Colligative Properties and Determination of Molar Mass MCQ Quiz - Objective Question with Answer for Colligative Properties and Determination of Molar Mass - Download Free PDF

CONCEPT:

Elevation in Boiling Point

• The boiling point of a solution increases when a non-volatile solute is added to it. This phenomenon is known as elevation in boiling point.
• The elevation in boiling point (ΔTb) is directly proportional to the molality of the solution and the van 't Hoff factor (i), given by:

  ΔTb = i × Kb × m

• Here:
  • i = Van 't Hoff factor (number of particles the solute dissociates into).
  • Kb = Boiling point elevation constant.
  • m = Molality of the solution.

EXPLANATION:

• Van 't Hoff factors for the given solutes:
  • Urea (0.01 M): Does not dissociate, i = 1.
  • KNO₃ (0.01 M): Dissociates into K⁺ and NO₃⁻, i = 2.
  • Na₂SO₄ (0.01 M): Dissociates into 2 Na⁺ and SO₄²⁻, i = 3.
  • C₆H₁₂O₆ (0.015 M): Does not dissociate, i = 1.
• Based on the formula ΔTb = i × Kb × m:
  • Higher i leads to a greater elevation in boiling point.
  • Na₂SO₄ (i = 3) will exhibit the highest boiling point among the solutions.

Therefore, the solution with 0.01 M Na₂SO₄ will exhibit the highest boiling point.

Explanation:

The elevation of the boiling point of a solution depends on the concentration of solute particles in the solution. The more the number of solute particles in the solution, the higher the elevation in boiling point.

Elevation in boiling point ∝ i × M

The given compounds and their respective aqueous solutions are

\(\begin{array}{lc|c} & \text { Solute } & \mathrm{i} \\ \hline \text { A. } & \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6 & 1 \\ \text { B. } & \mathrm{NaCl} & 2 \\ \text { C. } & \mathrm{MgCl}_2 & 3 \\ \text { D. } & \mathrm{AlCl}_3 & 4 \\ \text { E. } & \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3 & 5 \end{array}\)

Order of elevation in boiling point

E > D > C > B > A

CONCEPT:

Osmotic Pressure and Van't Hoff Factor

• Osmotic pressure (π) is a colligative property and is directly proportional to the molar concentration of the solute and the Van't Hoff factor (i), which accounts for dissociation or ionization of solutes in water.
• The formula for osmotic pressure is given by:\(\pi = i \times C \times R \times T\)
  • i is the Van't Hoff factor, which represents the number of particles the solute dissociates into.
  • C is the molar concentration of the solute.
  • R is the gas constant.
  • T is the temperature in Kelvin.
• For complete dissociation:
  • BaCl₂ dissociates into 3 ions: Ba²⁺ and 2Cl^-, so i = 3.
  • NaCl dissociates into 2 ions: Na⁺ and Cl^-, so i = 2.

EXPLANATION:

• For BaCl₂, the osmotic pressure is:
  • i_BaCl2 = 3 (since BaCl₂ dissociates into 3 ions)
  • Concentration (C) = 0.01 M
  • Osmotic pressure: \(\pi_1 = 3 \times 0.01 \times R \times T\)
• For NaCl, the osmotic pressure is:
  • i_NaCl = 2 (since NaCl dissociates into 2 ions)
  • Concentration (C) = 0.005 M
  • Osmotic pressure: \(\pi_2 = 2 \times 0.005 \times R \times T\)
• Now, let's find the ratio of the osmotic pressures:
  • Ratio: \(\frac{\pi_1}{\pi_2} = \frac{3 \times 0.01}{2 \times 0.005} = \frac{0.03}{0.01} = 3\)

CONCLUSION:

• The correct answer is: Option 1) 3:1

CONCEPT:

Boiling Point Elevation and Van't Hoff Factor

• Boiling point elevation is a colligative property, meaning it depends on the number of solute particles in a solution, not the nature of the solute.
• The equation for boiling point elevation is:
  • \(\Delta T_b = i \cdot K_b \cdot m \)
  where:
  • \( \Delta T_b \) = Boiling point elevation
  • \(i \) = Van't Hoff factor (number of particles the solute dissociates into)
  • \(K_b \) = Ebullioscopic constant (depends on the solvent)
  • \( m \) = Molality (moles of solute per kilogram of solvent)
• The Van't Hoff factor (\( i \)) increases with the number of ions a solute dissociates into.

EXPLANATION:

• NaCl dissociates into 2 ions: Na⁺ and Cl^-, so \(i = 2\) .
• Glucose does not dissociate in solution, so \(i = 1 \).
• MgCl₂ dissociates into 3 ions: Mg²⁺ and 2 Cl^-, so \(i = 3 \).
• AlCl₃ dissociates into 4 ions: Al³⁺ and 3 Cl^-, so \(i = 4 \).
• Since all solutions have the same concentration (0.1 M), the solute with the highest Van't Hoff factor will have the greatest boiling point elevation.

CONCLUSION:

The correct answer is option 4: 0.1 M AlCl₃ (i = 4).

Concept:

The freezing point depression (ΔT_f) is a colligative property, which means it depends on the number of solute particles in a solution and not on the nature of the solute. This property is observed when a non-volatile solute is added to a solvent, which causes the freezing point of the solvent to decrease.

The formula for freezing point depression is: ΔT_f = i × K_f × m, where i is the van 't Hoff factor, K_f is the cryoscopic constant, and m is the molality of the solution.

Explanation:

• Assertion (A): Addition of ethylene glycol (non-volatile) to water lowers the freezing point of water.

  • This statement is correct. Adding ethylene glycol to water introduces more solute particles in the solution, resulting in a lower freezing point for the solution.

• Reason (R): Addition of any substance to water lowers the freezing point of water.

  • This statement is incorrect. Only the addition of a non-volatile solute will cause freezing point depression. Some substances might not dissolve or might even raise the freezing point under certain conditions.

Conclusion:

Therefore, the correct statement is: A is correct but R is wrong

Explanation:

The elevation of the boiling point of a solution depends on the concentration of solute particles in the solution. The more the number of solute particles in the solution, the higher the elevation in boiling point.

Elevation in boiling point ∝ i × M

The given compounds and their respective aqueous solutions are

\(\begin{array}{lc|c} & \text { Solute } & \mathrm{i} \\ \hline \text { A. } & \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6 & 1 \\ \text { B. } & \mathrm{NaCl} & 2 \\ \text { C. } & \mathrm{MgCl}_2 & 3 \\ \text { D. } & \mathrm{AlCl}_3 & 4 \\ \text { E. } & \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3 & 5 \end{array}\)

Order of elevation in boiling point

E > D > C > B > A

CONCEPT:

Elevation in Boiling Point

• The boiling point of a solution increases when a non-volatile solute is added to it. This phenomenon is known as elevation in boiling point.
• The elevation in boiling point (ΔTb) is directly proportional to the molality of the solution and the van 't Hoff factor (i), given by:

  ΔTb = i × Kb × m

• Here:
  • i = Van 't Hoff factor (number of particles the solute dissociates into).
  • Kb = Boiling point elevation constant.
  • m = Molality of the solution.

EXPLANATION:

• Van 't Hoff factors for the given solutes:
  • Urea (0.01 M): Does not dissociate, i = 1.
  • KNO₃ (0.01 M): Dissociates into K⁺ and NO₃⁻, i = 2.
  • Na₂SO₄ (0.01 M): Dissociates into 2 Na⁺ and SO₄²⁻, i = 3.
  • C₆H₁₂O₆ (0.015 M): Does not dissociate, i = 1.
• Based on the formula ΔTb = i × Kb × m:
  • Higher i leads to a greater elevation in boiling point.
  • Na₂SO₄ (i = 3) will exhibit the highest boiling point among the solutions.

Therefore, the solution with 0.01 M Na₂SO₄ will exhibit the highest boiling point.

Explanation:-:

Refrigerants and Cooling Methods

• Different substances and mixtures can reach different minimum temperatures when used for cooling purposes.
• Commonly used cooling mixtures and their approximate temperatures:
  • Ether + Dry Ice:
    • Not commonly used or optimal for reaching extremely low temperatures.
  • NH₄Cl (Ammonium Chloride):
    • Typically used in cooling packs and not for extreme low temperatures.
  • Acetone + Dry Ice:
    • This mixture can reach temperatures around -78 °C.
  • CaCl₂.2H₂O (Calcium Chloride Dihydrate):
    • Often used in cooling mixtures, but not for the lowest temperatures achievable by common means.

The mixture that reaches the lowest temperature is Acetone + Dry Ice

Correct answer: 1 and 2) 

Concept:

• The properties that depend on the number of solute particles irrespective of their nature relative to the total number of particles present in the solution are called colligative properties.
• There are four colligative properties: 1. Relative Lowering of vapour Pressure 2. Elevation in Boiling Point 3. Depression in freezing point 4. Osmotic pressure.
• When a non-volatile solute is added to a solvent, the vapour pressure decreases.

Explanation:

• A colligative property is a property of a solution that is dependent on the ratio between the total number of solute particles (in the solution) to the total number of solvent particles.
• Colligative properties are not dependent on the chemical nature of the solution's components.
• When only one component of a binary mixture either solvent or solute is volatile it causes deviation from ideal behaviour and vapour pressure of the solution which causes a change in colligative property.
• Thus, Colligative properties are observed when a non-volatile solute is added to a volatile solvent
• Hence (1) and (2) are correct.

Conclusion:

Thus, Colligative properties are observed when a non-volatile solid is dissolved in a volatile liquid and a non-volatile liquid is dissolved in another volatile liquid.

Additional Information

Explanation:

The elevation of the boiling point of a solution depends on the concentration of solute particles in the solution. The more the number of solute particles in the solution, the higher the elevation in boiling point.

Elevation in boiling point ∝ i × M

The given compounds and their respective aqueous solutions are

\(\begin{array}{lc|c} & \text { Solute } & \mathrm{i} \\ \hline \text { A. } & \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6 & 1 \\ \text { B. } & \mathrm{NaCl} & 2 \\ \text { C. } & \mathrm{MgCl}_2 & 3 \\ \text { D. } & \mathrm{AlCl}_3 & 4 \\ \text { E. } & \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3 & 5 \end{array}\)

Order of elevation in boiling point

E > D > C > B > A

Explanation:

The elevation in boiling point depends on the number of solute particles present in the solution. According to Van't Hoff factor, the number of solute particles in the solution is given by:

\(i =\;\frac{moles\; of\; solute\; particles\; in\; solution}{moles\; of\; solute\; dissolved}\)

For ionic compounds, i depends on the extent of dissociation in solution, while for non-electrolytes, i is 1.

Now, let's consider each compound in the given solution:

Statement A:  NH₂CONH₂ is a non-electrolyte and will not dissociate in solution. Thus the vale of i is 1.

Statement B: AlCl₃ is an ionic compound that dissociates into four ions (Al³⁺ and three Cl^-) in solution as follows;

\(AlCl_{3}(aq)\rightleftharpoons Al^{3+}(aq) \;+3Cl^{-}(aq)\)

Thus, total number of ions is 4 or i =4

Statement C: Na₂SO₄ is an ionic compound that dissociates into three ions (two Na⁺ and one SO4^2-) in solution as follows;

\(Na_{2}SO_{4}(aq)\rightleftharpoons 2Na^{+}(aq)+SO_{4}^{2-}(aq)\)

Thus, total number of ions is 3 or i =3

Statement D: Al₂(SO4)₃ is an ionic compound that dissociates into five ions (two Al³⁺ and three SO4^2-) in solution as follows; 

\(Al_{2}(SO_{4})_{3}(aq)\rightleftharpoons 2Al^{3+}(aq)+3SO_{4}^{2-}(aq)\)

Thus, total number of ions is 5 or i =5

Statement E: NaCl is an ionic compound that dissociates into two ions (Na⁺ and Cl^-) in solution as follows; 

\(NaCl(aq)\rightleftharpoons Na^{+}(aq)+Cl^{-}(aq)\)

Now, we can arrange the given compounds in decreasing order of elevation in boiling point as:

D > B > C > E > A

This is because compounds with higher values of i will have a greater number of solute particles in solution, leading to a greater elevation in boiling point.

Conclusion:

Therefore, option 4), D>B>C>E>A is the correct answer.

Concept:

The freezing point depression (ΔT_f) is a colligative property, which means it depends on the number of solute particles in a solution and not on the nature of the solute. This property is observed when a non-volatile solute is added to a solvent, which causes the freezing point of the solvent to decrease.

The formula for freezing point depression is: ΔT_f = i × K_f × m, where i is the van 't Hoff factor, K_f is the cryoscopic constant, and m is the molality of the solution.

Explanation:

• Assertion (A): Addition of ethylene glycol (non-volatile) to water lowers the freezing point of water.

  • This statement is correct. Adding ethylene glycol to water introduces more solute particles in the solution, resulting in a lower freezing point for the solution.

• Reason (R): Addition of any substance to water lowers the freezing point of water.

  • This statement is incorrect. Only the addition of a non-volatile solute will cause freezing point depression. Some substances might not dissolve or might even raise the freezing point under certain conditions.

Conclusion:

Therefore, the correct statement is: A is correct but R is wrong

Concept:

Colligative properties are properties of solutions that depend on the number of solute particles but not on their nature. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Intensive properties are those that are independent of the amount of material present.

Explanation:

• Statement I: Except for osmotic pressure, all other colligative properties depend on the nature of the solvent.

  • This statement is incorrect because all colligative properties, including osmotic pressure, depend on the number of particles in the solution and not on the nature of the solvent.

• Statement II: Colligative properties are intensive properties.

  • This statement is correct because colligative properties do not depend on the quantity of the solvent or solute, but rather on the ratio of their quantities.

Conclusion:

Therefore, the correct option is: Statement I is INCORRECT, but Statement II is CORRECT

CONCEPT:

Boiling Point Elevation and Van't Hoff Factor

• Boiling point elevation is a colligative property, meaning it depends on the number of solute particles in a solution, not the nature of the solute.
• The equation for boiling point elevation is:
  • \(\Delta T_b = i \cdot K_b \cdot m \)
  where:
  • \( \Delta T_b \) = Boiling point elevation
  • \(i \) = Van't Hoff factor (number of particles the solute dissociates into)
  • \(K_b \) = Ebullioscopic constant (depends on the solvent)
  • \( m \) = Molality (moles of solute per kilogram of solvent)
• The Van't Hoff factor (\( i \)) increases with the number of ions a solute dissociates into.

EXPLANATION:

• NaCl dissociates into 2 ions: Na⁺ and Cl^-, so \(i = 2\) .
• Glucose does not dissociate in solution, so \(i = 1 \).
• MgCl₂ dissociates into 3 ions: Mg²⁺ and 2 Cl^-, so \(i = 3 \).
• AlCl₃ dissociates into 4 ions: Al³⁺ and 3 Cl^-, so \(i = 4 \).
• Since all solutions have the same concentration (0.1 M), the solute with the highest Van't Hoff factor will have the greatest boiling point elevation.

CONCLUSION:

The correct answer is option 4: 0.1 M AlCl₃ (i = 4).

Concept:

Gas Law is a law that relates the pressure, volume, and temperature of a gas.

• PV = nRT
• Where, P = pressure, V = volume, R = gas constant, T = temperature, and n = molar mass.
• Pressure decreases as the altitude of the Earth increases.

Explanation:

From gas law,

P ∝ T

• As we know that the pressure at higher altitudes is low also the temperature is directly proportional to pressure, 
• So, the atmospheric pressure at higher altitudes is low as compared to that at sea level, so, water boils below 100°C at higher altitudes.
• At sea level at a pressure of 1.013 bar, water begins to boil at a temperature of 100°C.

Example-

• On Mount Everest at an altitude of 8849 m, the air pressure is only around 0.325 bar.
• Due to this significantly reduced pressure, the water already begins to boil at a temperature of around 71°C.
• However, since the temperature does not rise any further during boiling, the cooking of foods such as potatoes or pasta thus takes significantly longer (As temperature remains constant during a change of state.)