The Fraction of Ionization of HX in a Solution

How can we determine the fraction of ionization of HX in a solution?

Explanation:

To determine the fraction of ionization of HX, also known as the van't Hoff factor i, we need to use the freezing point depression formula: ΔTf = Kf × m × i. First, we calculate the experimental molality (m) of the solution using the observed freezing point depression (ΔTf) and the molal freezing-point-depression constant of water (Kf), which is given as 1.86 °C/m. The observed freezing point depression is -0.47°C. To calculate molality:
ΔTf = Kf × m
-0.47 °C = 1.86 °C/m × m
m = -0.47 °C / 1.86 °C/m
m = 0.2527 mol/kg

Then we calculate the theoretical molality, which assumes no ionization of HX:
Theoretical molality (m°) = moles of HX / kg of solvent
m° = 0.020 mol / 0.115 kg
m° = 0.1739 mol/kg

Finally, calculate the van't Hoff factor i by dividing the experimental molality by the theoretical molality:
i = m / m°
i = 0.2527 mol/kg / 0.1739 mol/kg
i = 1.453 (not one of the provided options)

The fraction of ionization of HX is determined by the van't Hoff factor, i, which indicates the extent to which HX disassociates in solution. However, using the options provided, we would have to determine which option would come closest to the calculated value of i.