids. A vapour mixture containing 65 mol % water at 373 K and 101.3 kPa is cooled slowly at constant pressure until condensation is complete. Construct a plot for the process showing temperature versus equilibrium mole fraction of heptane in the residual vapour. For n-heptane,

The vapour pressure of water is

\ln P^S=16.26205-\frac{3799.887}{T-46.854}where P is in kPa and T in K.

**Problem 7.64: **Toluene (1) and water (2) are essentially immiscible in the liquid state. Determine the dew-point temperature and the composition of the first drops of liquid formed when the vapour mixtures of these species contain (a) 23 mol % toluene and (b) 77 mol % toluene at 101.3 kPa. At 101.3 kPa, what are the bubble-point temperature and the composition of the last drop of vapour in each case? The vapour pressure of toluene is

The vapour pressure of water is

\ln P^S=16.26205-\frac{3799.887}{T-46.854}where P is in kPa and T is in K.

**Problem 7.65: **Components 1 and 2 are insoluble in the liquid phase. Estimate the dew-point temperature and the compositions of the first drops of liquid formed when vapour mixtures of components 1 and 2 containing (a) 75 mol % component 1 and (b) 25 mol % component 1 are cooled at a constant pressure of 101.33 kPa. The vapour pressures of the pure components in kPa are given against temperature in K in the following table.

T (K) | 358 | 363 | 368 | 373 | 378 | 383 | 388 | 393 | 398.6 |

P_{1}^{S} (kPa) | 23.53 | 33.56 | 39.58 | 46.59 | 54.62 | 63.97 | 74.32 | 86.34 | 101.33 |

P_{2}^{S} (kPa) | 57.82 | 70.13 | 84.53 | 101.33 | 120.79 | 143.28 | 169.02 | 198.51 | 239.54 |

**Problem 7.66 **An aqueous solution containing 20% by weight dissolved non-volatile solute (MW = 120) is sent to a flash distillation chamber maintained at 5 kPa and 330 K. The effective vapour pressure of the solution (p) is given as

where x_{w} and P_{w}^{S} are the mole fraction of water in the solution and the vapour pressure of pure water respectively. The vapour pressure of water at 330 K is 17.147 kPa. Per 100 kg of the solution, determine the following: (a) The amount of pure water obtained as vapour (b) The concentration of the solute in the liquid leaving the chamber.

**Problem 7.67: **A liquid mixture consisting of 15% A, 70% B and 15% C is flashed at 250 K and 10 kPa. All compositions are on a mole basis. The vapour pressure of component C is negligible in comparison with those of A and B. The vaporization equilibrium constants of A and B may be taken as 5.25 and 0.65 respectively. Determine the following: (a) The moles of liquid and vapour at equilibrium (b) The mole fractions in the liquid and vapour.

**Problem 7.68: **The normal boiling point of a 5-molal solution of sodium chloride in water is found to be 379.2 K. The vapour pressure of water at this temperature is 124.8 kPa. Assuming that the relative vapour pressure is independent of temperature, determine the vapour pressure of the solution at 300 K if the vapour pressure of water at 300 K is 3.5 kPa.

**Problem 7.69: **The normal boiling point of a 5-molal solution of sodium chloride in water is found to be 379.2 K. What will be the boiling point of the solution at 80 kPa? The vapour pressure of water is given by

where P is in kPa and T is in K. Assume that the relative vapour pressure is independent of temperature.

**Problem 7.70: **The normal boiling point of a 10 molal solution of sodium nitrate in water is 382 K. Determine the following: (a) The boiling point elevation of the solution (b) The boiling point elevation at 50 kPa. Assume that the vapour pressure of water is given by the Antoine equation

where P is in kPa and T is in K, and the relative vapor pressure is independent of temperature.