A solution of 10g of a nonvolatile compound in 25g of water boils at 100.78C at 1 atm. What is the molecular mass of the solute?
The normal boiling point of water is 100.00 C. This boils at 100.78; therefore, delta T = 100.78-100.00 = ?
Then delta T = Kb*molality. Substitute and solve for m = molality.
m = mols/kg solvent. You have kg solvent and m, solve for mols.
mol = grams/molar mass. You have mols and grams, solve for molar mass.
To find the molecular mass of the solute, we need to use the concept of boiling point elevation. Boiling point elevation occurs when a nonvolatile solute is added to a solvent, resulting in an increase in the boiling point of the solvent.
The equation we can use to calculate the boiling point elevation is:
ΔTb = Kb * m
Where:
ΔTb = change in boiling point (in Celsius)
Kb = molal boiling point elevation constant (in Celsius kg/mol)
m = molality of the solution (in mol/kg)
In this case, we know:
ΔTb = 100.78 - 100 (as pure water boils at 100C at 1 atm)
m = (moles of solute) / (mass of water in kg)
First, let's calculate the molality (m). We know that molality can be calculated as the ratio of the number of moles of solute to the mass of the solvent in kg.
Given that we have a solution of 10g of solute in 25g of water, we can assume that the mass of the water is effectively the same as the mass of the solution since the solute is nonvolatile. So, m = (10g) / (25g) = 0.4 mol/kg.
Now, we need to find the molal boiling point elevation constant (Kb) for water. The Kb for water is approximately 0.512 °C kg/mol.
Substituting the values we have into the equation, we get:
100.78 - 100 = (0.512 °C kg/mol) * (0.4 mol/kg)
Simplifying the equation gives:
0.78 = 0.205 mol °C/kg
Now, to find the molecular mass of the solute, we use the formula:
Molecular mass = (moles of solute) / (mass of solute in grams)
We know the moles of solute is 0.4 mol and the mass of solute is 10g. So, substituting those values into the formula gives:
Molecular mass = 0.4 mol / 10g = 0.04 mol/g
Therefore, the molecular mass of the solute is 0.04 g/mol.
So, the molecular mass of the solute is 0.04 g/mol.