A 1.80 g sample of a large boimolecule was dissolved in 21.0 g of carbon tetrachloride. The boiling point of this solution was determined to be 77.85°C. Calculate the molar mass of the biomolecule. For carbon tetrachloride, the boiling point constant is 5.03°C·kg/mol, and the boiling point of pure carbon tetrachloride is 76.50°C.
delta T = kb*molality
You know delta T and Kb.
Solve for m
molality = moles unknown/kg solvent
Solve for moles unknown.
moles = grams/molar mass
You have moles unknown and grams unknown,
solve for molar mass of unknown.
To calculate the molar mass of the biomolecule, we need to use the formula:
ΔTb = Kb * m * i
Where:
ΔTb is the change in boiling point,
Kb is the boiling point constant of the solvent,
m is the molality of the solution, and
i is the van't Hoff factor.
First, we need to calculate the molality (m) of the solution, which is defined as the moles of solute (biomolecule) divided by the mass of the solvent (carbon tetrachloride) in kilograms:
m = moles of solute / mass of solvent (in kg)
To find the moles of solute, we divide the mass of the biomolecule by its molar mass:
moles of solute = mass of biomolecule / molar mass of biomolecule
Given that the mass of the biomolecule is 1.80 g, and the mass of the solvent (carbon tetrachloride) is 21.0 g, we can calculate:
moles of solute = 1.80 g / molar mass of biomolecule
Next, we need to convert the mass of the solvent to kilograms:
mass of solvent (in kg) = 21.0 g / 1000
Now, we can substitute the values into the molality equation:
m = (1.80 g / molar mass of biomolecule) / (21.0 g / 1000)
Simplifying the equation:
m = (1.80 g * 1000) / (molar mass of biomolecule * 21.0 g)
Now, let's calculate the change in boiling point (ΔTb) using the equation:
ΔTb = (boiling point of solution - boiling point of pure solvent)
Given that the boiling point of the solution is 77.85°C and the boiling point of pure carbon tetrachloride is 76.50°C:
ΔTb = 77.85°C - 76.50°C
Finally, we can substitute the values into the formula to calculate the molar mass of the biomolecule:
ΔTb = Kb * m * i
molar mass of biomolecule = (Kb * m) / (ΔTb * i)
Given that the boiling point constant of carbon tetrachloride is 5.03°C·kg/mol, and assuming that the van't Hoff factor (i) is 1 (since most biomolecules do not dissociate in solution):
molar mass of biomolecule = (5.03°C·kg/mol * m) / (ΔTb)
Substituting the values of m and ΔTb calculated earlier, we can find the molar mass of the biomolecule.