A solution containing 4.5 grams of non-electrolyte dissolved in 125 grams of water freezes at -0.372 degrees. Calculate the molar weight of the solute.
delta T = Kf*molality
Solve for molality.
m = moles/kg solvent
solve for moles.
moles = grams/molar mass]
solve for molar mass.
To calculate the molar weight of the solute, we need to use the formula for freezing point depression:
ΔT = K_f * m
where:
- ΔT is the freezing point depression (difference between the freezing point of the pure solvent and the freezing point of the solution)
- K_f is the cryoscopic constant (a characteristic property of each solvent)
- m is the molality of the solution (moles of solute per kilogram of solvent)
First, let's calculate the molality (m). Molality is defined as moles of solute per kilogram of solvent. Given that 4.5 grams of solute (non-electrolyte) is dissolved in 125 grams of water (solvent), we need to convert the masses to moles.
Molar mass of water (H₂O) = 18.015 g/mol
Molar mass of solute = ?
moles of solute = mass of solute / molar mass of solute
moles of solute = 4.5 g / molar mass of solute
moles of water = mass of water / molar mass of water
moles of water = 125 g / 18.015 g/mol
Since the water acts as the solvent, we use its mass and molar mass to calculate its moles.
Next, we need to divide the moles of solute by the mass of water in kilograms to get the molality.
m = moles of solute / (mass of water in kg)
m = (4.5 g / molar mass of solute) / (125 g / 1000)
Now, let's calculate the freezing point depression (ΔT) using the given freezing point depression value.
ΔT = -0.372 degrees
Finally, we need to find the cryoscopic constant (K_f) of water. The cryoscopic constant of water is 1.86 °C·kg/mol.
Now we can rearrange the freezing point depression formula to solve for the molar mass of the solute:
molar mass of solute = (moles of solute / m) * (ΔT / K_f)
Substituting the previously calculated values:
molar mass of solute = (4.5 g / molar mass of solute) / (125 g / 1000) * (-0.372 / 1.86)
To solve this equation, we can use an iterative approach or numerical methods to determine the molar mass of the solute.