Derive a formula for the molar mass of the solute in terms of the freezing point depression, deltaT, the freezing-point constant, Kf, and the masses of solvent, msolvent, and solute, msolute, used in an experiment like this one. SHow your work and include all unites in your final formula.
This is my attemps at the formula:
ΔT = Kf * (msolvent + msolute / nsolvent + nsolute)
I think what you need to do is as follows:
delta T = Kf*molality
molality = mols solute/kg solvent
mols solute = mass solute/molar mass.
Substitute equation 2 into equation 1 for molality.
Then, substitute mols solute into the resulting equation and solve for molar mass.
I see, thanks a lot Bob!
To derive the formula for the molar mass of the solute in terms of the freezing point depression (ΔT), the freezing-point constant (Kf), and the masses of the solvent (msolvent) and solute (msolute), we need to consider the concepts of molality and freezing point depression.
The molality (m) of a solution is defined as the number of moles of solute (nsolute) per kilogram of solvent (nsolvent). It is given by the formula:
molality (m) = nsolute / nsolvent
The freezing point depression (ΔT) is a colligative property of a solution, which means it depends on the concentration of solute particles in the solution but not on their identity. It is related to the molality of the solution by the equation:
ΔT = Kf * m
where Kf is the freezing-point constant, which is specific to the solvent.
We can rearrange the equation ΔT = Kf * m to solve for m:
m = ΔT / Kf
For a given solution, we can express the molality (m) in terms of the masses of the solvent (msolvent) and solute (msolute) using their respective molar masses (Msolvent and Msolute) and the formula:
m = (msolute / Msolute) / (msolvent / Msolvent)
Rearranging the formula for molality:
m = (msolute * Msolvent) / (Msolute * msolvent)
Substituting this expression for molality (m) into the equation ΔT = Kf * m:
ΔT = Kf * [(msolute * Msolvent) / (Msolute * msolvent)]
Now, rearranging the above equation to solve for the molar mass of the solute (Msolute):
Msolute = (msolute * Kf * Msolvent) / (ΔT * msolvent)
Final formula for the molar mass of the solute:
Msolute = (msolute * Kf * Msolvent) / ΔT
Make sure to include the appropriate units in your calculation, such as grams and degrees Celsius.
Please note that this formula assumes ideal behavior of the solute and solvent and no dissociation or association of solute particles.