A 1.00 molal aqueous solution of trichloroacetic acid (CCl3COOH) is heated to its boiling point. The solution has the boiling point of 100.18 °C. Determine the van’t Hoff factor for trichloroacetic acid. (Kft for water = 0.512 K kg mol-1)
The correct answer and explanation is :
To determine the van’t Hoff factor ((i)) for trichloroacetic acid (CCl₃COOH) in the given aqueous solution, we will use the formula for boiling point elevation:
[
\Delta T_b = i \cdot K_b \cdot m
]
Where:
- (\Delta T_b) is the change in boiling point,
- (i) is the van’t Hoff factor,
- (K_b) is the ebullioscopic constant (boiling point elevation constant) of the solvent,
- (m) is the molality of the solution.
Step 1: Calculate the change in boiling point
The boiling point of pure water is 100.00 °C. The boiling point of the solution is given as 100.18 °C. Thus, the change in boiling point ((\Delta T_b)) is:
[
\Delta T_b = 100.18 \,^\circ C – 100.00 \,^\circ C = 0.18 \,^\circ C
]
Step 2: Identify known values
- Molality ((m)) = 1.00 mol/kg (given in the problem).
- (K_b) for water = 0.512 K kg mol(^{-1}) (also given).
- The boiling point elevation formula becomes:
[
0.18 = i \cdot 0.512 \cdot 1.00
]
Step 3: Solve for (i)
Rearranging the formula to solve for (i):
[
i = \frac{0.18}{0.512} = 0.3516
]
Step 4: Interpretation of the van’t Hoff factor
The van’t Hoff factor ((i)) represents the number of particles into which a solute dissociates in a solution. If trichloroacetic acid were a non-electrolyte (not dissociating), (i) would be 1. However, as we are getting a value for (i) that is lower than 1, it suggests that trichloroacetic acid does not dissociate completely in water, or some association might occur between molecules in solution, leading to a smaller-than-expected van’t Hoff factor.
Conclusion:
The van’t Hoff factor ((i)) for trichloroacetic acid is approximately 0.352, indicating partial dissociation or association in water.