Chapter 17

The conditions at the triple point of methanol are \(-98.15^{\circ} \mathrm{C}\) and 0.5 atm while those at its critical point are \(240^{\circ} \mathrm{C}\) and 78.5 atm. Use this information to sketch (not to scale) and fully label a phase diagram for methanol. (Section \(17.1)\).

Sulfur melts at a temperature of \(115.2^{\circ} \mathrm{C}\) under a pressure of 1 atm. In one process for its mining, sulfur is melted and pumped from underground deposits as a liquid under a pressure of 6 bar Use the Clapeyron equation to estimate the lowest temperature at which sulfur is a liquid at this pressure. (Section 17.2 ) (The enthalpy change of fusion at \(115.2^{\circ} \mathrm{C}\) is \(53.67 \mathrm{Jg}^{-1}\) and the densities of solid and liquid sulfur are \(2.15 \mathrm{gcm}^{-3}\) and \(1.811 \mathrm{gcm}^{-3},\) respectively.

The vapour pressure of tetrachloromethane \(\left(\mathrm{CCl}_{4}\right)\) at \(0^{\circ} \mathrm{C}\) is \(44.0 \mathrm{mbar}\) and at \(50^{\circ} \mathrm{C}\) it is \(422.0 \mathrm{mbar}\). Use these data to estimate the enthalpy change of vaporization of \(\mathrm{CCl}_{4}\) and to estimate its standard boiling point. (Section 17.2 )

Calculate the energy of attraction between a \(\mathrm{Mg}^{2+}\) ion and a CI ion separated by \(0.2 \mathrm{nm}\) in a vacuum. (Section 17.3 )

Compare the energy of interaction between two singly charged ions separated by a distance of \(0.1 \mathrm{nm}\) in (a) vacuum, (b) water (relative permittivity \(=78\) ), (c) a hydrocarbon oil (relative permittivity \(=2\) ). (Section 17.3 )

For each of the following pairs, which compound would you expect to have the higher enthalpy change of vaporization? Give the reason for your answer in each case. (Section 17.3 ) (a) Ethanol and methoxymethane (b) Propane and methoxymethane (c) Butane and propanone (d) \(E)-1,2\) -dichloroethene and \((Z)-1,2-\) dichloroethene

Arrange the following in order of increasing boiling point, giving detailed reasons for your answer. (Section 17.3 ) \\[\mathrm{He}, \mathrm{H}_{2} \mathrm{O}, \mathrm{Ar}, \mathrm{N}_{2}, \mathrm{HCl}, \mathrm{NaCl}\\]

A diver descends to a depth where the pressure is 5 atm. The diver's body contains around \(5 \mathrm{dm}^{3}\) of blood. The Henry's law constant for \(\mathrm{N}_{2}(\mathrm{g})\) in water at \(310 \mathrm{K}\) is \(1.07 \times 10^{5} \mathrm{atm}\) (Section \(17.4)\) (a) Calculate the amount of nitrogen gas absorbed from the air in the diver's blood at a pressure of 1 atm and at 5 atm. (Assume that the solubility of nitrogen in the blood is the same as in water.) (b) If all the gas dissolved at 5 atm was suddenly released, what volume would it occupy at 1 atm and \(298 \mathrm{K} ?\)

The vapour pressure of pure \(\mathrm{CHCl}_{3}\) at \(318 \mathrm{K}\) is \(58 \mathrm{kPa}\). What would be the partial vapour pressure of \(\mathrm{CHCl}_{3}\) above a mixture of \(1 \mathrm{mol}\) of \(\mathrm{CHCl}_{3}\) with \(1 \mathrm{mol}\) of ethanol, assuming the mixture behaves as an ideal solution? Comment on the fact that the measured value of the partial vapour pressure of \(\mathrm{CHCl}_{3}\) above the mixture is \(42 \mathrm{kPa} \text { . (Section } 17.4)\).

Ethanol and methanol form nearly ideal solutions. At \(20^{\circ} \mathrm{C}\), the vapour pressure of pure ethanol is 5930 Pa and of methanol is \(11830 \mathrm{Pa}\). (Section 17.4 ) Calculate (a) the vapour pressure of each compound and (b) the total vapour pressure over a solution formed by mixing \(50 g\) of each. \\[\left(M_{r}\left(\mathrm{CH}_{3} \mathrm{OH}\right)=32.04 ; \mathrm{M}_{r}\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)=46.07 .\right)\\]

A protein has a molar mass of \(69000 \mathrm{gmol}^{-1}\). Assuming ideal behaviour, calculate the osmotic pressure of a solution containing \(20 \mathrm{g} \mathrm{dm}^{-3}\) of the protein at \(298 \mathrm{K}\). (Section 17.4 )

A solution of iodoethane, \(1,\) and propanone, \(P\), with a mole fraction of \(I, x_{1}=0.55,\) had a partial vapour pressure of I of \(28.44 \mathrm{kPa}\) and a partial vapour pressure of \(\mathrm{P}\) of \(19.21 \mathrm{kPa}\) at \(50^{\circ} \mathrm{C} .\) At this temperature, the saturated vapour pressure of I is \(47.12 \mathrm{kPa}\) and of \(\mathrm{P}\) is \(37.38 \mathrm{kPa}\). Calculate the activity coefficients of both components in the solution. (Section 17.4 )

When a patient suffers severe dehydration, why will medical treatment involve giving 'saline' solution rather than pure water? (Section \(17.4)\)

The vapour pressure of pure toluene is 0.0285 bar at \(20^{\circ} \mathrm{C}\) and that of benzene is 0.0974 bar. One mole of each compound were mixed and formed an ideal solution. Calculate the mole fraction of each compound in the vapour over the solution. (Section \(17.4)\).