Question

Which of the following formulae is used to obtain depression in freezing point?

• A. $\Delta T_f = T_f^\circ T_f$
• B. $\Delta T_f = T_f^\circ - T_f$
• C. $\Delta T_f - T_f = T_f^\circ$
• D. $\Delta T_f = T_f / T_f^\circ$

Hint:

Be careful not to mix this up with the formula for the elevation in boiling point ($\Delta T_b$). Since boiling points rise when a solute is added, that formula is flipped: $\Delta T_b = T_b - T_b^\circ$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem asks for the fundamental thermodynamic algebraic formula used to define the colligative property known as the depression in freezing point ($\Delta T_f$).

Step 2: Key Formula or Approach:
When a non-volatile solute is added to a volatile solvent, the vapor pressure drops, causing the freezing point of the solution to decrease below that of the pure solvent. The change is expressed as: $$\Delta T_f = \text{Freezing point of pure solvent} - \text{Freezing point of solution}$$

Step 3: Detailed Explanation:
Let's match our thermodynamic definitions to the standard variables: Let $T_f^\circ$ be the normal freezing point of the pure, uncontaminated solvent. Let $T_f$ be the lowered freezing point of the resulting solution. Because the freezing point drops when a solute is added, the temperature of the pure solvent is higher than the temperature of the solution ($T_f^\circ \gt T_f$). To ensure that the change in temperature ($\Delta T_f$) is expressed as a positive value, we subtract the lower value from the higher value: $$\Delta T_f = T_f^\circ - T_f$$ This matches the structural formulation shown in option (B).

Step 4: Final Answer:
The correct formula for the depression in freezing point is $\Delta T_f = T_f^\circ - T_f$, corresponding to option (B).