Topic 4 – Gases in Solution & Colligative Properties

Significant Figures

• Definition: digits in a measured number that convey meaningful information about its precision.

• Rule set (Figure 3.20):

  • All non-zero digits are always significant.

  • Zeros – significance depends on position:

  • Between non-zero digits ⇒ significant

    • Examples: 704 (3 s.f.), 5.02 (3 s.f.), 173.05 (5 s.f.)

  • Trailing zeros in a number containing a decimal point ⇒ significant

    • $0.500$ (3 s.f.); $25.160$ (5 s.f.); $3.00$ (3 s.f.)

  • Leading zeros before the first non-zero digit ⇒ NOT significant (placeholders)

    • $0.00921$ (3 s.f.); $0.02501$ (4 s.f.)

  • Trailing zeros with no decimal point ⇒ ambiguous; use scientific notation to clarify

    • $1000$ could have 1–4 s.f.; write as $1 \times 10^{3},\;1.0 \times 10^{3},\;1.00 \times 10^{3},\;1.000 \times 10^{3}$

    • $590$ ⇒ $5.9 \times 10^{2}$ (2 s.f.) or $5.90 \times 10^{2}$ (3 s.f.)

• Exact numbers (counting quantities, unit definitions) have infinite significant figures and zero uncertainty.

Applying Significant Figures in Calculations (Figure 3.21)

• Multiplying a measurement by a constant ⇒ answer keeps the same number of s.f. as the measurement.

• Multiplication/Division of two or more measurements ⇒ answer limited by the least precise (fewest s.f.).

• Addition/Subtraction ⇒ match the smallest number of decimal places among operands.

• Logarithms/Antilogarithms ⇒ number of digits to the right of the decimal in result equals number of s.f. in original number.

Thermodynamics of Dissolution – Gases in Gases

• Governing equation: $\Delta G = \Delta H - T\Delta S$

• For mixing ideal gases:

  • $\Delta H \approx 0$ (enthalpy change negligible).

  • Positive entropy change \big(\Delta S > 0\big) drives spontaneity ⇒ \Delta G < 0.

  • Diffusion results because disorder increases.

Thermodynamics of Dissolution – Gases in Liquids

• $\Delta G = \Delta H - T\Delta S$ still applies, but enthalpy now matters.

• $\Delta_{sol}H$ (enthalpy of solution) can be endothermic or exothermic depending on solvent–solute interactions.

• Entropy term often still favourable (gas spreads through liquid), but may not overcome large positive $\Delta_{sol}H$.

Energetics & Mechanistic Steps of Dissolution in Organic Solvents

• Two-step conceptual model (Figures with AH₁ and AH₂):

  1. Expand solvent to create cavities (endothermic, \Delta H_1>0).

  2. Mix gaseous solute with expanded solvent (often exothermic, \Delta H_2<0).

• Net $\Delta{sol}H = \Delta H1 + \Delta H_2$ can be positive (overall endothermic) or negative.

• Dissolution requires more energy when solvent–solvent interactions are strong (harder to separate molecules). Mentimeter poll reinforced this.

“Like Dissolves Like” Principle

• Polar solvents (e.g., water, ethanol) dissolve polar or ionic solutes; non-polar solvents (e.g., hexane) dissolve non-polar solutes.

• Ethanol structure: polar OH plus non-polar alkyl → good at dissolving a range of species.

• Demonstration: Water > Ethanol > Hexane for dissolving table salt.

nhn Product (Ksp)

• Heterogeneous equilibrium constant for sparingly soluble ionic solids.

• General form: $\text{A}m\text{B}n(s) \rightleftharpoons m\,\text{A}^{n+}(aq) + n\,\text{B}^{m-}(aq)$
  $K_{sp}= [\text{A}^{n+}]^{m}[\text{B}^{m-}]^{n}$ (solid excluded from expression).

• Use symbol $s$ for molar solubility (instead of $x$).

• Examples:

  • $\text{BaSO}{4}(s) \rightleftharpoons \text{Ba}^{2+}+\text{SO}{4}^{2-}$
    $K{sp}= [\text{Ba}^{2+}][\text{SO}{4}^{2-}]$

  • $\text{PbI}{2}(s) \rightleftharpoons \text{Pb}^{2+}+2\text{I}^-$ $K{sp}= [\text{Pb}^{2+}][\text{I}^-]^{2}$

• Worked example (Medical barium meal):

2.45 mg $\text{BaSO}_4$ dissolves in 1 L at $25\,^{\circ}\text{C}$.

$n = \frac{0.00245\,\text{g}}{233.37\,\text{g·mol}^{-1}} = 1.05\times10^{-5}\,\text{mol}$
$s = 1.05\times10^{-5}\,\text{M}$

• $K_{sp}=s^{2}=1.10\times10^{-10}$

Common Ion Effect

• Presence of a shared ion suppresses solubility.

• Conceptual analogy: harder to dissolve sugar in honey (already concentrated).

• Example problem (SnF₂ in 0.30 M NaF):

  • $\text{SnF}_{2}(s) \rightleftharpoons \text{Sn}^{2+} + 2\text{F}^-$

  • ICE table with initial $[\text{F}^-]=0.30\,\text{M}$.

  • $K_{sp}=3.6\times10^{-8}=s(0.30)^{2}$ ⇒ $s=4.0\times10^{-7}\,\text{M}$ (dramatic decrease vs pure water).

Colligative Properties – Overview

• Depend solely on solute particle concentration, not identity (must be non-volatile solute):

  • Freezing point depression (ΔTₒ lower).

  • Boiling point elevation (ΔTᵦ higher).

  • Vapour pressure lowering.

  • Osmotic pressure.

• Expressed using molality $b$ because mass of solvent (kg) is temperature-independent.

Raoult’s Law – Vapour Pressure Lowering

• $P{solution}=x{solvent}P_{solvent}^{\ast}$

  • $P_{solution}$ = vapour pressure of solution.

  • $x_{solvent}$ = mole fraction of solvent.

  • $P_{solvent}^{\ast}$ = vapour pressure of pure solvent.

• Vanilla extract example: Water–ethanol mixture at $20^{\circ}\text{C}$ with $x{water}=0.9$, $P^{\ast}{water}=2.3\,\text{kPa}$ ⇒ $P_{solution}=2.07\,\text{kPa}$.

• Dead Sea calculation (32 % w/w NaCl):

  • In 100 g solution: 68 g water (3.78 mol); 32 g NaCl (0.548 mol).

  • $x_{water}=\frac{3.78}{3.78+0.548}=0.873$.

  • $P_{solution}=0.873\times2.3\,\text{kPa}=2.01\,\text{kPa}$.

Freezing Point Depression & Boiling Point Elevation

• Equations:

  • $\Delta Tf = Kf\,b$ (negative sign indicates lowering).

  • $\Delta Tb = Kb\,b$.

• Road-salt example (MgCl₂ for –10 °C streets):

• Desired $\Delta T_f = 10\,^{\circ}\text{C}$.

• $K_f\,(water)=1.86\,^{\circ}\text{C·kg·mol}^{-1}$.

$b=\frac{10}{1.86}=5.376\,\text{mol·kg}^{-1}$.

• Molar mass $M{\text{MgCl}2}=95.21\,\text{g·mol}^{-1}$ ⇒ need $m=511.9\,\text{g}$ per kg of water.

Osmotic Pressure

• Semipermeable membrane allows solvent through, not solute.

• Osmotic pressure (π) opposes further solvent flow.

• Conceptual apparatus: solution side B rises until hydrostatic pressure equals π.

• Formula (ideal dilute): $\pi = iRTc$ where $i$ is van ’t Hoff factor, $R$ universal gas constant, $T$ absolute temperature, $c$ molarity.

Practice & Conceptual Connections

• Mentimeter polls used for real-time checks: entropy questions, dissolution energetics, “easiest to dissolve,” definition of solute, saturated solutions.

• Kitchen-chemistry proposal: Determine maximum sugar mass that still allows an icy-pole to freeze; must consider colligative freezing-point depression.

  • Required data/equipment: accurate mass balance, volumetric flasks, freezer with stable temperature, thermometer.

  • Errors: measurement uncertainty, temperature fluctuations, supercooling.

Study & Exam Tips

• Work through remaining Topic 4 materials before next class.

• Complete Topic 3 & 4 quizzes promptly.

• Keep a separate sheet summarising all $K<em>{sp}$ values and $K</em>f/K_b$ constants provided.

• Practise setting up ICE tables quickly; watch significant-figure rules when reporting answers.

• Connect thermodynamic concepts (ΔG, ΔH, ΔS) to observable solution behaviour.