A solution which contains 40.3 g of an unknown molecular compound in 360 g of water freezes at -5.07°C.
What is the molar mass of the unknown?
delta T = Kf*m
Substitute and solve for molality.
molality = mols/kg solvent.
Substitute and solve for mols.
mols = grams/molar mass. You know grams and mols, solve for molar mass.
To find the molar mass of the unknown compound, we can use the concept of freezing point depression. Freezing point depression is the phenomenon where the freezing point of a solution is lower than the freezing point of the pure solvent. The amount of depression in the freezing point is directly proportional to the molality (moles of solute per kilogram of solvent) of the solution.
In this case, we have a solution where the freezing point is lowered to -5.07°C. To calculate the molality (m) of the solution, we need to determine the change in freezing point (∆T) and the freezing point depression constant (Kf) for water.
The change in freezing point (∆T) can be calculated using the equation:
∆T = Kf * m
Where ∆T is the change in freezing point, Kf is the freezing point depression constant for water (-1.86°C/m), and m is the molality of the solution.
In this case, ∆T = -5.07°C and the molality (m) is the moles of solute per kilogram of solvent. We know that the solvent is water, which has a molecular weight of 18.015 g/mol. So, we need to calculate the moles of solute.
The moles of solute (n) can be calculated using the equation:
n = mass of solute / molar mass of solute
In this case, the mass of solute is 40.3 g. We need to find the molar mass of the unknown compound.
Therefore, rearranging the equation:
molar mass of solute = mass of solute / n
So, to find the molar mass of the unknown compound, we need to calculate the molality (m) using the freezing point depression equation, then calculate the moles of solute (n) using the mass of solute, and finally divide the mass of solute by the moles of solute to find the molar mass of the unknown compound.