1.10g of an unknown compound reduces the freezing point of 75.22g benzene from 5.53C to 4.92C. What is the molar mass of the compound?
120 g/mol
delta T = Kf*molality
Solve for molality
molality = moles/kg solvent
Solve for moles
moles = grams/molar mass
Solve for molar mass.
Well, it seems like our unknown compound really knows how to cool things down! Let's put on our chemistry clown hats and figure this out.
To find the molar mass, we can use the formula:
ΔT = Kf * m * i
Where:
ΔT = Change in freezing point
Kf = Freezing point depression constant for benzene (-5.12 °C/m)
m = Molality of the solution (mol solute / kg solvent)
i = Van't Hoff factor (which we'll assume is 1 for simplicity)
Plugging in the given values, we have:
ΔT = 5.53 °C - 4.92 °C = 0.61 °C
Kf = -5.12 °C/m
m = 1.10 g / (75.22 g/mol) = 0.0146 mol/kg
Now, we can rearrange the formula to solve for the molar mass (M):
M = (ΔT / (Kf * m)
Plugging in the values, we have:
M = (0.61 °C) / ((-5.12 °C/m) * (0.0146 mol/kg))
And after crunching the numbers, we find that the molar mass of the unknown compound is approximately 284 g/mol.
So, our silent guest has a molar mass of 284 g/mol!
To find the molar mass of the unknown compound, you can use the equation for freezing point depression. This equation relates the change in freezing point to the molality (moles of solute per kilogram of solvent) and the cryoscopic constant of the solvent.
The equation for freezing point depression is:
ΔTf = Kf * molality
Where:
ΔTf is the change in freezing point
Kf is the cryoscopic constant of the solvent
molality is the moles of solute per kilogram of solvent
First, we need to calculate the molality of the unknown compound.
Given:
Mass of benzene (solvent) = 75.22g
Change in freezing point (ΔTf) = 5.53C - 4.92C = 0.61C
Mass of the compound = 1.10g
Step 1: Calculate the moles of benzene.
To calculate the moles of benzene, we need to divide the mass of benzene by its molar mass. The molar mass of benzene is 78.11 g/mol.
moles of benzene = mass of benzene / molar mass of benzene
= 75.22g / 78.11 g/mol
Step 2: Calculate the molality of the compound.
To calculate molality, we divide the moles of the compound by the mass of the solvent (benzene) in kg.
molality = moles of compound / mass of benzene (kg)
= 1.10g / (75.22g / 1000g/kg)
Now we have the molality of the compound.
Step 3: Calculate the molar mass of the compound.
We can rearrange the freezing point depression equation to solve for the molar mass of the compound:
molar mass of the compound = ΔTf / (Kf * molality)
The cryoscopic constant for benzene is 5.12 K kg/mol.
molar mass of the compound = 0.61C / (5.12 K kg/mol * molality)
Plug in the values and calculate the molar mass.