The normal freeing point of cyclohexane if 6.6 degrees Celsius. A 0.2g sample of an unknown solute is dissolved in 50 ml of cyclohexane (d-0.8g/ml, Kf=20 degreesCelsius/m. If the freezing point of the solution is 3.6 degrees Celsius, what is the molar mass of the solute?
delta T = Kf*molality
Solve for molality.
molality = moles/kg solvent. Use the density to convert 50 mL solvent to mass.
Solve molality equation for moles.
moles = grams/molar mass. You have moles and grams, solve for molar mass.
what grams do i use to solve for "moles = grams/molar mass?
It's the mass of the unknown that you want to determine the molar mass of. That is 0.2 g sample from the problem.
To find the molar mass of the solute, we need to use the equation:
ΔT = Kf * m
Where:
ΔT = change in freezing point temperature (in degrees Celsius)
Kf = cryoscopic constant (in degrees Celsius per molal)
m = molality (in mol solute per kg solvent)
First, let's calculate the molality of the solution.
Given:
Mass of solute (molar mass) = 0.2 g
Mass of solvent (cyclohexane) = 50 ml * 0.8 g/ml = 40 g
Molality (m) = mol solute / kg solvent
Mass of solute (g) = molar mass (g/mol) * moles of solute
Molar mass (g/mol) = mass of solute (g) / moles of solute
Since we don't have the number of moles of solute, we can calculate it using the molality formula and the freezing point depression:
ΔT = Kf * m
Rearranging the equation:
m = ΔT / Kf
ΔT = normal freezing point of solvent - freezing point of solution
= 6.6 °C - 3.6 °C
= 3 °C
Plugging in the values, we get:
m = 3 °C / 20 °C/m
≈ 0.15 molal
Now, let's calculate the moles of solute:
moles of solute = m * kg solvent
Mass of solvent (kg) = mass of solvent (g) / 1000
= 40 g / 1000
= 0.04 kg
moles of solute = 0.15 molal * 0.04 kg
= 0.006 mol
Now that we have the moles of solute, we can calculate the molar mass.
Molar mass (g/mol) = mass of solute (g) / moles of solute
Molar mass (g/mol) = 0.2 g / 0.006 mol
≈ 33.3 g/mol
Therefore, the molar mass of the solute is approximately 33.3 g/mol.