Solutions and Colligative Properties — MHT-CET Chemistry

Formulas (3)

• Concentration Terms: Which Ones Change With Temperature · Concentration terms
  $$M = \frac{n}{V(\text{L})} \ (\text{T-dependent}),\qquad m = \frac{n}{W_{\text{solvent}}(\text{kg})},\qquad x = \frac{n}{n_{\text{total}}}$$
• Solubility of Solids: Like Dissolves Like, ΔH of Solution, and the Salt That Dissolves Less on Heating · Enthalpy of solution
  $$\Delta H_{\text{sol}} = \Delta H_{\text{lattice}} + \Delta H_{\text{hyd}}$$
• Henry's Law: S = K_H · P, and Partial Pressures From Mole Fractions · Henry and Dalton
  $$S = K_H\,P \qquad K_H = \frac{S}{P} \qquad P_i = x_i\,P_{\text{total}}$$

Reference tables (1)

Watch out for (4)

• Naming the solvent first
  → Types of Solutions by the States of Solute and Solvent
• Ignoring the water of crystallisation
  → Concentration Terms: Which Ones Change With Temperature
• Subtracting the hydration enthalpy
  → Solubility of Solids: Like Dissolves Like, ΔH of Solution, and the Salt That Dissolves Less on Heating
• Dividing by the pressure
  → Henry's Law: S = K_H · P, and Partial Pressures From Mole Fractions

Formulas (2)

• Raoult's Law for Two Volatile Liquids: P = x_A P_A° + x_B P_B° · Raoult's law
  $$P_{\text{total}} = x_A P_A^\circ + x_B P_B^\circ \qquad y_A = \frac{x_A P_A^\circ}{P_{\text{total}}}$$
• Relative Lowering of Vapour Pressure = Mole Fraction of the Solute · Relative lowering
  $$\frac{P^\circ - P}{P^\circ} = x_2 = \frac{n_2}{n_1 + n_2} \approx \frac{W_2\,M_1}{M_2\,W_1}$$

Reference tables (1)

Watch out for (3)

• Using the given mole fraction for the wrong component
  → Raoult's Law for Two Volatile Liquids: P = x_A P_A° + x_B P_B°
• Dividing by the solution's pressure, or reporting the solvent's mole fraction
  → Relative Lowering of Vapour Pressure = Mole Fraction of the Solute
• Calling chloroform + acetone positive
  → Ideal and Non-Ideal Solutions: Which Way a Mixture Deviates

Formulas (3)

• ΔTb = Kb · m: Solve for Any One of Molality, Kb, Moles or Solvent Mass · Boiling point elevation
  $$\Delta T_b = K_b\,m = K_b\,\frac{n_2}{W_1(\text{kg})} \qquad T_b = T_b^\circ + \Delta T_b$$
• Molar Mass From ΔTb: M₂ = 1000 Kb W₂ / (ΔTb W₁) · Molar mass
  $$M_2 = \frac{1000\,K_b\,W_2}{\Delta T_b\,W_1}$$
• Ranking Electrolyte Solutions: Compare i × m · Electrolyte elevation
  $$\Delta T_b = i\,K_b\,m \qquad \text{rank by } i \times m$$

Watch out for (3)

• Grams where kilograms belong
  → ΔTb = Kb · m: Solve for Any One of Molality, Kb, Moles or Solvent Mass
• Swapping W₁ and W₂
  → Molar Mass From ΔTb: M₂ = 1000 Kb W₂ / (ΔTb W₁)
• Counting AlPO₄ as five ions
  → Ranking Electrolyte Solutions: Compare i × m

Formulas (3)

• ΔTf = Kf · m: Molality, Kf, or ΔTf From a Freezing Point · Freezing point depression
  $$\Delta T_f = K_f\,m,\qquad \Delta T_f = T_f^\circ - T_f \qquad (K_f^{\text{water}} = 1.86\ \text{K kg mol}^{-1})$$
• Molar Mass From ΔTf: M₂ = 1000 Kf W₂ / (ΔTf W₁) · Molar mass
  $$M_2 = \frac{1000\,K_f\,W_2}{\Delta T_f\,W_1}$$
• Highest and Lowest Depression: Compare i × m · Electrolyte depression
  $$\Delta T_f = i\,K_f\,m \qquad \text{rank by } i \times m$$

Watch out for (3)

• Reading a freezing point as the depression
  → ΔTf = Kf · m: Molality, Kf, or ΔTf From a Freezing Point
• Choosing the formula with W₁ on top
  → Molar Mass From ΔTf: M₂ = 1000 Kf W₂ / (ΔTf W₁)
• Ranking by molality alone
  → Highest and Lowest Depression: Compare i × m

Formulas (3)

• π = CRT: Solve for π, C, T or n · Van't Hoff equation
  $$\pi = CRT = \frac{n}{V}RT \qquad (R = 0.082\ \text{dm}^3\,\text{atm K}^{-1}\text{mol}^{-1})$$
• Molar Mass From Osmotic Pressure: M = W R T / (π V) · Molar mass
  $$M = \frac{W\,R\,T}{\pi\,V}$$
• Isotonic and Hypertonic Solutions, and π = iCRT for Electrolytes · Electrolytes and isotonicity
  $$\pi = i\,C\,R\,T \qquad \text{isotonic} \iff \pi_1 = \pi_2 \iff (iC)_1 = (iC)_2$$

Watch out for (3)

• Volume in millilitres
  → π = CRT: Solve for π, C, T or n
• Leaving V in millilitres
  → Molar Mass From Osmotic Pressure: M = W R T / (π V)
• Comparing grams per litre directly
  → Isotonic and Hypertonic Solutions, and π = iCRT for Electrolytes

Formulas (2)

• The Van't Hoff Factor: i = ΔTf(observed)/(Kf · m), and the Ion Count for Complete Dissociation · Van't Hoff factor
  $$i = \frac{\text{observed}}{\text{calculated}} = \frac{\Delta T_f^{\text{obs}}}{K_f\,m} = \frac{M_{\text{calc}}}{M_{\text{obs}}}$$
• Degree of Dissociation From i: α = (i − 1)/(n − 1) · Degree of dissociation
  $$i = 1 + (n - 1)\alpha \ \Rightarrow\ \alpha = \frac{i - 1}{n - 1} \qquad \text{association: } i = 1 - \alpha + \frac{\alpha}{n}$$

Reference tables (1)

Watch out for (3)

• Using the calculated ΔTf as the observed one
  → The Van't Hoff Factor: i = ΔTf(observed)/(Kf · m), and the Ion Count for Complete Dissociation
• Dividing by n instead of n − 1
  → Degree of Dissociation From i: α = (i − 1)/(n − 1)
• Marking 'boiling point elevation' as the non-colligative one
  → Which Properties Are Colligative, and the Statements the Exam Tests