Solutions — Practice Quiz

A Chemistry cheat sheet for Solutions — every key formula with its symbols defined — plus a medium-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. Which of the following terms represents the energy change associated with the separation of solvent molecules during the dissolution process, as described by the enthalpy of solution formula?

    • $\Delta H_{\text{solute}}$
    • $\Delta H_{\text{solvent}}$
    • $\Delta H_{\text{mix}}$
    • $\Delta H_{\text{soln}}$

    Answer: $\Delta H_{\text{solvent}}$

  2. If the Henry's law constant for a gas in water at $25^\circ \text{C}$ is $0.015 \text{ mol/(L} \cdot \text{atm)}$, what is the solubility of the gas when its partial pressure above the solution is $2.0 \text{ atm}$?

    • $0.0075 \text{ mol/L}$
    • $0.015 \text{ mol/L}$
    • $0.030 \text{ mol/L}$
    • $0.060 \text{ mol/L}$

    Answer: $0.030 \text{ mol/L}$

  3. A solution is prepared by dissolving $25.0 \text{ g}$ of $\text{NaCl}$ in $225.0 \text{ g}$ of water. What is the mass percentage of $\text{NaCl}$ in this solution?

    • $10.0 \%$
    • $11.1 \%$
    • $8.0 \%$
    • $9.0 \%$

    Answer: $10.0 \%$

  4. Which concentration unit is most suitable for calculations involving colligative properties, as it is independent of temperature changes?

    • Molarity ($M$)
    • Molality ($m$)
    • Mass percentage
    • Mole fraction ($X_A$)

    Answer: Molality ($m$)

  5. A solution contains a non-volatile solute. If the mole fraction of the solvent is $0.80$ and the vapor pressure of the pure solvent is $100 \text{ mmHg}$, what is the vapor pressure of the solution according to Raoult's Law?

    • $20 \text{ mmHg}$
    • $80 \text{ mmHg}$
    • $100 \text{ mmHg}$
    • $120 \text{ mmHg}$

    Answer: $80 \text{ mmHg}$

  6. A $0.50 \text{ m}$ aqueous solution of a non-electrolyte has a boiling point elevation constant ($K_b$) for water of $0.512 \text{ }^\circ \text{C/m}$. What is the boiling point elevation of this solution?

    • $0.128 \text{ }^\circ \text{C}$
    • $0.256 \text{ }^\circ \text{C}$
    • $0.512 \text{ }^\circ \text{C}$
    • $1.024 \text{ }^\circ \text{C}$

    Answer: $0.256 \text{ }^\circ \text{C}$

  7. What is the freezing point depression of a $0.20 \text{ m}$ aqueous solution if the freezing point depression constant ($K_f$) for water is $1.86 \text{ }^\circ \text{C/m}$?

    • $0.093 \text{ }^\circ \text{C}$
    • $0.186 \text{ }^\circ \text{C}$
    • $0.372 \text{ }^\circ \text{C}$
    • $0.744 \text{ }^\circ \text{C}$

    Answer: $0.372 \text{ }^\circ \text{C}$

  8. Calculate the osmotic pressure ($\Pi$) of a $0.10 \text{ M}$ solution at $27^\circ \text{C}$ ($300 \text{ K}$). Use $R = 0.0821 \text{ L} \cdot \text{atm/(mol} \cdot \text{K)}$.

    • $0.246 \text{ atm}$
    • $2.46 \text{ atm}$
    • $24.6 \text{ atm}$
    • $246 \text{ atm}$

    Answer: $2.46 \text{ atm}$

  9. A mixture contains $2.0 \text{ moles}$ of component A and $8.0 \text{ moles}$ of component B. What is the mole fraction of component A ($X_A$)?

    • $0.20$
    • $0.25$
    • $0.80$
    • $0.75$

    Answer: $0.20$

  10. When a solute is added to a solvent, and the rate of dissolution equals the rate of crystallization, what state has the solution reached?

    • Supersaturation
    • Unsaturation
    • Dynamic equilibrium
    • Precipitation

    Answer: Dynamic equilibrium

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