Match the laws given in Column I with expressions given in Column II.
`{:("Column I","Column II"),("(i) Raoult's law","(a) "DeltaT_(f)=K_(f)m),("(ii) Henry'law","(b) "pi=CRT),("(iii) Elevation of boiling point","(c) "p=x_(1)p_(1)^(@)+x_(2)p_(2)^(@)),("(iv) Depression is freezing point","(d) "DeltaT_(b)=K_(b)m),("(v) Osmotic pressure","(e) "p=K_(H)x):}`

Answer

To solve the problem of matching the laws in Column I with the expressions in Column II, we will go through each law and identify the corresponding expression step by step.

### Step-by-Step Solution:

1. **Raoult's Law**:
- **Definition**: Raoult's Law states that the partial vapor pressure of each component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.
- **Expression**: The total vapor pressure of the solution is given by the sum of the partial pressures of the components.
- **Match**: This corresponds to expression **(c)**: \( p = x_1 p_1^@ + x_2 p_2^@ \).
- **Conclusion**: (i) Raoult's Law → (c)

2. **Henry's Law**:
- **Definition**: Henry's Law states that the amount of gas that dissolves in a liquid at a given temperature is proportional to the partial pressure of that gas above the liquid.
- **Expression**: The relationship is given by \( p = K_H x \), where \( p \) is the partial pressure, \( K_H \) is Henry's law constant, and \( x \) is the mole fraction of the gas.
- **Match**: This corresponds to expression **(e)**: \( p = K_H x \).
- **Conclusion**: (ii) Henry's Law → (e)

3. **Elevation of Boiling Point**:
- **Definition**: The elevation of boiling point occurs when a non-volatile solute is added to a solvent, resulting in an increase in the boiling point of the solution.
- **Expression**: The formula is given by \( \Delta T_b = K_b m \), where \( \Delta T_b \) is the elevation in boiling point, \( K_b \) is the ebullioscopic constant, and \( m \) is the molality of the solution.
- **Match**: This corresponds to expression **(d)**: \( \Delta T_b = K_b m \).
- **Conclusion**: (iii) Elevation of Boiling Point → (d)

4. **Depression of Freezing Point**:
- **Definition**: The depression of freezing point occurs when a solute is added to a solvent, resulting in a decrease in the freezing point of the solution.
- **Expression**: The formula is given by \( \Delta T_f = K_f m \), where \( \Delta T_f \) is the depression in freezing point, \( K_f \) is the cryoscopic constant, and \( m \) is the molality of the solution.
- **Match**: This corresponds to expression **(a)**: \( \Delta T_f = K_f m \).
- **Conclusion**: (iv) Depression of Freezing Point → (a)

5. **Osmotic Pressure**:
- **Definition**: Osmotic pressure is the pressure required to prevent the flow of solvent into a solution via osmosis.
- **Expression**: The formula is given by \( \pi = CRT \), where \( \pi \) is the osmotic pressure, \( C \) is the molar concentration of the solute, \( R \) is the gas constant, and \( T \) is the temperature.
- **Match**: This corresponds to expression **(b)**: \( \pi = CRT \).
- **Conclusion**: (v) Osmotic Pressure → (b)

### Final Matches:
- (i) Raoult's Law → (c)
- (ii) Henry's Law → (e)
- (iii) Elevation of Boiling Point → (d)
- (iv) Depression of Freezing Point → (a)
- (v) Osmotic Pressure → (b)