Match List I with List II. Choose the correct answer from the options given below:List – I List – II A. Raoult’s Law I. ΔTb = kb ⋅ m B. Henry’s Law II. ΔTf = kf ⋅ m C. Elevation in boiling point III. p = x₁ p°₁ + x₂ p°₂ D. Depression in freezing point IV. P = KH ⋅ x
A-III, B-IV, C-I, D-II
Matching Solution Laws and Colligative Properties
This question asks us to match important laws related to solutions and colligative properties with their corresponding mathematical expressions or descriptions. Let's analyze each item in List I and find its correct match in List II.
- A. Raoult’s Law: Raoult's Law describes the vapor pressure of a solution. For a solution containing two volatile components, say 1 and 2, the total vapor pressure \(p\) above the solution is the sum of the partial vapor pressures of the components. The partial vapor pressure of each component is proportional to its mole fraction in the solution multiplied by its vapor pressure in the pure state (\(p_1 = x_1 p_1^\circ\) and \(p_2 = x_2 p_2^\circ\)). Thus, the total vapor pressure is given by \(p = p_1 + p_2 = x_1 p_1^\circ + x_2 p_2^\circ\). This matches item III in List II.
- B. Henry’s Law: Henry's Law deals with the solubility of a gas in a liquid. It states that the partial pressure of the gas above the solution is proportional to its mole fraction in the solution. The relationship is given by \(P = K_H \cdot x\), where \(P\) is the partial pressure of the gas, \(x\) is its mole fraction in the solution, and \(K_H\) is Henry's constant. This matches item IV in List II (using P instead of p).
- C. Elevation in boiling point: This is a colligative property, which means it depends on the number of solute particles, not their identity. The elevation in boiling point (\(\Delta T_b\)) of a solvent upon adding a non-volatile solute is directly proportional to the molality (\(m\)) of the solute in the solution. The formula is \(\Delta T_b = K_b \cdot m\), where \(K_b\) is the molal boiling point elevation constant (ebullioscopic constant). This matches item I in List II (using kb instead of \(K_b\)).
- D. Depression in freezing point: This is another colligative property. The depression in freezing point (\(\Delta T_f\)) of a solvent upon adding a non-volatile solute is directly proportional to the molality (\(m\)) of the solute in the solution. The formula is \(\Delta T_f = K_f \cdot m\), where \(K_f\) is the molal freezing point depression constant (cryoscopic constant). This matches item II in List II (using kf instead of \(K_f\)).
Based on this analysis, the correct matching is:
| List I | List II | Match |
|---|---|---|
| A. Raoult’s Law | III. \(p = x₁ p°₁ + x₂ p°₂\) | A-III |
| B. Henry’s Law | IV. \(P = K_H \cdot x\) | B-IV |
| C. Elevation in boiling point | I. \(\Delta T_b = k_b \cdot m\) | C-I |
| D. Depression in freezing point | II. \(\Delta T_f = k_f \cdot m\) | D-II |
The correct combination of matches is A-III, B-IV, C-I, D-II.
Revision Table: Solution Laws & Colligative Properties
| Concept | Description | Formula |
|---|---|---|
| Raoult’s Law | Relates vapor pressure of a solution to mole fractions of components. | \(p = x_1 p_1^\circ + x_2 p_2^\circ\) (for volatile components) or \(p = x_1 p_1^\circ\) (for non-volatile solute) |
| Henry’s Law | Relates solubility of a gas in liquid to its partial pressure above the solution. | \(P = K_H \cdot x\) |
| Elevation in boiling point | Increase in boiling point of solvent due to non-volatile solute. | \(\Delta T_b = K_b \cdot m\) |
| Depression in freezing point | Decrease in freezing point of solvent due to non-volatile solute. | \(\Delta T_f = K_f \cdot m\) |
Additional Information: Solution Concepts
Understanding these laws and properties is crucial for studying solutions. Raoult's Law can be seen as a special case of Henry's Law for a volatile component where \(K_H\) equals the vapor pressure of the pure component (\(p^\circ\)). Colligative properties like boiling point elevation and freezing point depression depend only on the concentration of solute particles, not their nature. This makes them useful for determining the molar mass of an unknown solute. Molality (\(m\)) is defined as the number of moles of solute per kilogram of solvent. It is used in these colligative property calculations because it is temperature-independent, unlike molarity.
Important Questions from Coordination Compounds
Match List-I with List-II:
List-I List-II (A) Diamagnetic solid (I) CrO₂ (B) Ferromagnetic solid (II) Fe₃O₄ (C) Antiferromagnetic solid (III) NaCl (D) Ferrimagnetic solid (IV) MnO Choose the correct answer from the options given below:
[NiCl₂(PPh₃)₂] is named as:
Inner orbital complex among the following is:
(A) [Co(NH₃)₆]³⁺
(B) [CoF₆]³⁻
(C) [Ni(CN)4]²⁻
(D) [MnCl₆]³⁻
(E) [FeF₆]³⁻
Choose the correct answer from the options given below:
Which will form the most stable complex?
How many Cr-O bonds in dichromate ions are of the same bond length and are in resonance?
