Final answer:
To find the mass of iron(III) nitrate dissolved in the solvent, we apply the freezing point depression formula to determine the solution's molality, and then convert it to moles and ultimately to mass, using the molar mass of iron(III) nitrate.
Step-by-step explanation:
The student is asking to calculate the mass of iron(III) nitrate, Fe(NO₃)₃, that was dissolved in a solvent, given the normal freezing point of the solvent, the solution's freezing point, and the freezing point depression constant, Kf. To make the calculation, we use the formula for freezing point depression:
ΔTf = Kf × m
Where ΔTf is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution. The change in freezing point (ΔTf) is calculated by subtracting the solution's freezing point from the solvent's normal freezing point. Using the given values:
ΔTf = 1.40°C - (-2.3°C) = 3.7°C
Now we solve for molality (m``):
m = ΔTf / Kf = 3.7°C / -5.32°C kg/mol = -0.695 mol/kg
However, since molality is a positive value, we ignore the negative sign. The molality is then used to find the moles of Fe(NO₃)₃, and subsequently the mass of Fe(NO₃)₃, considering the mass of solvent (X) and the molar mass of Fe(NO₃)₃.