The freezing point depression of an aqueous solution is directly proportional to the concentration of solute particles. This relationship is described by the equation:
ΔTf = Kf x molality
where ΔTf is the change in freezing point, Kf is the freezing point depression constant for water, and molality is the concentration of solute particles in the solution.
The Van't Hoff factor (i) is the ratio of the number of solute particles in a solution to the number of solute particles in an ideal solution. In this case, the Van't Hoff factor can be calculated using the freezing point depression:
i = (ΔTf / (Kf x molality)) + 1
Given that the freezing point of the solution is -2.90 °C, the freezing point depression constant for water is 1.86 °C/m, and the molality of the solution is (mass of solute / mass of solvent) = (0.590 g / 1000 g) = 0.00059 m, we can calculate the Van't Hoff factor as:
i = (-2.90 / (1.86 x 0.00059)) + 1
i = 3
So, the Van't Hoff factor for this solution is 3, which means that for each solute particle in the solution, there are 3 solute particles in an ideal solution.