# Chapter 6: Vapor Pressure (Solution)

**Problem 6.1: **The vapor pressure of ethyl ether at 273 K is 25 kPa and its latent heat of vaporization is 4.185×10^{2} kJ/kg. Using the Clausius-Clapeyron equation, estimate the vapor pressure at 293 K and 308 K.

**Problem 6.2: **The vapor pressure of ethyl ether at 273 K is 25 kPa and at 293 K is 63.5 kPa. Estimate the latent heat of vaporization of ether in kJ/kg in this temperature range.

**Problem 6.3: **Using the Clausius-Clapeyron equation [Eq. (6.5)], calculate the vapor pressure of water as a function of temperature and compare the result with the following values taken from steam tables.

T (K) | 273 | 293 | 313 | 323 | 333 | 353 | 373 |

P^{S} (kPa) | 0.61 | 2.33 | 7.37 | 12.34 | 19.90 | 47.35 | 101.3 |

The latent heat of vaporization of water at the triple point (0.611 kPa, 273.16 K) is 45.05 kJ/mol and that at the normal boiling point (101.325 kPa, 373.15 K) is 40.66 kJ/mol. These may be assumed constant for the lower temperature range and the higher temperature range respectively.

**Problem 6.4: **Nitrogen from a cylinder is bubbled through acetone at 1.1 bar and 323 K at the rate of 2×10^{-4} m^{3}/min. The nitrogen saturated with acetone vapor leaves at 1.013 bar, 308 K at the rate of 3.83×10^{-4} m^{3}/min. What is the vapor pressure of acetone at 308 K?

**Problem 6.5: **Mercury has a density of 13.69×10^{3} kg/m^{3} in the liquid state and 14.193×10^{3} kg/m^{3} in the solid state both measured at the melting point of 234.33 K at 1 bar. If the heat of fusion of mercury is 9.7876 kJ/kg, what is the melting point of mercury at 10 bar?

**Problem 6.6: **The vapor pressure of chloroform is given by the Antoine equation

where pressure is in kPa and temperature in K. Determine (a) the boiling point of chloroform at 50 kPa and (b) the vapor pressure at 300 K.

**Problem 6.7: **The Antoine constants of acrylonitrile are A = 13.9103, B = 2782.21, and C = 51.15 when the vapor pressure is in kPa and temperature in K. Calculate the vapor pressure at 300 K.

**Problem 6.8: **How many kilograms of acetone must have vaporized before an atmospheric chamber of volume 10 cubic meters gets saturated with the vapors of acetone at 313 K? The Antoine constants (pressure in kPa and temperature in K) for acetone are A = 14.5463, B = 2940.46, and C = 49.15.

**Problem 6.9: **The vapor pressure of water (kPa) is represented by the equation

where A = 3.142 and b = 0.163 and temperature is in K. If the vapor pressure of water at 303.15 K is 4.241 kPa and the critical temperature of the water is 647.3 K, what is the vapor pressure of water at 350 K? Get the vapor pressure of water from steam tables and calculate the percent deviation.

**Problem 6.10: **Air at 300 K and 1.0 bar containing 0.02 moles water per mole dry air is compressed and stored at 100 bar and 300 K for use in an experimental wind tunnel. How much water will condense in the high-pressure storage vessel per 100 cubic meters of air compressed? The vapor pressure of water at 300 K = 3.564 kPa.

**Problem 6.11: **A stream of gas at 302 K and 100 kPa, 50% saturated with water vapor is passed through a drying tower where 90% of the water vapor is removed. For 100 cubic meters of gas admitted through the tower, how many kilograms of water is removed? The vapor pressure of water at 302 K is 4.0 kPa.

**Problem 6.12: **Prepare the Cox chart for n-heptane if the vapor pressures are 12.28 kPa at 313 K and 105.60 kPa at 373 K. Estimate the vapor pressure of n-heptane at 333 K using the chart. If the experimental value is 27.91 kPa, what is the percent deviation in the estimate? The following data for the vapor pressure of water is taken from steam tables:

T (K) | 273 | 293 | 313 | 323 | 333 | 353 | 373 |

P^{S} (kPa) | 0.61 | 2.33 | 7.37 | 12.34 | 19.90 | 47.35 | 101.3 |

**Problem 6.13: **Construct the Cox chart for predicting the vapor pressure of ethanol and using the chart estimate the normal boiling point of ethanol and the vapor pressure at 323 K. By how much % do these values depart from the actual values? The vapor pressure of ethanol at 293 K and 363 K are respectively, 5.76 kPa and 157.03 kPa. The vapor pressure of water is as follows:

T (K) | 273 | 293 | 313 | 323 | 333 | 353 | 373 |

P^{S} (kPa) | 0.61 | 2.33 | 7.37 | 12.34 | 19.90 | 47.35 | 101.3 |

The experimental value of the normal boiling point is 351.7 and the vapor pressure at 323 K is 29.2 kPa.

**Problem 6.14: **The following data refer to the vapor pressure of sulfur dioxide:

T (K) | 279.5 | 328.7 |

P^{S} (kPa) | 202.7 | 1013 |

(a) Fit the data into an equation of the form \ln P^S=A-\frac B{T-43} where P^{S} is in kPa and T in K. (b) What is the vapor pressure of sulfur dioxide at 373 K?

**Problem 6.15: **The boiling points of methanol, ethanol and n-propanol at 8 kPa are 285.25 K, 299.15 K, and 316.65 K respectively. Construct the Cox chart for methanol and ethanol given that their normal boiling points are 337.85 K and 351.7 K respectively. Using this chart predict the normal boiling point of n-propanol. How does your result compare with the experimental value of 370.95 K? The vapor pressure of water is given below:

T (K) | 273 | 293 | 313 | 323 | 333 | 353 | 373 |

P^{S} (kPa) | 0.61 | 2.33 | 7.37 | 12.34 | 19.90 | 47.35 | 101.3 |

**Problem 6.16: **The following table gives the vapor pressures of benzene and water. Plot the reference temperature vapor pressure curve with the logarithm of the vapor pressure of benzene on the y-axis and the logarithm of the vapor pressure of water on the x-axis.

T (K) | 288.6 | 299.3 | 315.4 | 333.8 | 353.3 | 377.0 | 415.7 | 452 |

(kPa) | 8 | 13.3 | 26.7 | 53.3 | 101.3 | 202.7 | 506.6 | 1013.0 |

(kPa) | 1.8 | 3.4 | 8.3 | 26.1 | 49.0 | 116.3 | 382.5 | 980.0 |

(a) Determine the vapor pressure of benzene at 373 K. (b) Determine the latent heat of vaporization of benzene at 298 K given that the latent heat of vaporization of water at 298 K is 2443 kJ/kg. Compare your result with the experimental value of 434 kJ/kg.

**Problem 6.17: **Construct the Dühring line for ethylene glycol if it is given that its normal boiling point is 470.45 K and the boiling point at a pressure of 8 kPa is 402.65 K. The vapor pressure of water is given below: \ln P^S=16.26205-\frac{3799.887}{T-46.854} (a) By how much does the vapor pressure of ethylene glycol at 432 K deviate from the experimental value of 26.66 kPa? (b) What is the boiling point of ethylene glycol at 2.67 kPa?

**Problem 6.18: **Construct the Dühring line for ethanol if it is known that the vapor pressure of ethanol at 299.1 K is 8 kPa and that at 351.55 K is 101.3 kPa. The vapor pressure of water is given by the Antoine equation

where pressure is in kPa and temperature is in K. Compare the vapor pressure of ethanol at 321.6 K given by the Dühring line with the experimental value 26.66 kPa.