2. When 0.354 g of an unknown nonelectrolyte compound was dissolved in 12.5 g of benzene a solution was formed that froze at 4.46°C.
(a) Calculate the molar mass of the unknown compound. The freezing point of benzene is 5.48°C, and the Kf of benzene is 5.12 °C/Molal. Show your work
To calculate the molar mass of the unknown compound, we need to use the freezing point depression equation:
ΔT = Kf * m * i
where:
ΔT is the change in freezing point (in °C),
Kf is the freezing point depression constant (in °C/molal),
m is the molality of the solution (in mol/kg),
i is the van't Hoff factor (which represents the number of particles the compound dissociates into when it dissolves, and for a nonelectrolyte like this one, i = 1).
First, we need to calculate the molality of the solution. Molality is defined as the number of moles of solute (in this case, the unknown compound) divided by the mass of the solvent (benzene) in kilograms.
Given:
Mass of unknown compound (solute) = 0.354 g
Mass of benzene (solvent) = 12.5 g
Molar mass of benzene (C6H6) = 78.11 g/mol
Moles of benzene = mass/molar mass
Moles of benzene = 12.5 g / 78.11 g/mol
Next, we need to convert g of unknown compound to moles of unknown compound.
Molar mass of unknown compound (M) = mass/moles
Molar mass of unknown compound (M) = 0.354 g / moles
Now, to calculate the molality, we use the formula:
Molality = Moles of solute / Mass of solvent (in kg)
Molality = moles of unknown compound (M) / mass of benzene (in kg)
To convert the mass of benzene from grams to kilograms, we divide it by 1000:
Mass of benzene (in kg) = 12.5 g / 1000 = 0.0125 kg
Now we can substitute the given values into the freezing point depression equation:
ΔT = Kf * m * i
ΔT = 4.46°C - 5.48°C = -1.02°C (note the freezing point depression is negative)
Kf = 5.12 °C/molal
i = 1 (since it's a nonelectrolyte)
We have all the values needed, so let's solve for the molality:
-1.02°C = 5.12 °C/molal * m * 1
Now we can solve for the molality:
m = -1.02°C / (5.12 °C/molal)
m = -0.1992 molal
Finally, we can calculate the moles of the unknown compound:
Molality = Moles of solute / Mass of solvent (in kg)
-0.1992 molal = moles of unknown compound (M) / 0.0125 kg
Now we can solve for the moles of the unknown compound:
moles (M) = (-0.1992 molal) * (0.0125 kg)
moles (M) = -0.00249 mol
Since we cannot have negative moles, this negative sign indicates an error in your calculations or measurement. Please recheck your values and recalculate.
Once you have the correct number of moles, you can calculate the molar mass of the unknown compound by dividing the mass (0.354 g) by the number of moles.