Butlylated hydroxytoluene (BHT) is used as an antioxidant in processed food. (It prevents fats and oils from becoming rancid.) A solution of 2.500 g of BHT in 100.0 g of benzene had a freezing point of 4.880⁰ C. What is the molecular weight of BHT? (Enter your answer in amu)
To find the molecular weight of BHT, we can use the concept of freezing point depression.
Freezing point depression occurs when a solute is added to a solvent, which lowers the freezing point of the solvent. The change in freezing point depends on the concentration of the solute and its molality.
We are given that the solution contains 2.500 g of BHT (solute) in 100.0 g of benzene (solvent), and the freezing point depression is 4.880⁰C.
First, let's convert the mass of BHT into moles using its molar mass. The molar mass of BHT can be calculated by adding the atomic masses of each element in its chemical formula, which is C15H24O.
C: 12.01 g/mol x 15 = 180.15 g/mol
H: 1.01 g/mol x 24 = 24.24 g/mol
O: 16.00 g/mol x 1 = 16.00 g/mol
Adding these up, we get:
Molar mass of BHT = 180.15 g/mol + 24.24 g/mol + 16.00 g/mol = 220.39 g/mol
Next, we need to calculate the molality of the solution. Molality (m) is defined as the number of moles of solute per kilogram of solvent. Since we know the mass of benzene (solvent) is 100.0 g, we convert this to kilograms by dividing by 1000.
Molality (m) = moles of solute / mass of solvent in kg
moles of solute = mass of BHT / molar mass of BHT
= 2.500 g / 220.39 g/mol
= 0.01135 mol
mass of solvent in kg = mass of benzene / 1000
= 100.0 g / 1000
= 0.100 kg
Molality (m) = 0.01135 mol / 0.100 kg
= 0.1135 mol/kg
The next step is to determine the freezing point depression constant (Kf) for benzene. This value can be found in reference books or online. For benzene, the Kf value is approximately 5.12 ⁰C/m.
Now we can use the freezing point depression equation to find the molecular weight (M) of BHT:
ΔT = Kf * m
4.880 ⁰C = 5.12 ⁰C/m * 0.1135 mol/kg
Finally, we can rearrange the equation to solve for the molecular weight (M):
M = ΔT / (Kf * m)
M = 4.880 ⁰C / (5.12 ⁰C/m * 0.1135 mol/kg)
Simplifying the equation, we get:
M = 4.880 ⁰C * kg * m / (5.12 * 0.1135 * mol)
M ≈ 98.20 g/mol
Therefore, the molecular weight of BHT is approximately 98.20 amu.