When 4.167 g of a unknown compound is added to 34.1 g of a particular solvent, the freezing point of that solvent decreases by 0.8 °C. Determine the molar mass of the unknown compound. (The freezing point constant of the solvent is 2.82 °C/m).
To determine the molar mass of the unknown compound, we can use the equation for the freezing point depression:
ΔT = K_f * m
Where:
ΔT is the change in freezing point (in °C)
K_f is the freezing point constant of the solvent (in °C/m)
m is the molality of the solution (in moles of solute per kilogram of solvent)
In this case, we know the change in freezing point (ΔT = -0.8 °C) and the freezing point constant of the solvent (K_f = 2.82 °C/m). We can calculate the molality (m) using the formula:
m = moles of solute / mass of solvent (in kg)
First, convert the mass of the unknown compound from grams to moles, using its molar mass (M):
moles of solute = mass of solute / molar mass
Now, determine the mass of the solvent in kilograms (kg):
mass of solvent = mass of solvent / 1000
Substitute the values into the formula to solve for the moles of solute:
moles of solute = mass of solute / molar mass = 4.167 g / M
Next, substitute the values into the molality formula:
m = moles of solute / mass of solvent = (4.167 g / M) / 34.1 g
Now, substitute the values into the freezing point depression equation and solve for the molar mass:
ΔT = K_f * m
-0.8°C = 2.82 °C/m * [(4.167 g / M) / 34.1 g]
Rearrange the equation and solve for the molar mass (M):
M = (4.167 g / (34.1 g * -0.8 °C / (2.82 °C/m)))
Calculate the result to determine the molar mass of the unknown compound.