Calculate the van’t Hoff factor of a 0.0500 m formic acid solution (HCO2H) which begins to freeze at -0.0984°C. *ΔTf = KfCmi, Kf = -1.86 °C/m
The Correct Answer and Explanation is :
To calculate the van’t Hoff factor (i) for the given solution, we need to use the freezing point depression formula:
[
\Delta T_f = K_f \cdot C_m \cdot i
]
Where:
- (\Delta T_f) is the freezing point depression (change in freezing point),
- (K_f) is the cryoscopic constant (given as -1.86 °C/m),
- (C_m) is the molality of the solution (given as 0.0500 m),
- (i) is the van’t Hoff factor (the number of particles into which a solute dissociates in solution).
Step 1: Calculate the freezing point depression (\Delta T_f)
The normal freezing point of water is 0.00°C. The solution begins to freeze at -0.0984°C, so the freezing point depression is:
[
\Delta T_f = 0.00°C – (-0.0984°C) = 0.0984°C
]
Step 2: Rearrange the freezing point depression equation to solve for (i)
The equation we have is:
[
\Delta T_f = K_f \cdot C_m \cdot i
]
Rearranging to solve for (i):
[
i = \frac{\Delta T_f}{K_f \cdot C_m}
]
Step 3: Plug in the known values
Now, substitute the values into the equation:
[
i = \frac{0.0984°C}{(-1.86°C/m) \cdot (0.0500 m)}
]
[
i = \frac{0.0984}{-0.093}
]
[
i \approx 1.06
]
Step 4: Interpretation of the result
The van’t Hoff factor (i) is approximately 1.06. This suggests that formic acid (HCO2H) dissociates very slightly in solution, but not completely. A value of 1 would indicate no dissociation, while a value greater than 1 (like 1.06) suggests a small amount of dissociation into ions or particles.
In the case of formic acid, it is a weak acid, so it partially dissociates into H⁺ and HCO₂⁻ ions. This result reflects the fact that the dissociation is minimal but contributes to the observed freezing point depression.