🧪 Abnormal Molar Mass

 

🧪 Abnormal Molar Mass

🔹 What is Molar Mass?

Molar mass is the mass of 1 mole of a substance (atoms, molecules, or ions).

• Unit: grams per mole (g/mol)

For example:

• Molar mass of H₂O = 18 g/mol

• Molar mass of NaCl = 58.5 g/mol

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🔹 What is Abnormal Molar Mass?

When the molar mass calculated using colligative properties (like depression in freezing point, elevation in boiling point, etc.) differs from the expected or actual molar mass, it is called abnormal molar mass.

This usually happens due to:

• Association of solute particles

• Dissociation of solute particles

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🔹 Why Does It Happen?

1. Association

Some solute molecules combine (associate) to form larger particles in solution.
🔸 Example: Acetic acid in benzene

• CH₃COOH molecules form dimers due to hydrogen bonding

• Number of particles decreases → colligative property decreases

• Molar mass appears higher than actual (abnormal increase)

2. Dissociation

Some solutes break into ions (dissociate) in solution.
🔸 Example: NaCl in water

• NaCl → Na⁺ + Cl⁻

• Number of particles increases → colligative property increases

• Molar mass appears lower than actual (abnormal decrease)

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🔹 How to Correct Abnormal Molar Mass?

We use the van't Hoff factor (i) to account for the abnormal behavior.

🧾 Van’t Hoff Factor (i)

$$i = \frac{\text{Observed colligative property}}{\text{Calculated colligative property assuming no association or dissociation}}$$

Or,

$$i = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}$$

👉 For dissociation:

• $i > 1$

👉 For association:

• $i < 1$
  

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🔍 Examples:

1. Association Example (Acetic Acid in Benzene)

• Expected molar mass = 60 g/mol

• Observed = 120 g/mol (due to dimerization)

• So, $i = \frac{60}{120} = 0.5$

2. Dissociation Example (KCl in Water)

• KCl → K⁺ + Cl⁻

• Ideally, $i=\mathrm{2<span\; class="base"><br></span>}$

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📌 Summary Table:

Phenomenon	Effect on Colligative Property	Observed Molar Mass	van't Hoff Factor (i)
Association	Decreases	Higher	Less than 1
Dissociation	Increases	Lower	Greater than 1

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🧪 1. Degree of Association (α)

🔹 What is Association?

When two or more molecules of a solute combine (associate) to form a bigger molecule in a solution, the number of particles decreases.
→ This reduces colligative properties → gives higher molar mass (abnormal molar mass)

🔹 Degree of Association (α)

It is the fraction of molecules that undergo association.

🔹 General Formula for Association

Let’s say n molecules of a solute associate to form 1 molecule:

$$nA \rightleftharpoons A_n$$

Then,

$$i = 1 - \alpha + \frac{\alpha}{n}$$

Where:

• $\mathrm{i=\; van’t\; Hoff\; factor}$

• $\alpha$ = degree of association

• $n$ = number of molecules associated together

✅ Example: Acetic Acid (CH₃COOH) in Benzene

• It dimerizes:

  $$2CH₃COOH \rightleftharpoons (CH₃COOH)_2$$
  

• So, $n = 2$
  

$$i = 1 - \alpha + \frac{\alpha}{2}$$

If you are given $i$, you can calculate $\alpha$ using this formula.

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🧪 2. Degree of Dissociation (α)

🔹 What is Dissociation?

When one molecule splits into more than one ion, the number of solute particles increases.
→ This increases colligative properties → gives lower molar mass

🔹 Degree of Dissociation (α)

It is the fraction of molecules that dissociate into ions.

🔹 General Formula for Dissociation

For a substance like:

$$A_xB_y \rightarrow xA^{y+} + yB^{x-}$$

Let the initial amount be 1 mole. After dissociation:

• Undissociated: $1 - \alpha$ mole

• Dissociated: $x\alpha + y\alpha = (x + y)\alpha$ moles of ions

So, total moles = $1 - \alpha + (x + y)\alpha = 1 + \alpha(x + y - 1)$

$$i = 1 + \alpha(n - 1)$$

Where:

• $n$ = total number of particles after dissociation

• $\alpha$ = degree of dissociation

✅ Example: KCl

$$KCl \rightarrow K^+ + Cl^- \Rightarrow n = 2$$
$$i = 1 + \alpha(2 - 1) = 1 + \alpha \Rightarrow \alpha = i - 1$$

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🔁 Quick Comparison:

Concept	What Happens?	No. of Particles	Molar Mass	van’t Hoff Factor (i)	α Value
Association	Molecules combine	↓ Decreases	Increases	i < 1	Use: $i = 1 - \alpha + \frac{\alpha}{n}$
Dissociation	Molecules split	↑ Increases	Decreases	i > 1	Use: $i = 1 + \alpha(n - 1)$

📝 Questions on Abnormal Molar Mass

Q1. What is meant by abnormal molar mass?
a) The molar mass of a compound calculated using ideal gas law
b) A molar mass that differs from its expected value due to association or dissociation
c) Molar mass that never changes
d) Molar mass of a pure solid only

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Q2. If a solute undergoes dissociation in solution, the observed molar mass will be:
a) Greater than the expected molar mass
b) Equal to the expected molar mass
c) Less than the expected molar mass
d) Zero

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Q3. Acetic acid dimerizes in benzene. This leads to:
a) Increase in number of particles
b) Decrease in molar mass
c) Decrease in number of particles
d) No change in colligative properties

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Q4. What is the van’t Hoff factor (i) if a compound dissociates completely into 3 ions?
a) 1
b) 2
c) 3
d) 4

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Q5. The formula to calculate abnormal molar mass using van’t Hoff factor is:
a) i = observed molar mass / normal molar mass
b) i = normal molar mass / abnormal molar mass
c) i = abnormal molar mass × 100
d) i = observed pressure / actual pressure

answers:

Q1. b
Q2. c
Q3. c
Q4. c
Q5. b

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📝 Questions on Colligative Properties

Q1. Which of the following is not a colligative property?
a) Boiling point elevation
b) Vapour pressure lowering
c) Heat of combustion
d) Freezing point depression

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Q2. Colligative properties depend on:
a) Nature of solute
b) Nature of solvent
c) Number of solute particles
d) Volume of solvent

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Q3. Which colligative property is used to determine the molar mass of a solute in a solution?
a) Heat capacity
b) Osmotic pressure
c) Solubility
d) Surface tension

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Q4. The elevation in boiling point is directly proportional to:
a) Volume of solute
b) Molality of solution
c) Molarity of solution
d) Temperature of solute

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Q5. Which of the following solutions will show the maximum freezing point depression, if all have same concentration?
a) Urea (non-electrolyte)
b) NaCl
c) MgCl₂
d) Glucose

Answers:

Q1. c
Q2. c
Q3. b
Q4. b
Q5. c

WORKSHEET

1.  Define molality and mole fraction. How are they related in the context of a solution?

2. State Henry's law. How does the solubility of a gas in a liquid vary with temperature and pressure?

3. Differentiate between ideal and non-ideal solutions with suitable examples.

4. What is Raoult's law? How is it applied to determine the vapor pressure of a solution?

5. Explain the concept of colligative properties. List four colligative properties and describe any one in detail.

6. Calculate the boiling point elevation when 0.5 mol of a non-volatile solute is dissolved in 1 kg of water. (Given: K_b for water = 0.52 K kg/mol)

7. Describe the phenomenon of osmosis and osmotic pressure. How can osmotic pressure be used to determine the molar mass of a solute?

8. What is the van't Hoff factor? How does it affect the calculation of colligative properties for electrolytic solutions?

9. A solution containing 1.8 g of glucose (C₆H₁₂O₆) in 100 g of water freezes at -0.093°C. Calculate the molar mass of glucose. (Given: K_f for water = 1.86 K kg/mol)

10. Explain the term 'abnormal molar mass'. What causes the observed molar mass of a solute to deviate from its expected value in a solution?

ANSWERS:👇

1. Define molality and mole fraction. How are they related in the context of a solution?

Molality (m): It is defined as the number of moles of solute present in 1 kilogram of solvent.

$$m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$$

Mole Fraction (χ): It is the ratio of the number of moles of a component to the total number of moles of all components in the solution.​

$$\chi_{\text{solute}} = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}}$$

Relation: While molality focuses on the mass of the solvent, mole fraction considers the ratio of moles between components. Both are independent of temperature and provide insights into the composition of the solution.​

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2. State Henry's law. How does the solubility of a gas in a liquid vary with temperature and pressure?

Henry's Law: The solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Mathematically:​

$$C = k_H \times P$$

Where:

• $C$ = concentration of the gas in the liquid​

• $k_H$ = Henry's law constant​

• $P$ = partial pressure of the gas​

Effect of Pressure: Increasing the pressure increases the solubility of the gas.​

Effect of Temperature: Increasing the temperature generally decreases the solubility of gases in liquids because gas molecules gain kinetic energy and escape more readily.​

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3. Differentiate between ideal and non-ideal solutions with suitable examples.

Ideal Solution:

• Obeys Raoult's law at all concentrations.​

• No enthalpy change upon mixing ($\Delta H_{\text{mix}} = 0$).​

• No volume change upon mixing ($\Delta V_{\text{mix}} = 0$).​

• Example: Benzene and toluene mixture.​

Non-Ideal Solution:

• Does not obey Raoult's law.​

• Enthalpy change upon mixing is not zero.​

• Volume change upon mixing is not zero.​

• Example: Ethanol and water mixture.​

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4. What is Raoult's law? How is it applied to determine the vapor pressure of a solution?

Raoult's Law: The partial vapor pressure of each volatile component in a solution is directly proportional to its mole fraction.​

$$P_A = \chi_A \times P_A^0$$

Where:

• $P_A$ = partial vapor pressure of component A​

• $\chi_A$ = mole fraction of component A​

• $P_A^0$ = vapor pressure of pure component A​

Application: For a solution with multiple components, the total vapor pressure is the sum of the partial pressures:​

$$P_{\text{total}} = P_A + P_B = \chi_A P_A^0 + \chi_B P_B^0$$

This helps in determining the vapor pressure of the solution based on the composition and vapor pressures of the pure components.​

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5. Explain the concept of colligative properties. List four colligative properties and describe any one in detail.

Colligative Properties: These are properties of solutions that depend on the number of solute particles in a given quantity of solvent, regardless of their nature.​

Four Colligative Properties:

1. Relative lowering of vapor pressure​

2. Elevation of boiling point​

3. Depression of freezing point​

4. Osmotic pressure​

Depression of Freezing Point: When a solute is dissolved in a solvent, the freezing point of the solution is lower than that of the pure solvent. The decrease in freezing point ($\Delta T_f$) is given by:​

$$\Delta T_f = K_f \times m$$

Where:

• $K_f$ = molal freezing point depression constant​

• $m$ = molality of the solution​

This principle is used in applications like antifreeze in car radiators.​

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6. Calculate the boiling point elevation when 0.5 mol of a non-volatile solute is dissolved in 1 kg of water. (Given: $K_b$ for water = 0.52 K kg/mol)

Solution:

The elevation in boiling point ($\Delta T_b$) is calculated using:​

$$\Delta T_b = K_b \times m$$

Where:

• $$Kb=0.52 K kg/mol
  

• $$m=0.5 mol1 kg=0.5 mol/kg
  ​

Calculating:​

$$\Delta T_b = 0.52 \times 0.5 = 0.26 \, \text{K}$$

Thus, the boiling point of the solution is elevated by 0.26 K.

7. Osmosis & Osmotic Pressure

• Osmosis: Flow of solvent through a semi-permeable membrane from dilute to concentrated solution.

• Osmotic Pressure (π):

$$\pi = \frac{wRT}{MV}$$

Where:

• $w$ = mass of solute

• $M$ = molar mass

• $V$ = volume in L

• $R$ = gas constant

• $T$ = temperature in K

Used to find molar mass:

$$M = \frac{wRT}{\pi V}$$

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8. van’t Hoff Factor (i)

• Adjusts for dissociation/association of solute particles.

$$i = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}} = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}$$

• i > 1 → dissociation (e.g., NaCl)

• i < 1 → association (e.g., acetic acid in benzene)

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9. Molar Mass via Freezing Point Depression

Given:

• Glucose = 1.8 g

• Water = 100 g = 0.1 kg

• $\Delta T_f = 0.093^\circ C$, $K_f = 1.86$
  

Formula:

$$\Delta T_f = K_f \cdot \frac{1000 \cdot w}{M \cdot W}$$ $$0.093 = 1.86 \cdot \frac{1800}{100 \cdot M} \Rightarrow M = \frac{33480}{9.3} \approx \textbf{180 g/mol}$$

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10. Abnormal Molar Mass

• Occurs when experimental molar mass ≠ theoretical molar mass.

Causes:

• Dissociation: More particles → lower observed molar mass

• Association: Fewer particles → higher observed molar mass

Observed molar mass=Normal molar mass/i​​