Chapter 11

Saccharin Determine the melting point of an aqueous solution made by adding \(186 \mathrm{mg}\) of saccharin \(\left(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{NS}\right)\) to \(\left.1.00 \mathrm{mL} \text { of water (density }=1.00 \mathrm{g} / \mathrm{mL}, K_{f}=1.86^{\circ} \mathrm{C} / \mathrm{m}\right)\)

Determine the boiling point of an aqueous solution that is \(2.50 \mathrm{m}\) ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right) ; K_{\mathrm{b}}\) for water is \(0.52^{\circ} \mathrm{C} / \mathrm{m} .\) Assume that the boiling point of pure water is \(100.00^{\circ} \mathrm{C}\)

Which aqueous solution has the lowest freezing point: \(0.5 \mathrm{m}\) glucose, \(0.5 \mathrm{m} \mathrm{NaCl},\) or \(0.5 \mathrm{m} \mathrm{CaCl}_{2} ?\)

Which aqueous solution has the highest boiling point: \(0.5 \mathrm{m}\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right), 0.5 \mathrm{m} \mathrm{KI},\) or \(0.5 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4} ?\)

Which of the following aqueous solutions should have the highest boiling point: \(0.0200 \mathrm{m}\) ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)\) \(0.0125 \mathrm{m} \mathrm{LiClO}_{4},\) or \(0.0100 \mathrm{m} \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Which of the following aqueous solutions should have the lowest freezing point: \(0.0500 \mathrm{m} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}, 0.0300 \mathrm{m} \mathrm{KBr}\) or \(0.0150 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4} ?\)

Arrange the following aqueous solutions in order of increasing boiling point: a. \(0.06 \mathrm{m} \mathrm{FeCl}_{3}(i=3.4)\) b. \(0.10 m \mathrm{MgCl}_{2}(i=2.7)\) c. \(0.20 \mathrm{m} \mathrm{KCl}(i=1.9)\)

The following pairs of aqueous solutions are separated by a semipermeable membrane. In which direction will the solvent flow? a. \(A=1.00 \mathrm{L}\) of \(0.48 M \mathrm{NaCl} ; \mathrm{B}=55.85 \mathrm{g}\) of \(\mathrm{NaCl}\) dissolved in \(1.00 \mathrm{L}\) of solution b. \(A=100 \mathrm{mL}\) of \(0.982 M \mathrm{CaCl}_{2} ; \mathrm{B}=16 \mathrm{g}\) of \(\mathrm{NaCl}\) in \(100 \mathrm{mL}\) of solution c. \(A=100 \mathrm{mL}\) of \(6.56 \mathrm{m} M \mathrm{MgSO}_{4} ; \mathrm{B}=5.24 \mathrm{g}\) of \(\mathrm{Mg} \mathrm{Cl}_{2}\) in 250 mL of solution

Calculate the osmotic pressure of each of the following aqueous solutions at \(20^{\circ} \mathrm{C}:\) a. \(2.39 M\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) b. \(9.45 \mathrm{mM} \mathrm{MgCl}_{2}\) c. \(40.0 \mathrm{mL}\) of glycerol \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) in \(250.0 \mathrm{mL}\) of aqueous solution (density of glycerol \(=1.265 \mathrm{g} / \mathrm{mL}\) ) d. \(25 \mathrm{g}\) of \(\mathrm{CaCl}_{2}\) in \(350 \mathrm{mL}\) of solution

Calculate the osmotic pressure of each of the following aqueous solutions at \(27^{\circ} \mathrm{C}\) a. \(10.0 \mathrm{g}\) of \(\mathrm{NaCl}\) in \(1.50 \mathrm{L}\) of solution b. \(10.0 \mathrm{mg} / \mathrm{L}\) of \(\mathrm{LiNO}_{3}\) c. \(0.222 M\) glucose d. \(0.00764 M \mathrm{K}_{2} \mathrm{SO}_{4}\)

Determine the molarity of each of the following solutions from its osmotic pressure at \(25^{\circ} \mathrm{C} .\) Include the van 't Hoff factor for the solution when the factor is given. a. \(\Pi=0.0259\) atm for a solution of urea \(\left[\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\right]\) b. \(\Pi=1.56\) atm for a solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) c. \(\Pi=0.697\) atm for a solution of \(\mathrm{KI}, i=1.90\)

Is the following statement true or false? For solutions of the same reverse osmotic pressure at the same temperature, the molarity of a solution of NaCl will always be less than the molarity of a solution of \(\mathrm{CaCl}_{2} .\) Explain your answer.

What cffect does dissolving a solute have on the following properties of a solvent? (a) its osmotic pressure; (b) its freezing point; (c) its boiling point

How can measurements of osmotic pressure, freezing point depression, and boiling point elevation be used to find the molar mass of a solute? Why are such determinations usually carried out on molecular substances as opposed to ionic ones?

Throat Lozenges A 188 -mg sample of a nonelectrolyte isolated from throat lozenges was dissolved in enough water to make \(10.0 \mathrm{mL}\) of solution at \(25^{\circ} \mathrm{C} .\) The osmotic pressure of the resulting solution was 4.89 atm. Calculate the molar mass of the compound.

Antibiotic An unknown compound \((27.40 \mathrm{mg})\) with antibiotic properties was dissolved in water to make \(100.0 \mathrm{mL}\) of solution. The solution did not conduct clectricity and had an osmotic pressure of 9.94 torr at \(23.6^{\circ} \mathrm{C} .\) Elemental analysis revealed the substance to

Cloves Eugenol is one of the compounds responsible for the flavor of cloves. A 111 -mg sample of eugenol was dissolved in \(1.00 \mathrm{g}\) of chloroform \(\left(K_{\mathrm{b}} 53.63^{\circ} \mathrm{C} / \mathrm{m}\right),\) increasing the boiling point of the chloroform by \(2.45^{\circ} \mathrm{C} .\) Calculate eugenol's molar mass. Eugenol is \(73.1796 \mathrm{C}, 7.32 \%\) H, and \(19.51 \%\) O by mass. What is the molecular formula of eugenol?

Caffeine The freezing point of a solution prepared by dissolving 150 mg of caffeine in \(10.0 \mathrm{g}\) of camphor is lower than that of pure camphor \(\left(K_{f}=39.7^{\circ} \mathrm{C} / \mathrm{m}\right)\) by \(3.07^{\circ} \mathrm{C}\) What is the molar mass of caffeine? Elemental analysis of caffeine yields the following results: \(49.49 \%\) C \(, 5.15 \% \mathrm{H}\) \(28.87 \% N,\) and the remainder O. What is the molecular formula of caffeine?

Which substance has the least negative lattice energy? (a) \(\mathrm{Sr} \mathrm{I}_{2} ;\) (b) \(\mathrm{CaBr}_{2} ;\) (c) \(\mathrm{CaCl}_{2} ;\) (d) \(\mathrm{Mg} \mathrm{F}_{2}\)

Explain why the boiling point of pure sodium chloride is much higher than the boiling point of an aqueous solution of sodium chloride.

Melting lce \(\mathrm{CaCl}_{2}\) is often used to melt ice on sidewalks. Could \(\mathrm{CaCl}_{2}\) melt ice at \(-20^{\circ} \mathrm{C}\) ? Assume that the solubility of \(\mathrm{CaCl}_{2}\) at this temperature is \(70.1 \mathrm{g}\) of \(\mathrm{CaCl}_{2} / 100.0 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) and that the van 't Hoff factor for a saturated solution of \(\mathrm{CaCl}_{2}\) is 2.5

Making Ice Cream A mixture of table salt and ice is used to chill the contents of hand-operated ice-cream makers. What is the melting point of a mixture of 2.00 lb of \(\mathrm{NaCl}\) and 12.00 lb of ice if exactly half of the ice melts? Assume that all the NaCl dissolves in the melted ice and that the van 't Hoff factor for the resulting solution is 1.44

Physiological Saline One hundred milliliters of a solution of physiological saline \((0.92 \%\) NaCl by mass) is diluted by the addition of \(250.0 \mathrm{mL}\) of water. What is the osmotic pressure of the final solution at \(37^{\circ} \mathrm{C} ?\) Assume that \(\mathrm{NaCl}\) dissociates completely into \(\mathrm{Na}^{+}(a q)\) and \(\mathrm{Cl}^{-}(a q)\)

One hundred milliliters of \(2.50 \mathrm{mM} \mathrm{NaCl}\) is mixed with \(80.0 \mathrm{mL}\) of \(3.60 \mathrm{mM} \mathrm{MgCl}_{2}\) at \(20^{\circ} \mathrm{C} .\) Calculate the osmotic pressure of each starting solution and that of the mixture, assuming that the volumes are additive and that both salts dissociate completely into their component ions.

Kidney Dialysis Hemodialysis, a method of removing waste products from the blood if the kidneys have failed, uses a tube made of a cellulose membrane that is immersed in a large volume of aqueous solution. Blood is pumped through the tube and is then returned to the patient's vein. The membrane does not allow passage of large protein molecules and cells but does allow small ions, urea, and water to pass through it. Assume that a physician wants to decrease the concentration of sodium ion and urea in a patient's blood while maintaining the concentration of potassium ion and chloride ion in the blood. What materials must be dissolved in the aqueous solution in which the dialysis tube is immersed? How must the concentrations of ions in the immersion fluid compare with those in blood?