Match the entries of column I with appropriate entries of column II and choose the correct option out of the four options given.

(i)-(c), (ii)-(d), (iii)-(a), (iv)-(b)

The correct answer is option 3. (i)-(c), (ii)-(d), (iii)-(a), (iv)-(b).

Let us match the entries from Column I with the appropriate entries from Column II:

i. Raoult's Law: c.\(p = x_1P^o_1 + x_2p^o_2\)

Raoult's Law states that the partial vapor pressure of a solvent in a solution is proportional to its mole fraction. For a solution of two components, it is given by:

\(p = x_1 p_{01} + x_2 p_{02}\)

where \( p \) is the total vapor pressure, \( x_1 \) and \( x_2 \) are the mole fractions, and \( p_{01} \) and \( p_{02} \) are the vapor pressures of the pure components.

ii. Henry's Law: b.\(\pi = cRT\)

Henry's Law states that the partial pressure of a gas above a solution is proportional to its mole fraction in the solution. This is expressed as:

\(p = K_H \cdot \chi\)

where \( p \) is the partial pressure of the gas, \( K_H \) is the Henry's law constant, and \( \chi \) is the mole fraction of the gas in the solution.

iii. Elevation in Boiling Point: a. \(\Delta T_b = K_bm\)

Elevation in Boiling Point refers to the increase in boiling point when a non-volatile solute is added to a solvent. It 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.

4. Osmotic Pressure:d. \(p = K_HX\)

Osmotic Pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is given by:

\(\pi = CRT\)

where \( \pi \) is the osmotic pressure, \( C \) is the concentration of the solute, \( R \) is the gas constant, and \( T \) is the temperature.

Therefore, the correct option is: (i)-(c), (ii)-(d), (iii)-(a), (iv)-(b).