An aqueous solution containing 35.1 grams of an unknown molecular (noneolectrolyte) compound in 152.5 grams of water was found to have a freezing point of -1.8 degrees C. Calculate the molar mass of the unknown compound.
delta T = Kf*molality
Solve for molality
molality = moles/kg solvent
Solve for moles
moles = grams/molar mass
solve for molar mass.
To calculate the molar mass of the unknown compound, we need to use the colligative property known as the freezing point depression.
The freezing point depression occurs when a solute is added to a solvent, causing the freezing point of the solution to be lower than that of the pure solvent. The relationship between the freezing point depression and the molality of the solution is described by the equation:
ΔTf = Kf * m
Where:
ΔTf = change in freezing point
Kf = cryoscopic constant (a characteristic property of the solvent)
m = molality of the solution (moles of solute per kilogram of solvent)
In this case, we are given the value of the freezing point depression (ΔTf = -1.8 °C), and the mass of the solvent (152.5 g of water). We want to find the molality of the solution and use it to determine the molar mass of the unknown compound.
To find the molality, we need to convert the mass of the solute (35.1 g) into moles and calculate the mass of the water in kilograms.
1) Convert the mass of the solute to moles:
Moles = mass / molar mass
Here, the mass of the solute is 35.1 g.
2) Calculate the mass of the water in kilograms:
Mass (kg) = mass (g) / 1000
3) Calculate the molality using the following formula:
Molality = moles of solute / mass of water (kg)
4) Rearrange the freezing point depression equation to solve for the molar mass:
m = ΔTf / (Kf * Molality)
Since Kf is a known property of water, you can find it in reference tables.
Substitute the given values into the equation and solve for the molar mass of the unknown compound.