Chapter 10

Beaker \(\mathrm{A}\) has \(1.00 \mathrm{~mol}\) of chloroform, \(\mathrm{CHCl}_{3}\), at \(27^{\circ} \mathrm{C}\). Beaker \(\mathrm{B}\) has \(1.00 \mathrm{~mol}\) of carbon tetrachloride, \(\mathrm{CCl}_{4}\), also at \(27^{\circ} \mathrm{C}\). Equal masses of a nonvolatile, nonreactive solute are added to both beakers. In answering the questions below, the following data may be helpful. $$ \begin{array}{lll} \hline & \mathrm{CHCl}_{3}(\mathrm{~A}) & \mathrm{cCl}_{4}(\mathrm{~B}) \\ \hline \text { Vapor pressure at } 27^{\circ} \mathrm{C} & 0.276 \text { atm } & 0.164 \text { atm } \\ \text { Boiling point } & 61.26^{\circ} \mathrm{C} & 76.5^{\circ} \mathrm{C} \\\ k_{\mathrm{b}}\left({ }^{\circ} \mathrm{C} / \mathrm{m}\right) & 3.63 & 5.03 \\\ \hline \end{array} $$ Write \(<,>,=\), or more information needed in the blanks provided. (a) Vapor pressure of solvent over beaker B of solvent over beaker \(\mathrm{A}\). (b) Boiling point of solution in beaker \(A\) boiling point of solution in beaker B. (c) Vapor pressure of pure \(\mathrm{CHCl}_{3} \longrightarrow\) vapor pressure of solvent over beaker \(\mathrm{A}\). (d) Vapor pressure lowering of solvent in beaker A pressure lowering of solvent in beaker B. (e) Mole fraction of solute in beaker \(\mathrm{A}\) mole fraction of solute in beaker \(\mathrm{B}\).

A solution contains \(158.2 \mathrm{~g}\) of \(\mathrm{KOH}\) per liter; its density is \(1.13 \mathrm{~g} / \mathrm{mL}\). A lab technician wants to prepare \(0.250 \mathrm{~m} \mathrm{KOH}\), starting with \(100.0 \mathrm{~mL}\) of this solution. How much water or solid KOH should be added to the \(100.0-\mathrm{mL}\) portion?

Show that the following relation is generally valid for all solutions: $$ \text { molality }=\frac{\text { molarity }}{d-\frac{\mathrm{MM}(\mathrm{molarity})}{1000}} $$ where \(d\) is solution density \(\left(\mathrm{g} / \mathrm{cm}^{3}\right)\) and \(\mathrm{MM}\) is the molar mass of the solute. Using this equation, explain why molality approaches molarity in dilute solution when water is the solvent, but not with other solvents.

The water-soluble nonelectrolyte \(\mathrm{X}\) has a molar mass of \(410 \mathrm{~g} / \mathrm{mol}\). A \(0.100\) -g mixture containing this substance and sugar \((\mathrm{MM}=342 \mathrm{~g} / \mathrm{mol})\) is added to \(1.00 \mathrm{~g}\) of water to give a solution whose freezing point is \(-0.500^{\circ} \mathrm{C}\). Estimate the mass percent of \(\mathrm{X}\) in the mixture.

When water is added to a mixture of aluminum metal and sodium hydroxide, hydrogen gas is produced. This is the reaction used in commercial drain cleaners: $$ 2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{OH}^{-}(a q) \longrightarrow 2 \mathrm{Al}(\mathrm{OH})^{4-}(a q)+3 \mathrm{H}_{2}(g) $$ A sufficient amount of water is added to \(49.92 \mathrm{~g}\) of \(\mathrm{NaOH}\) to make \(0.600 \mathrm{~L}\) of solution; \(41.28 \mathrm{~g}\) of \(\mathrm{Al}\) is added to this solution and hydrogen gas is formed. (a) Calculate the molarity of the initial \(\mathrm{NaOH}\) solution. (b) How many moles of hydrogen were formed? (c) The hydrogen was collected over water at \(25^{\circ} \mathrm{C}\) and \(758.6 \mathrm{~mm} \mathrm{Hg}\). The vapor pressure of water at this temperature is \(23.8 \mathrm{~mm} \mathrm{Hg}\). What volume of hydrogen was generated?

It is found experimentally that the volume of a gas that dissolves in a given amount of water is independent of the pressure of the gas; that is, if \(5 \mathrm{~cm}^{3}\) of a gas dissolves in \(100 \mathrm{~g}\) of water at 1 atm pressure, \(5 \mathrm{~cm}^{3}\) will dissolve at a pressure of 2 atm, 5 atm, 10 atm, .... Show that this relationship follows logically from Henry's law and the ideal gas law.