The boiling point of an aqueous 1.83 m (NH4)2SO4 (molar mass = 132.15 g/mol) solution is 102.5°C. Determine the value of the van't Hoff factor for this solute if the Kb for water is 0.512°C/m.
To determine the value of the van't Hoff factor, we can use the equation:
ΔTb = i * Kb * m
where:
ΔTb = change in boiling point
i = van't Hoff factor
Kb = boiling point elevation constant for water (0.512°C/m)
m = molality of the solution
We're given that the molality (m) of the solution is 1.83 m, and the change in boiling point (ΔTb) is 102.5°C. We can rearrange the equation to solve for the van't Hoff factor (i):
i = ΔTb / (Kb * m)
Substituting in the given values:
i = 102.5°C / (0.512°C/m * 1.83 m)
i ≈ 102.5 / (0.93696)
i ≈ 109.52
Therefore, the value of the van't Hoff factor (i) for this solute is approximately 109.52.