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
delta T = kf*m
Substitute and solve for m
m = mols/kg solvent
Substitute and solve for m
mols = grams/molar mass. You know mols and grams, solve for molar mas.
To calculate the molar mass of the unknown compound, we can use the formula:
ΔT = Kf * m * i
Where:
ΔT = freezing point depression = Tb - Tf
Kf = freezing point depression constant for benzene = 5.12 °C/Molal
m = molality of the solution
i = vant Hoff factor (for a nonelectrolyte, i = 1)
First, we need to calculate the molality (m) of the solution:
m = moles of solute / mass of solvent (in kg)
Given:
Mass of solute = 0.354 g
Mass of solvent = 12.5 g of benzene = 0.0125 kg
Moles of solute = mass of solute / molar mass of solute
Since we're trying to find the molar mass of the unknown compound, let's represent it as M:
Moles of solute = 0.354 g / M
Now we can calculate the molality (m):
m = (0.354 g / M) / 0.0125 kg
The molality is given in molal, which means moles of solute per kilogram of solvent. We can simplify this expression by multiplying by 1000 to convert grams to kilograms:
m = (0.354 g / M) / (0.0125 kg * 1000 g/kg)
m = (0.354 g / M) / 12.5 kg
Now, let's substitute the values into the freezing point depression formula:
ΔT = Kf * m * i
Given:
ΔT = 5.48°C - 4.46°C = 1.02°C
Kf = 5.12 °C/Molal
m = (0.354 g / M) / 12.5 kg
i = 1
1.02°C = (5.12 °C/Molal) * [(0.354 g / M) / 12.5 kg] * 1
Now, we can solve for the unknown compound's molar mass (M):
M = (0.354 g * 1 Molal) / (5.12 °C * 12.5 kg / 1.02 °C)
Calculate the values in the numerator:
M = 0.354 g / 5.12 °C * 12.5 kg / 1.02 °C
M = 0.354 g / 5.12 * 12.5 kg / 1.02
M = 0.0684 g/Mol
Therefore, the molar mass of the unknown compound is approximately 0.0684 g/mol.
To calculate the molar mass of the unknown compound, we can use the formula for determining the molality of a solution and the formula for determining the freezing point depression.
The molality (m) of a solution is given by the equation:
molality (m) = moles of solute / mass of solvent (kg)
In this case, we are given that 0.354 g of the unknown compound is dissolved in 12.5 g of benzene. To convert the mass of the unknown compound to moles, we divide it by the molar mass (M) of the compound:
moles of solute = mass of solute (g) / molar mass (M)
Let's represent the molar mass of the unknown compound as M:
0.354 g / M = moles of solute
The mass of benzene is given as 12.5 g, so to get the mass in kg, we divide it by 1000:
mass of solvent (kg) = mass of solvent (g) / 1000
mass of solvent (kg) = 12.5 g / 1000 = 0.0125 kg
The freezing point depression (ΔTf) is given by the equation:
ΔTf = Kf * m
where Kf is the freezing point depression constant of the solvent (benzene), and m is the molality of the solution.
In this case, we are given that the freezing point depression is 4.46°C and the Kf of benzene is 5.12 °C/Molal. Rearranging the equation, we can solve for molality (m):
m = ΔTf / Kf
Plugging in the values, we have:
m = 4.46°C / 5.12 °C/Molal = 0.871 Molal
Now, we can substitute the values into the equation for molality:
0.871 Molal = moles of solute / 0.0125 kg
Solving for moles of solute:
moles of solute = 0.871 Molal * 0.0125 kg = 0.0109 mol
Finally, we can calculate the molar mass of the unknown compound by dividing the mass of solute by the number of moles:
M = mass of solute (g) / moles of solute
Plugging in the values, we have:
M = 0.354 g / 0.0109 mol ≈ 32.47 g/mol
Therefore, the molar mass of the unknown compound is approximately 32.47 g/mol.