The Properties of Mixtures: Solutions and Colloids

How would you prepare the following aqueous solutions? 

(a) 57.5 mL of $\mathbf{1}\mathbf{.}\mathbf{53}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{M}$ $\mathbf{Cr}{\left({\mathbf{NO}}_{\mathbf{3}}\right)}_{\mathbf{3}}$ from solid  $\mathbf{Cr}{\left({\mathbf{NO}}_{\mathbf{3}}\right)}_{\mathbf{3}}$.

(b) $\mathbf{5}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}{\mathbf{m}}^{\mathbf{3}}$  of 1.45 M  ${\mathbf{NH}}_{\mathbf{4}}{\mathbf{NO}}_{\mathbf{3}}$from 2.50 M ${\mathbf{NH}}_{\mathbf{4}}{\mathbf{NO}}_{\mathbf{3}}$.

Calculate the molality of the following: 

(a) A solution containing 85.4 g of glycine ( ${\mathbf{NH}}_{\mathbf{2}}{\mathbf{CH}}_{\mathbf{2}}\mathbf{COOH}$) dissolved in 1.270 kg of ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$. 

(b) A solution containing 8.59 g of glycerol (${\mathbf{C}}_{\mathbf{3}}{\mathbf{H}}_{\mathbf{8}}{\mathbf{O}}_{\mathbf{3}}$ ) in 77.0 g of ethanol  $\left({\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}\right)$.

Calculate the molality of the following: 

(a) A solution containing 174 g of HCl in 757 g of  ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$

(b) A solution containing 16.5 g of naphthalene (${\mathbf{C}}_{\mathbf{10}}{\mathbf{H}}_{\mathbf{8}}$ ) in 53.3 g of benzene  $\left({\mathbf{C}}_6{\mathbf{H}}_6\right)$.

What is the molality of a solution consisting of 44.0 mL of benzene ( ${\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{6}}$; d = 0.877 g/mL) in 167 mL of hexane (data-custom-editor="chemistry" ${\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{14}}$ ; d = 0.660 g/mL)?             

What is the molality of a solution consisting of 2.66 mL of carbon tetrachloride (${\mathbf{CCl}}_{\mathbf{4}}$ ; d = 1.59 g/mL) in 76.5 mL of methylene chloride  $\left({\mathrm{CH}}_2{\mathrm{Cl}}_2;d=1.33g/\mathrm{mL}\right)$?

How would you prepare the following aqueous solutions? 

(a)  $\mathbf{3}\mathbf{.}\mathbf{10}\mathbf{\times }{\mathbf{10}}^{\mathbf{2}}\mathbf{g}$ of 0.125 m ethylene glycol (${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}{\mathbf{O}}_{\mathbf{2}}$ ) from ethylene glycol and water. 

(b) 1.20 kg of 2.20 mass %  ${\mathbf{HNO}}_{\mathbf{3}}$ from 52.0 mass %  ${\mathbf{HNO}}_{\mathbf{3}}$.

How would you prepare the following aqueous solutions? 

(a) 1.50 kg of 0.0355 m ethanol (${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}$ ) from ethanol and water 

(b) 445 g of 13.0 mass % HCl from 34.1 mass % HCl.

A solution contains 0.35 mol of isopropanol (${\mathbf{C}}_{\mathbf{3}}{\mathbf{H}}_{\mathbf{7}}\mathbf{OH}$ ) dissolved in 0.85 mol of water.

(a) What is the mole fraction of iso-propanol? 

(b) The mass percent? 

(c) The molality?

A solution contains 0.100 mol of NaCl dissolved in 8.60 mol of water. 

(a) What is the mole fraction of NaCl? 

(b) The mass percent? 

(c) The molality?

What mass of cesium bromide must be added to 0.500 L of water (d = 1.00 g/mL) to produce a 0.400 m solution? What are the mole fraction and the mass percent of CsBr?

What are the mole fraction and the mass percent of a solution made by dissolving 0.30 g of KI in 0.400 L of water (d = 1.00 g/mL)?

Calculate the molality, molarity, and mole fraction of ${\mathbf{NH}}_{\mathbf{3}}$ in an 8.00 mass % aqueous solution (d = 0.9651 g/mL)?

Question: Classify the following substances as strong electrolytes, weak electrolytes, or non-electrolytes:

(a) Sodium permanganate (NaMnO₄)

(b) Acetic acid (CH₃COOH)

(c) Methanol (CH₃OH) 

(d) Calcium acetate [Ca(C₂H₃O₂₎₂]

Question: Classify the following substances as strong electrolytes, weak electrolytes, or non-electrolytes:

(a) Hydrogen chloride (HCl) 

(b) Potassium nitrate (KNO3)

(c) Glucose (C6H12O6) 

(d) Ammonia (NH3)

Question: The freezing point depression constants of the solvents cyclohexane and naphthalene are 20.1°C/m and 6.94°C/m, respectively. Which solvent would give a more accurate result if you are using freezing point depression to determine the molar mass of a substance that is soluble in either one? Why?

Question: Which aqueous solution has a boiling point closer to its predicted value, 0.050 m  NaF or 0.50 m ? Explain.

Question: Is the boiling point of 0.01 m KF (aq) higher or lower than that of 0.01 m glucose(aq)? Explain.

Question: Is the composition of the vapor at the top of a fractionating column different from the composition at the bottom? Explain.

Question: What is a non-volatile nonelectrolyte? Why is this type of solute the simplest case for examining colligative properties?

Question: The chemical formula of a solute does not affect the extent of the solution’s colligative properties. What characteristic of a solute does affect these properties? Name a physical property of a solution that is affected by the chemical formula of the solute.

How many moles of solute particles are present in 1 mL of each of the following aqueous solutions?

(a) 0.02M CuSO₄

(b) 0.004 MBa(OH)₂

(c) 0.08 M pyridine (C₅H₅N)

(d) 0.05 M (NH₄)₂CO₃ 

Question: How many moles of solute particles are present in 1 L of each of the following aqueous solutions?

$$\begin{gathered} \mathbf{\left(}\mathit{a}\mathbf{\right)}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{MKBr}\mathbf{ } \\ \mathbf{\left(}\mathit{b}\mathbf{\right)}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{065}{\mathbf{MHNO}}_{\mathbf{3}}\mathbf{ } \\ \mathbf{\left(}\mathit{c}\mathbf{\right)}\mathbf{ }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}{\mathbf{MKHSO}}_{\mathbf{4}}\mathbf{ }\mathbf{ }\mathbf{ } \\ \mathbf{\left(}\mathit{d}\mathbf{\right)}\mathbf{ }\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{06}\mathbf{Methanol}\left(C_2{H}_5\mathrm{OH}\right) \end{gathered}$$

The U.S. food and Drug administration lists dichloromethane  and carbon tetrachloride among the many cancer-causing chlorinated organic compounds. What are the partial pressures of these substances in the vapor above a solution of 1.60 mol of CH₂Cl₂ and 1.10 mol of CCl₄ at $23.5^{\circ }C$? the vapor pressure of pure CH₂Cl₂ and CCl₄ at $23.5^{\circ }C$are 352 torr and 118 torr, respectively.(assume ideal behavior)

what type of colloid is each of the following?

1. Milk
2. Fog
3. shaving cream

What is Brownian motion, and what causes it?

In a movie theatre, you can see the beam of project light. What phenomenon does this exemplify? Why does it occur?

Why don’t soap micelles coagulate and form large globules? Is soap more effective in fresh water or in sea water? Why?

The three aqueous ionic solutions below total volumes of 25mL in A, 50mL in B and 100mL in C. if each sphere represents 0.010mol of ions, calculate:

1. The total molarity of ions for each solution
2. The highest molarity of solute
3. The lowest molality of solute (assuming the solution densities are equal)
4. The highest osmotic pressure (assuming ideal behavior).

Because zinc has nearly the same atomic radius as copper $(d=8.95g/c{m}^3)$zinc atom substitute for some copper atoms in many types of brass. Calculate the density of the brass with

1. 10.0 atom % Zn and
2. 38.0 atom % Zn. 

Gold occurs in sea water at an average concentration of 1.1*10^-2 PPb. How many liters of sea water must be processed to recover one troy ounce of gold, assuming  81.5% efficiency (d of seawater = 1.025g/mol ; 1 troy ounce = 31.1g)?

Use atomic properties to explain why xenon is 11 times as soluble as helium in water at $0^{\circ }C$on a mole basis.

Which of the following best represent a molecular-scale view of an ionic compound in aqueous solution? Explain. 

Question: wastewater discharged into a stream by a sugar refinery contains 3.55g of sucrose (${\mathbf{C}}_{\mathbf{12}}{\mathbf{H}}_{\mathbf{22}}{\mathbf{O}}_{\mathbf{11}}$) per liter. A government-industry project is designed to test the feasibility of removing the sugar by reverse osmosis. What pressure must be applied to the apparatus at  to produce pure water?

Question: Which solution has the lower freezing point?

(a)  $\mathbf{11}\mathbf{.}\mathbf{0}{\mathbf{gofCH}}_{\mathbf{3}}\mathbf{OHin}\mathbf{100}\mathbf{.}\mathbf{gofH}\mathbf{2}\mathbf{Oor}\mathbf{22}\mathbf{.}\mathbf{0}{\mathbf{gofCH}}_{\mathbf{3}}{\mathbf{CH}}_{\mathbf{2}}\mathbf{OHin}\mathbf{200}\mathbf{.}\mathbf{gofH}\mathbf{2}\mathbf{O}$

(b)  $\mathbf{20}\mathbf{.}\mathbf{0}{\mathbf{gofH}}_{\mathbf{2}}\mathbf{Oin}\mathbf{1}\mathbf{.}\mathbf{00}{\mathbf{kgofCH}}_{\mathbf{3}}\mathbf{OHor}\mathbf{20}\mathbf{.}\mathbf{0}{\mathbf{gofCH}}_{\mathbf{3}}{\mathbf{CH}}_{\mathbf{2}}\mathbf{OHin}\mathbf{1}\mathbf{.}\mathbf{00}{\mathbf{kgofCH}}_{\mathbf{3}}\mathbf{OH}$

Is 50% by mass of methanol dissolved in ethanol different from 50% by mass of ethanol dissolved in methanol? Explain.

Answer each of the following briefly:

1. Why is cake alum [Al₂(SO₄)₃] added during water purification?
2. Why is water that contains large amounts of Ca²⁺and Mg²⁺ difficult to use for cleaning?
3. What is the meaning of “reverse” in reverse osmosis?
4. Why might a water treatment plant use ozone as a disinfectant instead of chlorine?
5. How does passing a saturated NaCl solution through a “spent” ion-exchange resin regenerate the resin?

A water treatment plant needs to attain a fluoride concentration of $\mathbf{4}\mathbf{.}\mathbf{50}\mathbf{\times }{\mathbf{10}}^{-5}\mathbf{\text{ M}}$.

(a) What mass of $\mathbf{NaF}$ must be added to a $\mathbf{5000}\mathbf{\text{ L}}$ blending tank of water?

(b) What mass per day of fluoride is ingested by a person who drinks $\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{ }\mathbf{L}$ of this water?

Four $\mathbf{\text{U}}$ tubes each have distilled water in the right arm, a solution in the left arm, and a semipermeable membrane between arms.

1. If the solute is $\mathbf{\text{KCl}}$, which solution is most concentrated?
2. If each solute is different but all the solutions have the same molarity, which contains the smallest number of dissolved ions?

$\mathbf{\beta }$ -Pinene $\mathbf{\left(}{\mathbf{C}}_{10}{\mathbf{H}}_{16}\mathbf{\right)}$ and $\mathbf{\alpha }$-terpineol $\mathbf{\left(}{\mathbf{C}}_{10}{\mathbf{H}}_{18}\mathbf{O}\mathbf{\right)}$ are used in cosmetics to provide a “fresh pine” scent. At $\mathbf{367}\mathbf{\text{ K}}$, the pure substances have vapor pressures of $\mathbf{100}\mathbf{.3}\mathbf{\text{ torr}}$ and $\mathbf{\text{9.8 torr}}$ respectively. What is the composition of the vapor (in terms of mole fractions) above a solution containing equal masses of these compounds at $\mathbf{367}\mathbf{\text{ K}}$? (Assume ideal behaviour.)

A solution of $\mathbf{\text{1.50 g}}$ of solute dissolved in $\mathbf{\text{25.0 mL}}$ of ${\mathbf{H}}_2\mathbf{O}$ at ${\mathbf{25}}^{\mathbf{\text{o}}}\mathbf{\text{C}}$ has a boiling point of $\mathbf{100}\mathbf{.}{\mathbf{45}}^{\mathbf{\text{o}}}\mathbf{\text{C}}$.

(a) What is the molar mass of the solute if it is a non-volatile nonelectrolyte and the solution behaves ideally ($\mathit{d}$ of ${\mathbf{H}}_2\mathbf{O}$ at $\mathbf{\text{25°C}}\mathbf{=}\mathbf{\text{0.997 }}\raisebox{1ex}{$\mathbf{\text{g}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{mL}}$}\right.$)?

(b) Conductivity measurements show the solute to be ionic of general formula ${\mathbf{\text{AB}}}_{\mathbf{\text{2}}}$ or ${\mathbf{\text{A}}}_{\mathbf{\text{2}}}\mathbf{\text{B}}$. What is the molar mass if the solution behaves ideally?

(c) Analysis indicates an empirical formula of ${\mathbf{\text{CaN}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{6}}}$. Explain the difference between the actual formula mass and that calculated from the boiling point elevation.

(d) Find the van’t Hoff factor $\left(i\right)$ for this solution.

A pharmaceutical preparation made with ethanol $\mathbf{\left(}{\mathbf{\text{C}}}_{\mathbf{\text{2}}}{\mathbf{\text{H}}}_{\mathbf{\text{5}}}\mathbf{\text{OH}}\mathbf{\right)}$ is contaminated with methanol $\mathbf{\left(}{\mathbf{\text{CH}}}_{\mathbf{\text{3}}}\mathbf{\text{OH}}\mathbf{\right)}$. A sample of vapor above the liquid mixture contains a $\raisebox{1ex}{$\mathbf{97}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{1}$}\right.$ mass ratio of ${\mathbf{\text{C}}}_{\mathbf{\text{2}}}{\mathbf{\text{H}}}_{\mathbf{\text{5}}}\mathbf{\text{OH}}$ to ${\mathbf{\text{CH}}}_{\mathbf{\text{3}}}\mathbf{\text{OH}}$. What is the mass ratio of these alcohols in the liquid? At the temperature of the liquid, the vapor pressures of ${\mathbf{\text{C}}}_{\mathbf{\text{2}}}{\mathbf{\text{H}}}_{\mathbf{\text{5}}}\mathbf{\text{OH}}$ and ${\mathbf{\text{CH}}}_{\mathbf{\text{3}}}\mathbf{\text{OH}}$ are $\mathbf{\text{60.5 torr}}$ and $\mathbf{\text{126.0 torr}}$, respectively.

Water treatment plants commonly use chlorination to destroy bacteria. A by-product is chloroform  $\mathbf{\left(}{\mathbf{\text{CHCl}}}_{\mathbf{\text{3}}}\mathbf{\right)}$, a suspected carcinogen, produced when $\mathbf{\text{HOCl}}$, formed by reaction of ${\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$ and water, reacts with dissolved organic matter. The United States, Canada, and the World Health Organization have set a limit of $\mathbf{\text{100 ppb}}$ of ${\mathbf{\text{CHCl}}}_{\mathbf{\text{3}}}$ in drinking water. Convert this concentration into molarity, molality, mole fraction, and mass percent.

: A biochemical engineer isolates a bacterial gene fragment and dissolves a $\mathbf{\text{10.0 mg}}$ sample in enough water to make $\mathbf{\text{30.0 mL}}$ of solution. The osmotic pressure of the solution is $\mathbf{\text{0.340 torr}}$ at $\mathbf{\text{25°C}}$.

(a) What is the molar mass of the gene fragment?

(b) If the solution density is $\mathbf{\text{0.997 }}\raisebox{1ex}{${\displaystyle \mathbf{\text{g}}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{mL}}$}\right.$, how large is the freezing point depression for this solution (${\mathbf{\text{K}}}_{\mathbf{f}}$ of water is  ${\mathbf{\text{1.86 }}}^{\mathbf{\text{o}}}\raisebox{1ex}{${\displaystyle \mathbf{\text{C}}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{m}}$}\right.$)?

A river is contaminated with $\mathbf{\text{0.65 }}\raisebox{1ex}{${\displaystyle \mathbf{\text{mg}}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{L}}$}\right.$ of dichloroethylene $\mathbf{\left(}{\mathbf{\text{C}}}_{\mathbf{\text{2}}}{\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}\mathbf{\right)}$. What is the concentration (in $\raisebox{1ex}{${\displaystyle \mathbf{\text{ng}}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{L}}$}\right.$ ) of dichloroethylene at $\mathbf{\text{21 }}\mathbf{°}\mathbf{\text{C}}$ in the air breathed by a person swimming in the river (${\mathbf{\text{k}}}_{\mathbf{\text{H}}}{\mathbf{\text{C}}}_{\mathbf{\text{2}}}{\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$ for in water is $\mathbf{0}\mathbf{.}\mathbf{033}\raisebox{1ex}{${\displaystyle \mathbf{\text{mol}}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{L}}\mathbf{\cdot }\mathbf{\text{atm}}$}\right.$ )?

At an air-water interface, fatty acids such as oleic acid lie in a one-molecule-thick layer (monolayer), with the heads in the water and the tails perpendicular in the air. When $\mathbf{2}\mathbf{.50}\mathbf{\text{ mg}}$ of oleic acid is placed on a water surface, it forms a circular monolayer $\mathbf{\text{38.6 cm}}$ in diameter. Find the surface area (in ${\mathbf{cm}}^2$ ) occupied by one molecule ($\mathbf{{\rm M}}$ of oleic acid is $\mathbf{283}\raisebox{1ex}{$\mathbf{\text{ g}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{mol}}$}\right.$ ).

Two beakers are placed in a closed container (left). One beaker contains water, the other a concentrated aqueous sugar solution. With time, the solution volume increases and the water decreases (right). Explain on the molecular level.

Although other solvents are available, dichloromethane $\mathbf{\left(}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}\mathbf{\right)}$ is still often used to “decaffeinate” drinks because the solubility of caffeine in ${\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$ is $\mathbf{\text{8.35}}$ times that in water.

(a) A $\mathbf{\text{100.0 mL}}$  sample of cola containing $\mathbf{\text{10.0 mg}}$ of caffeine is extracted with $\mathbf{\text{60.0 mL}}$  of ${\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$. What mass of caffeine remains in the aqueous phase?

(b) A second identical cola sample is extracted with two successive $\mathbf{\text{30.0 mL}}$ portions of  ${\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$. What mass of caffeine remains in the aqueous phase after each extraction?

(c) Which approach extracts more caffeine?

How do you prepare  $\mathbf{\text{250 g}}$ of $\mathbf{\text{0.150 m}}$ aqueous ${\mathbf{\text{NaHCO}}}_{\mathbf{\text{3}}}$ ?

Tartaric acid occurs in crystalline residues found in wine vats. It is used in baking powders and as an additive in foods. It contains $\mathbf{32}\mathbf{.3}\mathit{\%}$ by mass carbon and $\mathbf{3}\mathbf{.}\mathbf{97}\mathbf{\%}$ by mass hydrogen; the balance is oxygen. When $\mathbf{0}\mathbf{.981}\mathbf{\text{ g}}$ of tartaric acid is dissolved in $\mathbf{\text{11.23 g}}$ of water, the solution freezes at $\mathbf{-}\mathbf{126}\mathbf{°}\mathbf{\text{C}}$ . Find the empirical and molecular formulas of tartaric acid?

 Methanol $\mathbf{\left(}{\mathbf{\text{CH}}}_{\mathbf{\text{3}}}\mathbf{\text{OH}}\mathbf{\right)}$and ethanol $\mathbf{\left(}{\mathbf{\text{C}}}_{\mathbf{\text{2}}}{\mathbf{\text{H}}}_{\mathbf{\text{5}}}\mathbf{\text{OH}}\mathbf{\right)}$ are miscible because the major intermolecular force for each is hydrogen bonding. In some methanol-ethanol solutions, the mole fraction of methanol is higher, but the mass percent of ethanol is higher. What is the range of mole fraction of methanol for these solutions?