Thyroxine, an important hormone that controls the rate of metabolism in the body can be isolated from the thyroid gland. If 0.455 g of thyroxine is dissolved in 10.0 g of benzene, the freezing point of the solution could be measured as 5.144°C. Pure benzene freezes at 5.444°C and has a value for the molal freezing-point-depression constant of Kf of 5.12°C/m. What is the approximate molar mass of thyroxine?
To find the approximate molar mass of thyroxine, we can use the formula:
ΔTf = Kf * m
where ΔTf is the freezing point depression, Kf is the molal freezing point depression constant, and m is the molality of the solution.
Given that the freezing point depression (ΔTf) is 5.444°C - 5.144°C = 0.3°C and Kf is 5.12°C/m, we can calculate the molality (m) of the solution:
m = ΔTf / Kf = 0.3°C / 5.12°C/m = 0.05859375 m
Now, we can use the formula for molality:
m = moles of solute / mass of solvent in kilograms
Given that the mass of thyroxine is 0.455 g and the mass of benzene is 10.0 g, we can calculate the moles of thyroxine:
moles of solute = mass of thyroxine / molar mass of thyroxine
Let's assume the molar mass of thyroxine is M:
0.05859375 m = 0.455 g / M
Rearranging the equation:
M = 0.455 g / 0.05859375 m ≈ 7.77 g/mol
Therefore, the approximate molar mass of thyroxine is approximately 7.77 g/mol.
To find the molar mass of thyroxine, we need to use the freezing point depression equation:
ΔT = Kf * m,
where:
- ΔT is the change in freezing point temperature
- Kf is the molal freezing-point-depression constant
- m is the molality of the solution
We already have the value of Kf for benzene, which is 5.12°C/m. To find the molality (m), we need to calculate the number of moles of thyroxine and benzene.
First, let's find the number of moles of benzene in the solution:
moles of benzene = mass of benzene / molar mass of benzene
Given that the mass of benzene is 10.0 g and its molar mass is approximately 78.11 g/mol, we have:
moles of benzene = 10.0 g / 78.11 g/mol
Next, let's find the molality (m) using the number of moles of thyroxine:
m = moles of thyroxine / mass of benzene
Given that the mass of thyroxine is 0.455 g, let's calculate the number of moles of thyroxine using its molar mass:
moles of thyroxine = mass of thyroxine / molar mass of thyroxine
Now we can substitute the values into the molality formula:
m = (moles of thyroxine / mass of benzene) / (moles of benzene / mass of benzene)
Simplifying the equation:
m = moles of thyroxine / moles of benzene
Now we can substitute the known values into the equation and solve for m.
Finally, once we have the value of m, we can substitute it into the freezing point depression equation to find ΔT.
Once we have ΔT, we can rearrange the equation to solve for the molar mass of thyroxine:
molar mass of thyroxine = ΔT / (Kf * m)
Substitute the known values and calculate to find the approximate molar mass of thyroxine.
delta T = Kf*molality
Solve for m
m = mols/kg solvent.
Substitute and solve for mols.
mols = grams/molar mass
Substitute and solve for molar mass.