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Solutions - Colligative Properties and Determination of Molar Mass

Grade 12CBSEChemistry

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Colligative properties are those properties of solutions which depend only on the number of solute particles (ions or molecules) and not on their chemical identity.

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Relative Lowering of Vapour Pressure: The ratio of the lowering of vapour pressure (p10−p1p_1^0 - p_1) to the vapour pressure of the pure solvent (p10p_1^0) is equal to the mole fraction of the solute (χ2\chi_2).

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Elevation of Boiling Point (ΔTb\Delta T_b): The boiling point of a solution is always higher than that of the pure solvent. This elevation is directly proportional to the molal concentration of the solute.

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Depression of Freezing Point (ΔTf\Delta T_f): The freezing point of a solution is lower than that of the pure solvent. This depression is directly proportional to the molality of the solution.

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Osmosis and Osmotic Pressure (π\pi): Osmosis is the flow of solvent molecules from a region of lower solute concentration to higher solute concentration through a semi-permeable membrane. Osmotic pressure is the excess pressure applied to the solution side to stop osmosis.

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Van't Hoff Factor (ii): Used to account for association or dissociation of solute particles. i=Observed Colligative PropertyCalculated Colligative Propertyi = \frac{\text{Observed Colligative Property}}{\text{Calculated Colligative Property}}.

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Abnormal Molar Mass: When a solute undergoes association or dissociation in a solvent, the molar mass determined using colligative properties differs from the theoretical value.

📐Formulae

p10−p1p10=χ2=n2n1+n2\frac{p_1^0 - p_1}{p_1^0} = \chi_2 = \frac{n_2}{n_1 + n_2}

ΔTb=i⋅Kb⋅m\Delta T_b = i \cdot K_b \cdot m

ΔTf=i⋅Kf⋅m\Delta T_f = i \cdot K_f \cdot m

π=i⋅C⋅R⋅T=i⋅n2V⋅R⋅T\pi = i \cdot C \cdot R \cdot T = i \cdot \frac{n_2}{V} \cdot R \cdot T

i=Normal Molar MassAbnormal Molar Massi = \frac{\text{Normal Molar Mass}}{\text{Abnormal Molar Mass}}

α=i−1n−1 (for dissociation, where n is number of ions)\alpha = \frac{i - 1}{n - 1} \text{ (for dissociation, where } n \text{ is number of ions)}

α=1−i1−1/n (for association, where n is number of molecules associated)\alpha = \frac{1 - i}{1 - 1/n} \text{ (for association, where } n \text{ is number of molecules associated)}

💡Examples

Problem 1:

Calculate the boiling point of a solution when 18 g18\text{ g} of glucose (C6H12O6C_6H_{12}O_6) is dissolved in 1 kg1\text{ kg} of water. (KbK_b for water = 0.52 K kg mol−10.52\text{ K kg mol}^{-1}, Boiling point of pure water = 373.15 K373.15\text{ K})

Solution:

  1. Molar mass of glucose (C6H12O6C_6H_{12}O_6) = 180 g mol−1180\text{ g mol}^{-1}.
  2. Number of moles (n2n_2) = 18 g180 g mol−1=0.1 mol\frac{18\text{ g}}{180\text{ g mol}^{-1}} = 0.1\text{ mol}.
  3. Molality (mm) = n2Mass of solvent in kg=0.11=0.1 mol kg−1\frac{n_2}{\text{Mass of solvent in kg}} = \frac{0.1}{1} = 0.1\text{ mol kg}^{-1}.
  4. ΔTb=Kb⋅m=0.52×0.1=0.052 K\Delta T_b = K_b \cdot m = 0.52 \times 0.1 = 0.052\text{ K}.
  5. Boiling point of solution Tb=Tb0+ΔTb=373.15+0.052=373.202 KT_b = T_b^0 + \Delta T_b = 373.15 + 0.052 = 373.202\text{ K}.

Explanation:

Since glucose is a non-electrolyte, i=1i = 1. The elevation in boiling point is calculated using the molality of the solution and the ebullioscopic constant of water.

Problem 2:

A 0.1 m0.1\text{ m} aqueous solution of K2SO4K_2SO_4 is found to freeze at −0.432∘C-0.432^{\circ}C. Calculate the Van't Hoff factor (ii) for the salt. (KfK_f for water = 1.86 K kg mol−11.86\text{ K kg mol}^{-1})

Solution:

  1. Observed ΔTf=0−(−0.432)=0.432 K\Delta T_f = 0 - (-0.432) = 0.432\text{ K}.
  2. Calculated ΔTf=Kf⋅m=1.86×0.1=0.186 K\Delta T_f = K_f \cdot m = 1.86 \times 0.1 = 0.186\text{ K}.
  3. i=Observed ΔTfCalculated ΔTf=0.4320.186≈2.32i = \frac{\text{Observed } \Delta T_f}{\text{Calculated } \Delta T_f} = \frac{0.432}{0.186} \approx 2.32.

Explanation:

The Van't Hoff factor ii is the ratio of the experimentally observed colligative property to the theoretically calculated value. Here, i>1i > 1 indicates dissociation of K2SO4K_2SO_4.