The normal freezing point of cyclohexane is 6.55 C. When 0.458 g of benzophenone is dissolved in 15.0 g of cyclohexane, the freezing point is found to be 3.19 C. What is the experimental molar mass of benzophenone? (Kf cyclohexane = 20.0 C m^-1).
A) 182
B) 866
C) 397
D) 191
(units are all g/mol)
i've tried to use the T2-T1=Kfm and solved for molality and then tried to use that to get grams of solute and molar mass equals moles/mass. but i don't get any of the above answers. So, i'm pretty sure i'm going about it the wrong way. what's the right answer and what steps should i do to get there ?
delta T = Kf*m
Solve for m
m = mols/kg solvent
Solve for mols.
mols = grams/molar mass.
Solve for molar mass.
I ran through it very fast and I obtained one of the answers.
To find the experimental molar mass of benzophenone, we can use the formula:
ΔT = Kf * m
where ΔT is the change in freezing point, Kf is the cryoscopic constant of the solvent (cyclohexane), and m is the molality of the benzophenone solution.
First, let's calculate the change in freezing point:
ΔT = T2 - T1 = 3.19°C - 6.55°C = -3.36°C
Next, let's convert the mass of benzophenone to molality:
Mass of benzophenone = 0.458 g
Mass of cyclohexane = 15.0 g
Molality (m) = moles of solute / mass of solvent (in kg)
To calculate moles of solute, we need to convert the grams of benzophenone to moles using its molar mass (M):
moles of solute = mass / molar mass
Assuming the formula of benzophenone is C6H5COCH3, its molar mass is:
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.008 g/mol
Molar mass of O = 16.00 g/mol
Total molar mass = (12.01 * 13) + (1.008 * 10) + 16.00 = 182.22 g/mol
Now we can calculate the moles of solute:
moles of solute = 0.458 g / 182.22 g/mol
Next, let's convert grams of cyclohexane to kg:
mass of cyclohexane = 15.0 g = 0.015 kg
Finally, let's substitute the values into the formula to find the molality:
m = moles of solute / mass of solvent (in kg)
m = (0.458 g / 182.22 g/mol) / 0.015 kg
Now we can calculate the experimental molar mass:
ΔT = Kf * m
-3.36°C = 20.0°C m^-1 * [(0.458 g / 182.22 g/mol) / 0.015 kg]
Simplifying the equation:
-3.36 = 20.0 * (0.458 / 182.22 / 0.015)
Finally, let's solve for the molar mass:
molar mass = (0.458 / 182.22 / 0.015) * (20.0 / -3.36)
Calculating this expression will give us the experimental molar mass of benzophenone.
To find the experimental molar mass of benzophenone, you need to use the freezing point depression equation:
ΔT = Kf * m
where ΔT is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution.
First, let's calculate the molality of the solution:
Molality (m) = moles of solute / mass of solvent (in kg)
Given:
Mass of benzophenone (solute) = 0.458 g
Mass of cyclohexane (solvent) = 15.0 g
We need to convert the masses to kilograms:
Mass of benzophenone = 0.458 g / 1000 = 0.000458 kg
Mass of cyclohexane = 15.0 g / 1000 = 0.015 kg
Since we know the mass of benzophenone, we can calculate the moles of benzophenone:
Molar mass of benzophenone (M) = moles / mass
Rearranging the equation, we have:
moles = Molar mass * mass
Now, we need to find the change in freezing point (ΔT). Given that the normal freezing point of cyclohexane is 6.55°C and the freezing point of the solution is 3.19°C, we have:
ΔT = T2 - T1 = 3.19°C - 6.55°C = -3.36°C
Next, we can substitute the values into the freezing point depression equation:
-3.36°C = (20.0°C/molality) * m
Solving for molality (m), we have:
m = -3.36°C / 20.0°C/molality
m = -0.168
Since molality cannot be negative, it seems there might be a mistake in the data or calculations. Please double-check the data and calculations to ensure their accuracy.
Once the correct value of molality is obtained, you can proceed to calculate the experimental molar mass of benzophenone using the equation:
Experimental molar mass = moles / mass of benzophenone
Hope this helps!