200 g of a non-electrolye is dissolved in 1000 g of water. The boiling point of the solution is then measured to be 101.5 C. What is the molar mass?
(the Kb for water is 0.51 C/m)
I know deltaT = 0.51 C/m but where do I go from there?
To find the molar mass of the non-electrolyte, you can use the equation:
ΔT = K_b * m * i
Where:
ΔT is the change in boiling point, which is 101.5 °C - 100.0 °C = 1.5 °C
K_b is the boiling point elevation constant for water, which is 0.51 °C/m
m is the molality of the solution, which is the number of moles of solute per kilogram of solvent
i is the van't Hoff factor, which represents the number of particles the solute breaks into
In this case, since the solute is a non-electrolyte, it does not dissociate into ions when dissolved in water, so the van't Hoff factor (i) is equal to 1.
Given:
ΔT = 1.5 °C
K_b = 0.51 °C/m
To find the molality (m), you need to calculate the number of moles of the non-electrolyte.
First, use the formula:
m = n_solute / mass_solvent
Given:
mass_solute = 200 g
mass_solvent = 1000 g
Calculate the moles of the solute (n_solute):
n_solute = mass_solute / molar_mass
Now you have both the moles of the solute (n_solute) and the moles of the solvent (n_solvent = mass_solvent / molar_mass_water), so you can calculate the molality (m):
m = n_solute / (mass_solvent / molar_mass_water)
m = (mass_solute / molar_mass) / (mass_solvent / molar_mass_water)
From this equation, you can solve for the molar mass (molar_mass), given the values for mass_solute, mass_solvent, molar_mass_water, and the known molality (m).
molar_mass = (mass_solute * molar_mass_water * K_b) / (mass_solvent * ΔT)
Substituting the given values:
molar_mass = (200 g * 18 g/mol * 0.51 °C/m) / (1000 g * 1.5 °C)
Simplifying:
molar_mass ≈ 12.24 g/mol
Therefore, the molar mass of the non-electrolyte is approximately 12.24 g/mol.