A solution of potassium nitrate in water
has a freezing point of -0.082◦C. What is
the concentration of KNO3 in this solution?
Kf = 1.86 ◦C/m for water.
moles/kgwater=.082/1.86
massKNO3/(molmass*kgwater)=.082/1.86
masskno3/kgwater= .082*molmass/1.86= concentration.
you can change that to percent w/w if you wish.
To find the concentration of KNO3 in the solution, we need to use the equation for calculating the change in freezing point.
∆T = Kf * i * m
Where:
∆T is the change in freezing point (given as -0.082◦C)
Kf is the freezing point depression constant for water (given as 1.86◦C/m)
i is the vant Hoff factor - the number of particles the solute dissociates into (for KNO3, i = 2 since it dissociates into K+ and NO3- ions)
m is the molality of the solution (concentration expressed in moles of solute per kilogram of solvent)
Now, rearranging the equation, we can solve for m:
m = ∆T / (Kf * i)
Plugging in the values we have:
m = (-0.082◦C) / (1.86◦C/m * 2)
m = -0.082 / (1.86 * 2)
m ≈ -0.022
However, since molality can't be negative, we can discard the negative sign. Therefore, the concentration of KNO3 in the solution is approximately 0.022 mol/kg.
To find the concentration of KNO3 in the solution, we can use the formula:
ΔT = Kf * m
where:
ΔT = change in freezing point
Kf = freezing point depression constant (1.86 °C/m for water)
m = molality of the solution (moles of solute per kilogram of solvent)
First, let's convert the freezing point from °C to °K:
Freezing point in °K = (freezing point in °C) + 273.15
Freezing point in °K = -0.082 + 273.15 = 273.068 °K
Next, we need to calculate the change in freezing point:
Change in freezing point (ΔT) = 273.068 °K - 273.15 °K = -0.082 °K
Now, we can substitute the values into the formula and solve for m:
-0.082 °K = 1.86 °C/m * m
Simplifying the equation:
-0.082 °K = 1.86 m°C
Dividing both sides by 1.86:
m = (-0.082 °K) / (1.86 °C/m)
m = -0.044 m
Since molality is always positive, we can take the absolute value:
m = 0.044 m
Therefore, the concentration of KNO3 in this solution is 0.044 mol/kg.