Calculate the freezing point of a solution of 20.0 g methyl salicylate, C7H6O2, dissolved in 800 g of benzene, C6H6. Kf for benzene is 5.10°C /m and the freezing point is 5.50°C for benzene.
A) -1.05°C
B) 1.05°C
C) 4.45°C
D) 6.54°C
To calculate the freezing point of the solution, we need to use the equation:
ΔT = Kf * molality
First, calculate the molality (m) of the solution:
Step 1: Calculate the moles of methyl salicylate (C7H6O2):
moles = mass / molar mass
The molar mass of C7H6O2:
= (7 * 12.01 g/mol) + (6 * 1.01 g/mol) + (2 * 16.00 g/mol)
= 138.12 g/mol
moles of C7H6O2 = 20.0 g / 138.12 g/mol = 0.1445 mol
Step 2: Calculate the molality of C7H6O2 in the solution:
molality = moles of solute / mass of solvent (in kg)
mass of solvent = 800 g = 800 g / 1000 g/kg = 0.8 kg
molality of C7H6O2 = 0.1445 mol / 0.8 kg = 0.1806 mol/kg
Step 3: Calculate the change in temperature (ΔT):
ΔT = Kf * molality
ΔT = 5.10°C/m * 0.1806 mol/kg
ΔT = 0.9223°C
Finally, calculate the freezing point:
Freezing point = Freezing point of solvent - ΔT
Freezing point = 5.50°C - 0.9223°C
Freezing point = 4.5777°C
Therefore, the freezing point of the solution is approximately 4.58°C.
The correct answer is C) 4.45°C.
To calculate the freezing point of a solution, we need to use the formula:
∆TF = Kf * m
where ∆TF is the change in freezing point, Kf is the cryoscopic constant, and m is the molality of the solute.
First, we need to calculate the molality (m) of the solute.
Molality (m) is defined as the moles of solute per kilogram of solvent.
Given:
Mass of methyl salicylate (C7H6O2) = 20.0 g
Mass of benzene (C6H6) = 800 g
Molar mass of methyl salicylate (C7H6O2) = 138.12 g/mol
First, we need to calculate the moles of methyl salicylate:
moles of methyl salicylate = mass / molar mass
= 20.0 g / 138.12 g/mol
≈ 0.1445 mol
Now, we can calculate the molality of the solute:
molality (m) = moles of solute / mass of solvent (in kg)
= 0.1445 mol / 0.8 kg
= 0.1806 mol/kg
Now, we can calculate the change in freezing point (∆TF):
∆TF = Kf * m
= 5.10°C/m * 0.1806 mol/kg
≈ 0.9231°C
Finally, to find the freezing point, we need to subtract the change in freezing point from the original freezing point of benzene:
Freezing point = 5.50°C - 0.9231°C
≈ 4.5769°C
Since the answer choices are rounded to two decimal places, the correct answer would be C) 4.45°C.
4.45
moles = grams/molar mass.
Solve for moles methyl salicylate.
molality = moles/kg solvent
Solve for molality
delta T = Kf*m
Solve for delta T
freezing point = 5.50 - delta T.