Questions & explanations
1. How is Henry's law related to Raoult's law for a component in an ideal solution?
- Henry's law constant (K_H) is equal to the vapor pressure of the pure component in the same phase
- Henry's law applies only to the solvent, while Raoult's law applies to the solute
- Henry's law constant is independent of temperature, while Raoult's law depends on temperature
- Raoult's law is a special case of Henry's law where the mole fraction approaches zero
Answer: Henry's law constant (K_H) is equal to the vapor pressure of the pure component in the same phase
For an ideal solution, the vapor pressure of a component is p = p^o x. Henry's law for a gas dissolved in a liquid is p = K_H x. In the limit where the solute behaves ideally over the entire concentration range (as in an ideal solution), K_H becomes equal to the vapor pressure of the pure liquid solute. Thus Raoult's law is a special case of Henry's law.
2. When a solute dissociates in solution, the molar mass determined experimentally using a colligative property is found to be:
- Equal to the theoretical molar mass
- Greater than the theoretical molar mass
- Less than the theoretical molar mass
- Unaffected by dissociation
Answer: Less than the theoretical molar mass
For a dissociating solute, the van't Hoff factor (i) is greater than 1. Colligative properties are inversely proportional to the molar mass. Because the measured colligative property is higher (due to more particles), the calculated molar mass becomes lower than the theoretical value. This is referred to as abnormal molar mass.
3. Which of the following pairs of liquids is expected to form an ideal solution?
- Ethanol and acetone
- Benzene and toluene
- Hydrochloric acid and water
- Acetone and chloroform
Answer: Benzene and toluene
Ideal solutions obey Raoult's law and have ΔHmix = 0 and ΔVmix = 0. Benzene and toluene have similar molecular structures and intermolecular forces, forming an ideal solution. The other pairs exhibit deviations due to differences in interactions (e.g., hydrogen bonding, dipole-dipole interactions).
4. For a solute that undergoes dissociation in solution, the van't Hoff factor (i) is typically:
- Equal to 1
- Less than 1
- Greater than 1
- Equal to 0
Answer: Greater than 1
When a solute dissociates into multiple particles, the number of particles in solution increases. The van't Hoff factor (i) is defined as the ratio of the observed colligative property to the expected value for a non-electrolyte. Since dissociation yields more particles, i becomes greater than 1.
5. For a binary solution of two volatile liquids A and B, Raoult's law states that the partial vapor pressure of A (p_A) is related to its mole fraction (x_A) and vapor pressure of pure A (p_A^o) as:
- p_A = p_A^o \times x_A
- p_A = p_A^o \times (1 - x_A)
- p_A = p_A^o / x_A
- p_A = p_A^o \times x_A^2
Answer: p_A = p_A^o \times x_A
Raoult's law for a volatile liquid in a solution states that the partial vapor pressure of each component is directly proportional to its mole fraction in the liquid phase, with the proportionality constant being the vapor pressure of the pure component. Thus p_A = p_A^o x_A is correct.
6. The van't Hoff factor (i) for a compound that undergoes complete dissociation in solution is:
- equal to the number of ions produced per formula unit
- always 1 for non-electrolytes
- less than 1 for association of solute particles
- All of the above
Answer: All of the above
Van't Hoff factor i is defined as the ratio of observed colligative property to expected colligative property. For complete dissociation, i equals the number of ions per formula unit. For non-electrolytes, i = 1. For association, i < 1. Thus all statements are correct.
7. Which of the following statements correctly describes a solution showing positive deviation from Raoult's law?
- A → B interactions are stronger than A → A and B → B interactions
- The vapor pressure of the solution is higher than that predicted by Raoult's law
- The solution has a lower volume than the sum of volumes of pure components
- The heat of mixing is negative (exothermic)
Answer: The vapor pressure of the solution is higher than that predicted by Raoult's law
Positive deviation occurs when the solute-solvent interactions are weaker than the pure component interactions. This results in easier escape of molecules, leading to higher vapor pressure than ideal. The volume expansion is usually positive and mixing is endothermic.
8. For a solution containing a non-volatile solute, Raoult's law is expressed in terms of relative lowering of vapor pressure. Which of the following is correct?
- (p^o - p)/p^o = n_2/(n_1 + n_2)
- (p^o - p)/p^o = n_1/n_2
- (p^o - p)/p^o = w_2/M_2 \times M_1/w_1
- (p^o - p)/p^o = mole fraction of solvent
Answer: (p^o - p)/p^o = n_2/(n_1 + n_2)
For a non-volatile solute, the relative lowering of vapor pressure equals the mole fraction of the solute. p^o is vapor pressure of pure solvent, p is vapor pressure of solution. n_2 is moles of solute, n_1 is moles of solvent. So (p^o - p)/p^o = n_2/(n_1 + n_2).
9. A solution of acetone and chloroform shows negative deviation from Raoult's law and forms a maximum-boiling azeotrope. This is due to:
- formation of hydrogen bonds between acetone and chloroform molecules
- weaker interactions between acetone and chloroform than between like molecules
- dissociation of acetone molecules in the solution
- volatility of both components being very high
Answer: formation of hydrogen bonds between acetone and chloroform molecules
Acetone and chloroform form intermolecular hydrogen bonds (Cl3C-H...O=C(CH3)2), making solute-solvent interactions stronger than pure component interactions. This leads to lower vapor pressure (negative deviation) and a maximum-boiling azeotrope.
10. Which of the following correctly distinguishes a minimum-boiling azeotrope from a maximum-boiling azeotrope?
- Minimum-boiling azeotropes result from negative deviation; maximum-boiling from positive deviation
- Minimum-boiling azeotropes have a boiling point lower than either pure component; maximum-boiling have a boiling point higher than either pure component
- Minimum-boiling azeotropes are formed by ideal solutions; maximum-boiling by non-ideal solutions
- Minimum-boiling azeotropes can be separated by fractional distillation; maximum-boiling cannot
Answer: Minimum-boiling azeotropes have a boiling point lower than either pure component; maximum-boiling have a boiling point higher than either pure component
Minimum-boiling azeotropes (e.g., ethanol-water) boil at a temperature lower than the boiling points of both pure components, while maximum-boiling azeotropes (e.g., nitric acid-water) boil at a temperature higher than either pure component.
11. A weak electrolyte AB dissociates in water as AB ⇌ A⁺ + B⁻. If the van't Hoff factor (i) for a 0.1 M solution is 1.4, what is the degree of dissociation (α) of AB?
- 0.2
- 0.4
- 0.6
- 0.8
Answer: 0.4
For a binary electrolyte like AB that dissociates into two ions, the relation between van't Hoff factor and degree of dissociation is i = 1 + α. Given i = 1.4, we have 1 + α = 1.4, so α = 0.4. Thus, 40% of the AB molecules are dissociated.
12. According to Henry's law, the solubility of a gas in a liquid is proportional to:
- partial pressure of the gas above the liquid
- total pressure of all gases above the liquid
- square of the partial pressure of the gas
- temperature of the liquid
Answer: partial pressure of the gas above the liquid
Henry's law states that at constant temperature, the concentration (solubility) of a gas in a liquid is directly proportional to the partial pressure of that gas in equilibrium with the liquid. Mathematically, p = K_H x, so x ∝ p.