For a solution containing a non-volatile solute in a volatile...

When a non-volatile solute is added to a volatile solvent, the vapor pressure of the solution decreases because a fraction of the surface area is occupied by non-volatile solute particles, reducing the escaping tendency of solvent molecules.

Let $P_1$ be the vapor pressure of the solvent in the solution and $P_1^0$ be the vapor pressure of the pure solvent. According to Raoult's law, the vapor pressure of the solution is directly proportional to the mole fraction of the solvent (X_1$).<br><br>$P_1 = P_1^0 X_1$<br><br>Since the mole fraction of the solvent in a solution is always less than 1 (X_1 < 1$), it follows that $P_1 < P_1^0$.

Due to the lowering of vapor pressure, the solution must be heated to a higher temperature to make its vapor pressure equal to the external pressure, resulting in an elevation in boiling point (T_b > T_b^0$).<br><br>Similarly, the freezing point of the solution is lower than that of the pure solvent, resulting in freezing point depression (T_f < T_f^0$).

Thus, the only correctly represented relationship among the given options is $P_1 < P_1^0$.

Answer: $P_1 < P_1^0$