The boiling point of diethyl ether CH3CH2OCH2CH3 is 34.500C at 1 atmosphere. A nonvolatile, nonelectrolyte that dissolves in diethyl ether is cholesterol .
How many grams of cholesterol, C27H46O (386.6 g/mol), must be dissolved in 263.0 grams of diethyl ether to raise the boiling point by 0.4500C ?
delta T = Kb*molality. You know delta T and Kb (somewhere in the problem or you have a table containing the information), solve for molality.
Then molality = moles/kg solvent, you know m and kg solvent, calculate moles.
Then moles = grams/molar mass, calculate grams.
and molality = moles/kg solvent.
To solve this problem, we can use the equation for the boiling point elevation:
ΔTb = Kb * m * i
Where:
- ΔTb is the change in boiling point
- Kb is the molal boiling point elevation constant
- m is the molality of the solution
- i is the van't Hoff factor, which is 1 for a non-electrolyte
First, let's calculate the molality (m) of the solution. Molality is defined as the number of moles of solute per kilogram of solvent.
To find the number of moles of cholesterol, we can use the equation:
moles = mass / molar mass
moles of cholesterol (C27H46O) = mass / molar mass
moles of cholesterol = (263.0 g diethyl ether) * (1 mole diethyl ether / molar mass of diethyl ether)
Next, we need to find the molality of the solution. This can be calculated by:
molality (m) = moles of solute / mass of solvent in kg
mass of solvent in kg = mass of diethyl ether / 1000
Finally, we can substitute the values into the boiling point elevation equation to get the answer.
Let's calculate all the steps:
1. Calculate the moles of cholesterol:
moles of cholesterol = (263.0 g) * (1 mole diethyl ether / molar mass of diethyl ether)
moles of cholesterol = (263.0 g) * (1 mole / 74.12 g/mol) (approx. molar mass of diethyl ether)
moles of cholesterol = 3.5509 moles
2. Calculate the mass of the solvent in kg:
mass of solvent in kg = mass of diethyl ether / 1000
mass of solvent in kg = 263.0 g / 1000
mass of solvent in kg = 0.2630 kg
3. Calculate the molality (m) of the solution:
molality (m) = moles of solute / mass of solvent in kg
molality (m) = 3.5509 moles / 0.2630 kg
molality (m) ≈ 13.5009 mol/kg
4. Calculate the change in boiling point (ΔTb):
ΔTb = Kb * m * i
ΔTb = Kb * 13.5009 mol/kg * 1
5. Finally, we need to rearrange the equation to solve for the mass of cholesterol:
ΔTb = Kb * m * i
ΔTb / (Kb * i) = m
mass of cholesterol = ΔTb / (Kb * i)
Plug in the given values:
ΔTb = 0.4500°C (change in boiling point)
Kb = boiling point elevation constant (specific to the solvent, diethyl ether)
i = 1 (van't Hoff factor)
Now you have all the information you need to calculate the mass of cholesterol. Just substitute the values into the equation:
mass of cholesterol = ΔTb / (Kb * i)
mass of cholesterol = 0.4500°C / (Kb * 1)
Since you haven't provided the boiling point elevation constant (Kb) specific to diethyl ether, I cannot calculate the mass of cholesterol for you. Please provide the value of Kb to continue the calculation.