Chapter 10

Assume that you place a freshwater plant into a saltwater solution and examine it under a microscope. What happens to the plant cells? What if you placed a saltwater plant in pure water? Explain. Draw pictures to illustrate your explanations.

How does \(\Delta H_{\text {soln }}\) relate to deviations from Raoult's law? Explain.

You have read that adding a solute to a solvent can both increase the boiling point and decrease the freezing point. A friend of yours explains it to you like this: "The solute and solvent can be like salt in water. The salt gets in the way of freezing in that it blocks the water molecules from joining together. The salt acts like a strong bond holding the water molecules together so that it is harder to boil." What do you say to your friend?

You drop an ice cube (made from pure water) into a saltwater solution at \(0^{\circ} \mathrm{C}\). Explain what happens and why.

Using the phase diagram for water and Raoult's law, explain why salt is spread on the roads in winter (even when it is below freezing).

You and your friend are each drinking cola from separate \(2-\mathrm{L}\) bottles. Both colas are equally carbonated. You are able to drink 1 L of cola, but your friend can drink only about half a liter. You each close the bottles and place them in the refrigerator. The next day when you each go to get the colas, whose will be more carbonated and why?

Is molality or molarity dependent on temperature? Explain your answer. Why is molality, and not molarity, used in the equations describing freezing-point depression and boiling point elevation?

Consider a beaker of salt water sitting open in a room. Over time, does the vapor pressure increase, decrease, or stay the same? Explain.

Rubbing alcohol contains 585 g isopropanol \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right)\) per liter (aqueous solution). Calculate the molarity.

What mass of sodium oxalate \(\left(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is needed to prepare \(0.250 \mathrm{L}\) of a \(0.100-M\) solution?

What volume of \(0.25 \mathrm{M}\) HCl solution must be diluted to prepare 1.00 L of \(0.040 M\) HCl?

What volume of a \(0.580-M\) solution of \(\mathrm{CaCl}_{2}\) contains \(1.28 \mathrm{g}\) solute?

Calculate the sodium ion concentration when \(70.0 \mathrm{mL}\) of 3.0 \(M\) sodium carbonate is added to \(30.0 \mathrm{mL}\) of \(1.0 \mathrm{M}\) sodium bicarbonate.

Write equations showing the ions present after the following strong electrolytes are dissolved in water. a. \(\mathrm{HNO}_{3}\) b. \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) c. \(A I\left(N O_{3}\right)_{3}\) d. \(\operatorname{SrBr}_{2}\) e. \(\mathrm{KClO}_{4}\) f. \(\mathrm{NH}_{4} \mathrm{Br}\) g. \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) h. \(\mathrm{CuSO}_{4}\) i. \(\quad\) NaOH

The weak electrolyte \(\mathrm{NH}_{3}(g)\) does not obey Henry's law. Why? \(\mathrm{O}_{2}(g)\) obeys Henry's law in water but not in blood (an aqueous solution). Why?

When pure methanol is mixed with water, the resulting solution feels warm. Would you expect this solution to be ideal? Explain.

For an acid or a base, when is the normality of a solution equal to the molarity of the solution and when are the two concentration units different?

In order for sodium chloride to dissolve in water, a small amount of energy must be added during solution formation. This is not energetically favorable. Why is NaCl so soluble in water?

Which of the following statements is(are) true? Correct the false statements. a. The vapor pressure of a solution is directly related to the mole fraction of solute. b. When a solute is added to water, the water in solution has a lower vapor pressure than that of pure ice at \(0^{\circ} \mathrm{C}\). c. Colligative properties depend only on the identity of the solute and not on the number of solute particles present. d. When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} \mathrm{C}\) because sugar has a higher boiling point than water.

Explain the terms isotonic solution, crenation, and hemolysis.

What is ion pairing?

A solution of phosphoric acid was made by dissolving \(10.0 \mathrm{g}\) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) in \(100.0 \mathrm{mL}\) water. The resulting volume was \(104 \mathrm{mL}\) Calculate the density, mole fraction, molarity, and molality of the solution. Assume water has a density of \(1.00 \mathrm{g} / \mathrm{cm}^{3}\).

An aqueous antifreeze solution is \(40.0 \%\) ethylene glycol \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\right)\) by mass. The density of the solution is \(1.05 \mathrm{g} / \mathrm{cm}^{3}\) Calculate the molality, molarity, and mole fraction of the ethylene glycol.

In lab you need to prepare at least \(100 \mathrm{mL}\) of each of the following solutions. Explain how you would proceed using the given information. a. \(2.0 \mathrm{m} \mathrm{KCl}\) in water (density of \(\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{g} / \mathrm{cm}^{3}\) ) b. \(15 \%\) NaOH by mass in water \(\left(d=1.00 \mathrm{g} / \mathrm{cm}^{3}\right)\) c. \(25 \%\) NaOH by mass in \(\mathrm{CH}_{3} \mathrm{OH}\left(d=0.79 \mathrm{g} / \mathrm{cm}^{3}\right)\) d. 0.10 mole fraction of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) in water \(\left(d=1.00 \mathrm{g} / \mathrm{cm}^{3}\right)\)

A solution is prepared by mixing 25 mL pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}, d=\right.\) \(\left.0.63 \mathrm{g} / \mathrm{cm}^{3}\right)\) with \(45 \mathrm{mL}\) hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}, d=0.66 \mathrm{g} / \mathrm{cm}^{3}\right)\) Assuming that the volumes add on mixing, calculate the mass percent, mole fraction, molality, and molarity of the pentane.

A solution is prepared by mixing \(50.0 \mathrm{mL}\) toluene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3},\right.\) \(d=0.867 \mathrm{g} / \mathrm{cm}^{3}\) with \(125 \mathrm{mL}\) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}, d=0.874 \mathrm{g} / \mathrm{cm}^{3}\right)\) Assuming that the volumes add on mixing, calculate the mass percent, mole fraction, molality, and molarity of the toluene.

Calculate the molarity and mole fraction of acetone in a \(1.00-m\) solution of acetone \(\left(\mathrm{CH}_{3} \mathrm{COCH}_{3}\right)\) in ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right) .\) (Density of acetone \(=0.788 \mathrm{g} / \mathrm{cm}^{3} ;\) density of ethanol \(=0.789\) \(\mathrm{g} / \mathrm{cm}^{3} .\) ) Assume that the volumes of acetone and ethanol add.

A \(1.37-M\) solution of citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) in water has a density of \(1.10 \mathrm{g} / \mathrm{cm}^{3} .\) Calculate the mass percent, molality, mole fraction, and normality of the citric acid. Citric acid has three acidic protons.

Calculate the normality of each of the following solutions. a. \(0.250 M\space \mathrm {HCl}\) b. \(0.105 M\space \mathrm{H}_{2} \mathrm{SO}_{4}\) c. \(5.3 \times 10^{-2} M \space \mathrm{H}_{3} \mathrm{PO}_{4}\) d. \(0.134 M\space \mathrm{NaOH}\) e. \(0.00521 M \space \mathrm{Ca}(\mathrm{OH})_{2}\) What is the equivalent mass for each of the acids or bases listed above?

The lattice energy \(^{*}\) of Nal is \(-686 \mathrm{kJ} / \mathrm{mol}\), and the enthalpy of hydration is \(-694 \mathrm{kJ} / \mathrm{mol} .\) Calculate the enthalpy of solution per mole of solid NaI. Describe the process to which this enthalpy change applies.

a. Use the following data to calculate the enthalpy of hydration for calcium chloride and calcium iodide. $$\begin{array}{|llc|} \hline & \text { Lattice Energy } & \Delta H_{\text {soln }} \\ \hline \mathrm{CaCl}_{2}(s) & -2247 \mathrm{kJ} / \mathrm{mol} & -46 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{Cal}_{2}(s) & -2059 \mathrm{kJ} / \mathrm{mol} & -104 \mathrm{kJ} / \mathrm{mol} \\ \hline \end{array}$$ b. Based on your answers to part a, which ion, \(\mathrm{Cl}^{-}\) or \(\mathrm{I}^{-}\), is more strongly attracted to water?

The high melting points of ionic solids indicate that a lot of energy must be supplied to separate the ions from one another. How is it possible that the ions can separate from one another when soluble ionic compounds are dissolved in water, often with essentially no temperature change?

Which solvent, water or carbon tetrachloride, would you choose to dissolve each of the following? a. \(\mathrm{KrF}_{2}\) b. \(\mathrm{SF}_{2}\) c. \(\mathrm{SO}_{2}\) d. \(\mathrm{CO}_{2}\) {e} .\( \mathrm {M g F}_{2}\) {f .} \(\mathrm {C H}_{2} \mathbf{O}\) g. \(\mathrm{CH}_{2}=\mathrm{CH}_{2}\)

Which solvent, water or hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right),\) would you choose to dissolve each of the following? a. \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) b. \(\mathrm{CS}_{2}\) c. \(\mathrm{CH}_{3} \mathrm{OH}\) d. \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{CH}_{2} \mathrm{OH}\) e.\(\mathrm HCl\) {f .} \( \mathrm{C}_{6} \mathrm{H}_{6}\)

Which ion in each of the following pairs would you expect to be more strongly hydrated? Why? a. \(\mathrm{Na}^{+}\) or \(\mathrm{Mg}^{2+}\) b. \(\mathrm{Mg}^{2+}\) or \(\mathrm{Be}^{2+}\) c. \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) d. \(F^{-}\) or \(B r^{-}\) e. \(\mathrm{Cl}^{-}\) or \(\mathrm{ClO}_{4}^{-}\) f. \( \mathrm{ClO}_{4}^{-}\) or \(\mathrm{SO}_{4}^{2-}\)

Rationalize the trend in water solubility for the following simple alcohols: $$\begin{array}{lc} \text { Alcohol } & \begin{array}{c} \text { Solubility } \\ \left(\mathrm{g} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O} \text { at } 20^{\circ} \mathrm{C}\right) \end{array} \\ \hline \text { Methanol, } \mathrm{CH}_{3} \mathrm{OH} & \text { Soluble in all proportions } \\ \text { Ethanol, } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} & \text { Soluble in all proportions } \\ \text { Propanol, } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} & \text { Soluble in all proportions } \\ \text { Butanol, } \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{CH}_{2} \mathrm{OH} & 8.14 \\ \text { Pentanol, } \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{3} \mathrm{CH}_{2} \mathrm{OH} & 2.64 \\ \text { Hexanol, } \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CH}_{2} \mathrm{OH} & 0.59 \\ \text { Heptanol, } \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{5} \mathrm{CH}_{2} \mathrm{OH} & 0.09 \\ \hline \end{array}$$

In flushing and cleaning columns used in liquid chromatography to remove adsorbed contaminants, a series of solvents is used. Hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right),\) chloroform \(\left(\mathrm{CHCl}_{3}\right),\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right),\) and water are passed through the column in that order. Rationalize the order in terms of intermolecular forces and the mutual solubility (miscibility) of the solvents.

The solubility of nitrogen in water is \(8.21 \times 10^{-4} \mathrm{mol} / \mathrm{L}\) at \(0^{\circ} \mathrm{C}\) when the \(\mathrm{N}_{2}\) pressure above water is 0.790 atm. Calculate the Henry's law constant for \(\mathrm{N}_{2}\) in units of mol/L \cdot atm for Henry's law in the form \(C=k P,\) where \(C\) is the gas concentration in mol/L. Calculate the solubility of \(\mathrm{N}_{2}\) in water when the partial pressure of nitrogen above water is 1.10 atm at \(0^{\circ} \mathrm{C}\).

Calculate the solubility of \(\mathrm{O}_{2}\) in water at a partial pressure of \(\mathrm{O}_{2}\) of 120 torr at \(25^{\circ} \mathrm{C}\). The Henry's law constant for \(\mathrm{O}_{2}\) is \(1.3 \times 10^{-3} \mathrm{mol} / \mathrm{L} \cdot \mathrm{atm}\) for Henry's law in the form \(C=k P\) where \(C\) is the gas concentration (mol/L).

The vapor pressure of a solution containing 53.6 g glycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) in \(133.7 \mathrm{g}\) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is 113 torr at \(40^{\circ} \mathrm{C}\) Calculate the vapor pressure of pure ethanol at \(40^{\circ} \mathrm{C}\) assuming that glycerin is a nonvolatile, nonelectrolyte solute in ethanol.

The normal boiling point of diethyl ether is \(34.5^{\circ} \mathrm{C} .\) A solution containing a nonvolatile solute dissolved in diethyl ether has a vapor pressure of 698 torr at \(34.5^{\circ} \mathrm{C}\). What is the mole fraction of diethyl ether in this solution?

At a certain temperature, the vapor pressure of pure benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is 0.930 atm. A solution was prepared by dissolving \(10.0 \mathrm{g}\) of a nondissociating, nonvolatile solute in \(78.11 \mathrm{g}\) of benzene at that temperature. The vapor pressure of the solution was found to be 0.900 atm. Assuming the solution behaves ideally, determine the molar mass of the solute.

A solution is made by dissolving \(25.8 \mathrm{g}\) urea \(\left(\mathrm{CH}_{4} \mathrm{N}_{2} \mathrm{O}\right),\) a nonelectrolyte, in \(275 \mathrm{g}\) water. Calculate the vapor pressures of this solution at \(25^{\circ} \mathrm{C}\) and \(45^{\circ} \mathrm{C}\). (The vapor pressure of pure water is \(\left.23.8 \text { torr at } 25^{\circ} \mathrm{C} \text { and } 71.9 \text { torr at } 45^{\circ} \mathrm{C} .\right)\)

A solution of sodium chloride in water has a vapor pressure of 19.6 torr at \(25^{\circ} \mathrm{C} .\) What is the mole fraction of solute particles in this solution? What would be the vapor pressure of this solution at \(45^{\circ} \mathrm{C} ?\) The vapor pressure of pure water is 23.8 torr at \(25^{\circ} \mathrm{C}\) and 71.9 torr at \(45^{\circ} \mathrm{C},\) and assume sodium chloride exists as \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\) ions in solution.

Pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}\right)\) and hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) form an ideal solution. At \(25^{\circ} \mathrm{C}\) the vapor pressures of pentane and hexane are 511 and \(150 .\) torr, respectively. A solution is prepared by mixing \(25 \mathrm{mL} \text { pentane (density, } 0.63 \mathrm{g} / \mathrm{mL})\) with \(45 \mathrm{mL}\) hexane (density, 0.66 g/mL). a. What is the vapor pressure of the resulting solution? b. What is the composition by mole fraction of pentane in the vapor that is in equilibrium with this solution?

A solution is prepared by mixing 0.0300 mole of \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) and 0.0500 mole of \(\mathrm{CH}_{2} \mathrm{Br}_{2}\) at \(25^{\circ} \mathrm{C}\). Assuming the solution is ideal, calculate the composition of the vapor (in terms of molefractions) at \(25^{\circ} \mathrm{C} .\) At \(25^{\circ} \mathrm{C},\) the vapor pressures of pure \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) and pure \(\mathrm{CH}_{2} \mathrm{Br}_{2}\) are 133 and 11.4 torr, respectively.

Which of the following will have the lowest total vapor pressure at \(25^{\circ} \mathrm{C} ?\) a. pure water (vapor pressure \(=23.8\) torr at \(25^{\circ} \mathrm{C}\) ) b. a solution of glucose in water with \(\chi_{\mathrm{C}_{\mathrm{s}} \mathrm{H}_{\mathrm{l} 2} \mathrm{O}_{\mathrm{s}}}=0.01\) c. a solution of sodium chloride in water with \(\chi_{\mathrm{NaCl}}=0.01\) d. a solution of methanol in water with \(\chi_{\mathrm{CH_{3}}, \mathrm{OH}}=0.2\) (Consider the vapor pressure of both methanol \([143\) torr at \(\left.25^{\circ} \mathrm{C}\right]\) and water.

The vapor pressures of several solutions of water-propanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) were determined at various compositions, with the following data collected at \(45^{\circ} \mathrm{C}:\) $$\begin{array}{|lc|} \hline & \text { Vapor Pressure } \\ \chi_{\mathrm{H}_{2} \mathrm{O}} & \text { (torr) } \\ 0 & 74.0 \\ 0.15 & 77.3 \\ 0.37 & 80.2 \\ 0.54 & 81.6 \\ 0.69 & 80.6 \\ 0.83 & 78.2 \\ 1.00 & 71.9 \\ \hline \end{array}$$a. Are solutions of water and propanol ideal? Explain. b. Predict the sign of \(\Delta H_{\text {soln }}\) for water-propanol solutions. c. Are the interactive forces between propanol and water molecules weaker than, stronger than, or equal to the interactive forces between the pure substances? Explain. d. Which of the solutions in the data would have the lowest normal boiling point?

A \(2.00-\mathrm{g}\) sample of a large biomolecule was dissolved in 15.0 g carbon tetrachloride. The boiling point of this solution was determined to be \(77.85^{\circ} \mathrm{C}\). Calculate the molar mass of the biomolecule. For carbon tetrachloride, the boiling-point constant is \(5.03^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol},\) and the boiling point of pure carbon tetrachloride is \(76.50^{\circ} \mathrm{C}\)

What mass of glycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right),\) a nonelectrolyte, must be dissolved in \(200.0 \mathrm{g}\) water to give a solution with a freezing point of \(-1.50^{\circ} \mathrm{C} ?\)