A 0.100 m
K2SO4 solution has a freezing point of -0.43°C. What is the van't Hoff factor for this solution?
Kf
= 1.86°C/m
To find the van't Hoff factor for the solution, you can use the following equation:
i = ΔTf / Kf * m
Where:
i = van't Hoff factor
ΔTf = freezing point depression of the solution (given as -0.43°C)
Kf = molal freezing point depression constant (given as 1.86°C/m)
m = molality of the solution
Since the solution is a 0.100 m K2SO4 solution, the molality (m) is equal to 0.100 mol of K2SO4 per kg of solvent.
Now, we can substitute the given values into the equation:
i = -0.43°C / (1.86°C/m * 0.100 m)
Simplifying the equation:
i = -0.43°C / 0.186°C
i ≈ -2.32
Therefore, the van't Hoff factor for this solution is approximately -2.32.
To find the van't Hoff factor for the given solution, we need to use the formula:
ΔT = Kf * m * i
Where:
ΔT is the change in freezing point (in °C)
Kf is the cryoscopic constant or molal freezing point depression constant (in °C/m)
m is the molality of the solution (in mol solute/kg solvent), and
i is the van't Hoff factor.
In this case, we know the ΔT (-0.43°C) and the Kf (1.86°C/m), and we need to find the van't Hoff factor (i). Rearranging the formula, we get:
i = ΔT / (Kf * m)
Now, let's substitute the given values into the formula:
i = (-0.43°C) / (1.86°C/m * 0.100 mol/kg)
Simplifying the expression:
i = -0.43 / (1.86 * 0.100)
i = -0.43 / 0.186
i ≈ -2.31
Since the van't Hoff factor cannot be negative, we can round it up to the nearest whole number, which gives us an approximate van't Hoff factor of 2.