When 0.855 g of this solid was dissolved in 7.50 g of napthalene, the solution had a freezing point of 78.0° C. The pure solvent freezes at 80.0° C; its molal freezing point constant is 6.8° C/m. What is the molecular formula of the compound?
delta T = Kf*molality
Solve for molality
molality = moles/kg solvent
Solve for moles.
moles = grams/molar mass
Solve for molar mass.
To determine the molecular formula of the compound, we need to use colligative properties, specifically the freezing point depression equation. The freezing point depression equation is given by:
ΔTf = Kf * m
Where:
ΔTf = freezing point depression
Kf = molal freezing point constant
m = molality of the solution
First, we need to calculate the molality of the solution using the given masses:
mass of solute (molecular weight) = 0.855 g
mass of solvent (napthalene) = 7.50 g
molality (m) = moles of solute / mass of solvent (in kg)
To convert the mass of solute to moles, we divide it by the molecular weight of the compound. The molecular weight can be calculated by knowing the molar mass of napthalene (128.19 g/mol). Therefore:
moles of solute = 0.855 g / molecular weight
Next, we need to convert the mass of the solvent to kg:
mass of solvent (in kg) = 7.50 g / 1000
Now we can calculate the molality (m):
m = moles of solute / mass of solvent (in kg)
With the molality (m) calculated, we can use the freezing point depression equation to find ΔTf:
ΔTf = Kf * m
Substituting the given values:
ΔTf = 6.8° C/m * m
Finally, we substitute the values into the equation:
78.0° C - 80.0° C = 6.8° C/m * m
Solving this equation will give us the molality of the solution. Once we have the molality, we can use it to find the molecular formula by comparing it to the empirical formula of the compound.