Solutions — Hard Practice Quiz

A Chemistry cheat sheet for Solutions — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Enthalpy of Solution: The sum of enthalpy changes for separating solute, separating solvent, and mixing.

$$\Delta H_{\text{soln}} = \Delta H_{\text{solute}} + \Delta H_{\text{solvent}} + \Delta H_{\text{mix}}$$

Where: \(\Delta H\) = enthalpy change

Dissolution Equation: Example of an ionic solid dissolving in water.

$$\text{NaCl}(s) \rightarrow \text{Na}^+(aq) + \text{Cl}^-(aq)$$

Solution Equilibrium: Dynamic equilibrium between dissolution and crystallization.

$$\text{Solute} + \text{Solvent} \rightleftharpoons \text{Solution}$$

Henry's Law: The solubility of a gas is proportional to its partial pressure.

$$S_g = kP_g$$

Where: \(S_g\) = solubility, \(k\) = Henry's law constant, \(P_g\) = partial pressure

Mass Percentage: Ratio of component mass to total solution mass.

$$\text{Mass } \% \text{ of component} = \frac{\text{mass of component in soln}}{\text{total mass of soln}} \times 100$$

Parts per Million (ppm): Concentration unit for very dilute solutions.

$$\text{ppm of component} = \frac{\text{mass of component in soln}}{\text{total mass of soln}} \times 10^6$$

Mole Fraction: Ratio of moles of one component to total moles.

$$X_A = \frac{\text{moles of A}}{\text{total moles of all components}}$$

Where: \(X\) = mole fraction

Molarity: Moles of solute per liter of solution.

$$M = \frac{\text{moles of solute}}{\text{liters of soln}}$$

Where: \(M\) = molarity (mol/L)

Molality: Moles of solute per kilogram of solvent.

$$m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}$$

Where: \(m\) = molality (mol/kg)

Raoult's Law: Vapor pressure of a solution equals mole fraction of solvent times pure solvent vapor pressure.

$$P_{\text{soln}} = X_{\text{solvent}} P^\circ_{\text{solvent}}$$

Where: \(P\) = pressure, \(X\) = mole fraction

Vapor Pressure Lowering: The decrease in vapor pressure is proportional to solute mole fraction.

$$\Delta P = X_{\text{solute}} P^\circ_{\text{solvent}}$$

Where: \(\Delta P\) = vapor pressure lowering, \(X_{\text{solute}}\) = mole fraction of solute

Boiling Point Elevation: Increase in boiling point proportional to molality.

$$\Delta T_b = K_b m$$

Where: \(\Delta T_b\) = boiling point elevation, \(K_b\) = constant, \(m\) = molality

Freezing Point Depression: Decrease in freezing point proportional to molality.

$$\Delta T_f = K_f m$$

Where: \(\Delta T_f\) = freezing point depression, \(K_f\) = constant, \(m\) = molality

Osmotic Pressure: Pressure required to prevent osmosis.

$$\Pi = MRT$$

Where: \(\Pi\) = osmotic pressure, \(M\) = molarity, \(R\) = gas constant, \(T\) = temperature

Practice quiz

  1. A $15.0 \%$ by mass aqueous solution of urea ($CO(NH_2)_2$, molar mass $60.06 \text{ g/mol}$) has a density of $1.042 \text{ g/mL}$ at $25 \text{ \textdegree C}$. What is the molality of the solution?

    • $2.94 \text{ mol/kg}$
    • $2.50 \text{ mol/kg}$
    • $2.78 \text{ mol/kg}$
    • $3.12 \text{ mol/kg}$

    Answer: $2.94 \text{ mol/kg}$

  2. $18.0 \text{ g}$ of a non-volatile solute (molar mass $180.0 \text{ g/mol}$) is dissolved in $108.0 \text{ g}$ of water ($H_2O$, molar mass $18.0 \text{ g/mol}$) at $25 \text{ \textdegree C}$. If the vapor pressure of pure water at $25 \text{ \textdegree C}$ is $23.8 \text{ mmHg}$, what is the vapor pressure of the solution?

    • $23.56 \text{ mmHg}$
    • $23.32 \text{ mmHg}$
    • $23.10 \text{ mmHg}$
    • $22.86 \text{ mmHg}$

    Answer: $23.32 \text{ mmHg}$

  3. An aqueous solution of a non-electrolyte boils at $100.52 \text{ \textdegree C}$. Given that $K_b$ for water is $0.52 \text{ \textdegree C} \cdot \text{kg/mol}$ and the solution density is $1.02 \text{ g/mL}$, what is the molarity of the solution?

    • $0.98 \text{ M}$
    • $1.00 \text{ M}$
    • $1.02 \text{ M}$
    • $1.04 \text{ M}$

    Answer: $0.98 \text{ M}$

  4. A $0.10 \text{ M}$ aqueous solution of a non-electrolyte (molar mass $100 \text{ g/mol}$) at $27 \text{ \textdegree C}$ has a density of $1.01 \text{ g/mL}$. Given $K_f$ for water is $1.86 \text{ \textdegree C} \cdot \text{kg/mol}$, what is its freezing point?

    • $-0.186 \text{ \textdegree C}$
    • $-0.100 \text{ \textdegree C}$
    • $-0.093 \text{ \textdegree C}$
    • $-0.200 \text{ \textdegree C}$

    Answer: $-0.186 \text{ \textdegree C}$

  5. The solubility of a gas in water is $0.015 \text{ g/L}$ at a partial pressure of $1.0 \text{ atm}$. If the partial pressure of the gas is increased to $2.5 \text{ atm}$, what is the new concentration of the gas in parts per million (ppm) by mass, assuming the density of water is $1.0 \text{ g/mL}$?

    • $37.5 \text{ ppm}$
    • $15.0 \text{ ppm}$
    • $25.0 \text{ ppm}$
    • $30.0 \text{ ppm}$

    Answer: $37.5 \text{ ppm}$

  6. For a particular ionic compound, the dissolution process in water is highly exothermic. Which of the following statements best describes the relative magnitudes of the enthalpy changes involved?

    • The energy released during the mixing of solute and solvent is significantly greater than the energy required to separate the solute and solvent particles.
    • The energy required to separate the solute particles is much greater than the energy released during mixing.
    • The energy required to separate the solvent particles is the dominant factor, making the process exothermic.
    • The sum of the energy required to separate solute and solvent particles is approximately equal to the energy released during mixing.

    Answer: The energy released during the mixing of solute and solvent is significantly greater than the energy required to separate the solute and solvent particles.

  7. Two non-volatile, non-ionizing solutes, A and B, are dissolved in separate samples of the same solvent. If the solution containing solute A exhibits a vapor pressure lowering ($\Delta P_A$) that is three times greater than the vapor pressure lowering ($\Delta P_B$) of the solution containing solute B, what is the ratio of their freezing point depressions ($\Delta T_{f,A} / \Delta T_{f,B}$)? Assume ideal behavior and that the solutions are dilute enough that molality is proportional to mole fraction.

    • $3:1$
    • $1:3$
    • $9:1$
    • $1:9$

    Answer: $3:1$

  8. Derive an expression for the molality ($m$) of a solution in terms of its mass percentage ($w$, expressed as a decimal, e.g., $0.15$ for $15\%$) and the molar masses of the solute ($MM_{\text{solute}}$) and solvent ($MM_{\text{solvent}}$).

    • $m = \frac{1000w}{(1-w)MM_{\text{solute}}}$
    • $m = \frac{w \cdot MM_{\text{solvent}}}{(1-w) \cdot MM_{\text{solute}}}$
    • $m = \frac{1000(1-w)}{w \cdot MM_{\text{solute}}}$
    • $m = \frac{w \cdot MM_{\text{solute}}}{1000(1-w)}$

    Answer: $m = \frac{1000w}{(1-w)MM_{\text{solute}}}$

  9. A saturated aqueous solution of a solid salt is in equilibrium with undissolved solid at $20 \text{ \textdegree C}$. If the dissolution of this salt is an exothermic process, what will happen to the concentration of the dissolved salt if the temperature is increased to $50 \text{ \textdegree C}$?

    • The concentration of the dissolved salt will decrease.
    • The concentration of the dissolved salt will increase.
    • The concentration of the dissolved salt will remain unchanged.
    • The salt will become supersaturated, but the concentration will not change until precipitation occurs.

    Answer: The concentration of the dissolved salt will decrease.

  10. An aqueous solution of ethanol ($C_2H_5OH$, molar mass $46.07 \text{ g/mol}$) has a molarity of $2.0 \text{ M}$ and a density of $0.98 \text{ g/mL}$. Calculate the mole fraction of ethanol in this solution. (Molar mass of water is $18.02 \text{ g/mol}$).

    • $0.037$
    • $0.039$
    • $0.041$
    • $0.043$

    Answer: $0.037$

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