The Properties of Mixtures: Solutions and Colloids

A solution of $\mathbf{\text{5.0 g}}$ of benzoic acid $\mathbf{\left(}{\mathbf{\text{C}}}_{\mathbf{\text{6}}}{\mathbf{\text{H}}}_{\mathbf{\text{5}}}\mathbf{\text{COOH}}\mathbf{\right)}$ in $\mathbf{\text{100.0 g}}$ of carbon tetrachloride has a boiling point of $\mathbf{77}\mathbf{.}{\mathbf{5}}^o\mathbf{C}$.

(a) Calculate the molar mass of benzoic acid in the solution.

(b) Suggest a reason for the difference between the molar mass based on the formula and that found in part (a).

Derive a general equation that expresses the relationship between the molarity and the molality of a solution. Why are the numerical values of these two terms approximately equal for very dilute aqueous solutions?

A florist prepares a solution of nitrogen-phosphorus fertilizer by dissolving $\mathbf{\text{5.66 g}}$ of ${\mathbf{\text{NH}}}_{\mathbf{\text{4}}}{\mathbf{\text{NO}}}_{\mathbf{\text{3}}}$ and $\mathbf{\text{4.42 g}}$ of ${\left({\mathbf{NH}}_4\right)}_3{\mathbf{PO}}_4$  in enough water to make $\mathbf{\text{20.0 L}}$ of solution. What are the molarities of ${{\mathbf{NH}}_4}^{+}$  and ${{\mathbf{PO}}_4}^{3-}$ of in the solution?

Urea is a white crystalline solid used as a fertilizer, in the pharmaceutical industry, and in the manufacture of certain polymer resins. Analysis of urea reveals that, by mass, it is $\mathbf{20}\mathbf{.1}\mathit{\%}$ carbon, $\mathbf{6}\mathbf{.7}\mathit{\%}$ hydrogen,  $\mathbf{46}\mathbf{.5}\mathit{\%}$ nitrogen and the balance oxygen.

(a) Find the empirical formula of urea.

(b) A  $\mathbf{5}\mathbf{.0}\raisebox{1ex}{$\mathbf{\text{g}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{L}}$}\right.$ solution of urea in water has an osmotic pressure of  $\mathbf{2}\mathbf{.04}\mathbf{\text{ atm}}$, measured at ${\mathbf{25}}^o\mathbf{C}$. What is the molar mass and molecular formula of urea?

The total concentration of dissolved particles in blood is $\begin{array}{l}\mathbf{\text{0.30 M}}\end{array}$. An intravenous (IV) solution must be isotonic with blood, which means it must have the same concentration.

(a) To relieve dehydration, a patient is given $\begin{array}{l}\mathbf{\text{100 }}\raisebox{1ex}{$\mathbf{\text{mL}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{h}}$}\right.\end{array}$ of IV glucose $\mathbf{\left(}{\mathbf{C}}_6{\mathbf{H}}_{12}{\mathbf{O}}_6\mathbf{\right)}$ for $\mathbf{\text{2.5 h}}$. What mass $\left(\text{g}\right)$ of glucose did she receive?

(b) If isotonic saline $\left(\text{NaCl}\right)$ is used, what is the molarity of the solution?

(c) If the patient is given $\mathbf{\text{150 }}\raisebox{1ex}{$\mathbf{\text{mL}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{h}$}\right.$ of IV saline for $\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{h}$, how many grams of $\mathbf{NaCl}$ did she receive?

Deviations from Raoult’s law lead to the formation of azeotropes, constant boiling mixtures that cannot be separated by distillation, making industrial separations difficult. For components A and B, there is a positive deviation if the A-B attraction is less than A-A and B-B attractions (A and B reject each other), and a negative deviation if the A-B attraction is greater than A-A and B-B attractions. If the A-B attraction is nearly equal to the A-A and B-B attractions, the solution obeys Raoult’s law. Explain whether the behavior of each pair will be nearly ideal, have a positive deviation, or a negative deviation:

(a) Benzene $\mathbf{\left(}{\mathbf{\text{C}}}_{\mathbf{\text{6}}}{\mathbf{\text{H}}}_{\mathbf{\text{6}}}\mathbf{\right)}$ and methanol;

(b) Water and ethyl acetate;

(c) Hexane and heptane;

(d) Methanol and water;

(e) Water and hydrochloric acid.

Calculate the molality, molarity, and mole fraction of $\mathit{F}\mathit{e}\mathit{C}{\mathit{l}}_{\mathbf{3}}$  in a 28.8 mass % aqueous solution (d = 1.280 g/mL).

Wastewater from a cement factory contains 0.25 g of ${\mathbf{Ca}}^{\mathbf{2}\mathbf{+}}$ ion and 0.056 g of  ${\mathbf{Mg}}^{\mathbf{2}\mathbf{+}}$ ion per 100.0 L of solution. The solution density is 1.001 g/mL. Calculate the ${\mathbf{Ca}}^{\mathbf{2}\mathbf{+}}$ and ${\mathbf{Mg}}^{\mathbf{2}\mathbf{+}}$ concentrations in ppm (by mass).

An automobile antifreeze mixture is made by mixing equal volumes of ethylene glycol (d = 1.114 g/mL; ɱ = 62.07 g/mole) and water (d = 1.00 g/mL) at ${\mathbf{20}}^{\mathbf{o}}\mathbf{C}$. The density of the mixture is 1.070g/mL. Express the concentration of ethylene glycol as: 

(a) Volume percent                        

(b) Mass percent 

(c) Molarity                                   

 (d) Molality 

(e) Mole fraction                                     

In what sense is a strong electrolyte “strong”? What property of the substance makes it a strong electrolyte?

Express Raoult’s law in words. Is Raoult’s law valid for a solution of a volatile solute? Explain.

What are the most important differences between the phase diagram of a pure solvent and the phase diagram of a solution of the solvent?

Which aqueous solution has a freezing point closer to its predicted value, 0.01 m NaBr or 0.01 m MgCl₂? Explain.

Which solution has the higher boiling point?

(a) 38.0 g of ${\mathbf{C}}_{\mathbf{3}}{\mathbf{H}}_{\mathbf{8}}{\mathbf{O}}_{\mathbf{3}}$  in 250. g of ethanol or 38.0 g of ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}{\mathbf{O}}_{\mathbf{2}}$ in 250. g of ethanol

(b) 15 g of ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}{\mathbf{O}}_{\mathbf{2}}$  in 0.50 kg of  ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$ or 15 g of NaCl in 0.50 kg of  ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$.

Rank the following aqueous solutions in order of increasing

(a) osmotic pressure; (b) boiling point; (c) freezing point;

(d) vapor pressure at 50^oC:

(I) 0.100 m NaNO₃ (II) 0.100 m glucose (III) 0.100 m CaCl₂

Rank the following aqueous solutions in order of decreasing

(a) osmotic pressure; (b) boiling point; (c) freezing point; (d) vapor pressure at 298 K:

(I) 0.04 m urea $\left[{\left({\mathrm{NH}}_2\right)}_{2}C=O\right]$

(II) 0.01 m ${\mathbf{AgNO}}_{\mathbf{3}}$

(III) 0.03 m ${\mathbf{CuSO}}_{\mathbf{4}}$

Calculate the vapor pressure of a solution of 34.0 g of glycerol (C₃H₈O₃) in 500.0 g of water at ${\mathbf{25}}^{\mathbf{°}}\mathit{C}$. The vapor pressure of water at ${\mathbf{25}}^{\mathbf{°}}\mathit{C}$ is 23.76 torr. (Assume ideal behavior.)

Calculate the vapor pressure of a solution of 0.39 mol of cholesterol in 5.4 mol of toluene at ${\mathbf{32}}^{\mathbf{°}}\mathit{C}$. Pure toluene has a vapor pressure of 41 torr at ${\mathbf{32}}^{\mathbf{°}}\mathit{C}$. (Assume ideal behavior.)

What is the freezing point of 0.251 m urea in water?

What is the boiling point of 0.200 m lactose in water?

The boiling point of ethanol $\left({\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}\right)$ is $\mathbf{78}\mathbf{.}\mathbf{5}{}^{\mathbf{°}}\mathit{C}$. What is the boiling point of a solution of 6.4 g of vanillin $\left(M=152.14g/\mathrm{mol}\right)$ in 50.0 g of ethanol $\left(Kb of ethanol=1.22{}^{°}C/m\right)$?

The freezing point of benzene is 5.5^oC. What is the freezing point of a solution of 5.00 g of naphthalene (C₁₀H₈) in 444 g of benzene (of benzene = 4.90^oC/m)?

What is the minimum mass of ethylene glycol glycol (C₂H₆O₂) that must be dissolved in 14.5 kg of water to prevent the solution from freezing at -12.0^oF? (Assume ideal behaviour).

What is the minimum mass of glycerol (C₃H₈O₃) that must be dissolved in 11.0 mg of water to prevent the solution from freezing at =-15.0^oc? (Assume ideal behaviour.)

Calculate the molality and van’t Hoff factor (i) for the following aqueous solutions:

(a) 1.00 mass % NaCl, freezing point -0.593^oc 

(b) 0.500 mass % CH₃COOH, freezing point -0.159^oc 

Calculate the molality and van’t Hoff factor (i) for the following aqueous solutions:

(a) 0.500 mass % KCl, freezing point -0.234^oc 

(b) 1.00 mass % H₂SO₄, freezing point -0.423^oc