CHEM 120 - Chapter 13 Practice Exam Questions with Solutions

13-1) Vapor Pressure and Raoult's Law

• Raoult's Law: $P = X<em>{solvent}P</em>{solvent}^0$ (reduced vapor pressure), $\Delta P = X<em>{solute}P</em>{solvent}^0$ (change in vapor pressure), $P + \Delta P = P^0$ (pure solvent vapor pressure).
• Mole fraction: $X<em>{solute} = \frac{n</em>{solute}}{n<em>{total}}$, $X</em>{solvent} = \frac{n<em>{solvent}}{n</em>{total}}$, $X<em>{solute} + X</em>{solvent} = 1$.
• Example: Ethanol (solvent, 90.0 mmol) and naphthalene (solute, 10.0 mmol); Reduced vapor pressure of ethanol is $P_{ethanol} = 0.90 \times 0.459 atm = 0.413 atm$.

13-2) Osmotic Pressure

• Formula: $\Pi = MRT$, where $\Pi$ is osmotic pressure, M is molarity, R is the gas constant, and T is temperature.
• Calculation involves finding molarity (M) and using the appropriate R value (62.37 L torr/mol K for torr).
• Example: 1.0 g of solute (100,000 g/mol) in 100. g water (100.0 mL); $\Pi = (1.0 \times 10^{-4} M) \times (62.37 L torr/mol K) \times (300 K) = 1.87 torr$.

13-3) Miscible Liquids

• Miscible: Liquids that mix in all proportions (e.g., ethanol and water).
• Saturated: Maximum solute dissolved.
• Supersaturated: More solute dissolved than normally possible; unstable.
• Unsaturated: Less than maximum solute dissolved.

13-4) Molality

• Molality definition: Moles of solute per kilogram of solvent.

13-5) Van't Hoff Factor (i)

• Ideal van't Hoff factor: Number of particles per mole of solute when dissolved.
• Example: $(NH<em>4)</em>3PO<em>4$ produces 4 particles (3 $NH</em>4^+$ and 1 $PO_4^{3-}$), so i = 4.

13-6) "Like Dissolves Like"

• Polar solvents dissolve polar solutes, and nonpolar solvents dissolve nonpolar solutes due to favorable energy interactions.

13-7) Pressure and Solubility

• Pressure significantly affects the solubility of gases in liquids.
• Increased pressure increases gas solubility by increasing collision rate.

13-8) Solute Concentration Effects

• As solute concentration increases: vapor pressure decreases, boiling point increases, and freezing point decreases.

13-9) Molecular Weight Determination using Freezing Point Depression

• Formula: $\Delta T<em>f = K</em>f m$, where $\Delta T<em>f$ is the freezing point depression, $K</em>f$ is the freezing point depression constant, and m is molality.
• Molecular weight calculated as $g/mol$. Example: $m = \frac{0.44 ^oC}{5.12 ^oC/m} = 0.08594 m$. Molar mass is 6.5980 g/0.04297 mol = 153 g/mol

13-10) Unsaturated Solution

• Unsaturated solution: Concentration is lower than the solubility; can dissolve more solute.

13-11) Freezing Point Comparison

• Use the van't Hoff factor (i) to determine the effective molality (meffective = i * m).
• The solution with the highest effective molality will have the lowest freezing point.
• Example: KF (0.50 m, i=2) has meffective = 1.0 m resulting in the lowest freezing point.

13-12) Molality Calculation

• Definition: Moles solute / kg solvent.
• Example: 12.0 g $C<em>6H</em>6$ in 38.0 g $CCl_4$. Molality = 4.04 m.

13-13) Molarity to Molality Conversion

• Use density to convert volume-based molarity to mass-based molality.
• Example: 0.726 M $Pb(NO<em>3)</em>2$ solution with density 1.202 g/mL converts to 0.755 m.

13-14) Boiling Point Elevation

• Formula: $\Delta T<em>b = i m K</em>b$, where $K_b$ is the ebullioscopic constant.
• Example: 58 g NaCl in 4.01 kg water; $T_{new} = 100 + 0.257 = 100.257 ^oC$.

13-15) Mass Percent

• Mass percent: Mass of solute per 100 g of solution.
• Example: 28% phosphoric acid by mass means 100 g solution contains 28 g phosphoric acid.

13-16) Van't Hoff Factor from Osmotic Pressure

• Formula: $\Pi<em>{measured} = i \times \Pi</em>{calculated}$.
• Find i by dividing measured osmotic pressure by calculated osmotic pressure.
• Example: i = 2.67.

13-17) Supersaturated Solution (Graphical)

• Solution contains more dissolved solute than the solubility allows at a given temperature.

13-18) Colloids

• Colloid: A mixture where solute is dispersed, not dissolved (e.g., fog, smoke, whipped cream, homogenized milk).
• Air is a homogeneous mixture (solution), not a colloid.

13-19) Glucose Mass for Intravenous Injection

• Use osmotic pressure formula ($\Pi = MRT$) to find molarity, then convert to mass.
• The glucose solution should match blood's osmotic pressure.
• Example: 122 g $C<em>6H</em>{12}O_6$ needed.

13-20) Vapor Pressure Calculation (Nonvolatile Solute)

• Use Raoult’s Law: $P<em>{solvent} = P</em>{solvent}^0 \times X_{solvent}$.
• Example: Vapor pressure of water above urea solution is 20.8 torr.

13-21) Molality Calculation (HCl in Ethanol)

• Molality = Moles solute / kg solvent. Example: 0.75 m $C<em>9H</em>6O$.

13-22) Colligative Properties Exception

• Colligative properties depend on the number of solute particles, not temperature.
• Reaction rate increase with temperature is NOT a colligative property.

13-23) Van't Hoff Factor Calculation

• $\Pi<em>{measured} = i \times \Pi</em>{calculated}$. Example: i = 1.986

13-24) Freezing Point of Glycerin in Ethanol

• $m = \frac{mol\,solute}{kg\,solvent}$. Example: $C<em>3H</em>8O_3$ Freezing point of the new solution is -115.4 $^oC$.

13-25) Henry's Law

• The relationship between the solubility of a gas and its partial pressure $S = kP$. Example: solubility of oxygen gas increases from 0.041 g/L to 0.123 g/L

13-26) Molecular Weight of Nicotine

• Molar mass Nicotine is mass nicotine divided by the moles nicotine. Example: Mass is $162 g/mol$.

13-27) Molality of benzene in carbon tetrachloride.

• Molality of benzene is moles of solute divided by the kg solvent. Example: Benzene's molality is 0.735 m $C<em>6H</em>6$.

13-28) Solubility in Benzene

• Since Benzene is a non-polar, substances that are also non-polar are more likely to dissolve in it. Example: $C Cl_4$

13-29) Concentration Units and Temperature

• Of different concentration values, Molarity will change with the solutions temperature because it is defined as the moles per liter of solution.. Example: It is mass based.

13-30) Colligative Properties Dependency

• Colligative properties ideally depend only on the A) relative number of solute and solvent particles in a solution.

13-31) Gas Solubility Statements and Validity

• E) The solubility of a gas in water is inversely proportional to the molar mass of the gas. - Is an incorrect statement

13-32) Smallest Change in Freezing Point Change

• Multiply the van’t Hoff factor by the molality to get the Ideal effective molality. Then compare. Exmaple: A, NaCl is the smallest change in freezing point.

13-33) Calculating Molality of a solution.

• Solute is naphthalene, and the solvent is choloroform. $m = \frac{n}{V} = \frac{0.09129\,mol\,C<em>{10}H</em>8}{0.1042\,kg\,CHCl<em>3} = 0.876\,m\,C</em>{10}H_8$

13-34) Exothermic Dissolution Overview

• E) solvent-solute , solute-solute , solvent-solvent is the correct sequence for en exthothermic reaction

13-35) Van't Hoff Factor and more Calculations

• $ΔT<em>f = i m K</em>f = 1.88 × 0.50\,m × 1.86 \frac{^oC}{m} = 1.75 ^oC$

13-36) Oscillating Pressure Calculation and Values

• Π = MRT = 0.03564 M C12H22O11 × 0.08206 L atm mol K × 298 K = 0.8715 atm × \frac{760\,torr}{1\,atm} = 662 torr

13-37) True or False

• A solution where no additional solute can be dissolved is a supersaturated solution - False
• Two liquids that dissolve readily into each other are miscible liquids. - True
• Carbon tetrachloride dissolves in water. - False
• A colloid disperses the solute through the solvent. - True
• In a solution, there are more moles solvent than moles solute. - True