What is the freezing point of a soluton is which 10.0 g of naphthalene [C10H8(s)] is dissolved in 50.0 g of benzene [C6H6(l)]?
Extra info you might need: benzene= 5.12 degrees C m^-1
Answer should be: -2.46
See your posts above.
To find the freezing point of the solution, we can use the formula for freezing point depression, which is given by:
ΔTf = -Kf * m * i
Where:
ΔTf = freezing point depression
Kf = freezing point depression constant (molal freezing point constant) for the solvent
m = molality of the solute
i = van't Hoff factor (the number of particles that the solute dissociates into)
First, we need to calculate the molality (m) of the solute (naphthalene).
Step 1: Calculate the moles of naphthalene (C10H8)
Given: Mass of naphthalene = 10.0 g
Molar mass of naphthalene (C10H8) = 128.17 g/mol
We can use the formula:
moles = mass / molar mass
moles of naphthalene = 10.0 g / 128.17 g/mol
Step 2: Calculate the molality (m) of the solute
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
Given: Mass of benzene (solvent) = 50.0 g = 0.050 kg
molality (m) = moles of solute / mass of solvent (in kg)
molality (m) = moles of naphthalene / mass of benzene
molality (m) = (10.0 g / 128.17 g/mol) / 0.050 kg
Now we have the molality (m), let's substitute it along with the other given values into the freezing point depression formula:
ΔTf = -Kf * m * i
Given: Kf for benzene = 5.12 degrees C m^-1
Van't Hoff factor (i) for naphthalene is generally 1 (since it doesn't dissociate in benzene).
Now we can substitute the values:
ΔTf = -5.12 °C m^-1 * (10.0 g / 128.17 g/mol) / 0.050 kg * 1
Calculating this expression will give you the freezing point depression (ΔTf) of the solution. To find the freezing point of the solution, we subtract the freezing point depression from the freezing point of the pure solvent (benzene).
Freezing point of solution = Freezing point of pure solvent (benzene) - ΔTf
Given: Freezing point of pure benzene = 0 °C
Assuming ideal behavior, the freezing point of pure benzene is not affected by the presence of naphthalene (non-volatile solute).
Therefore, the freezing point of the solution is:
Freezing point of solution = 0 °C - (Calculated value of ΔTf)
By evaluating the expression and calculating the freezing point, you will find the final answer, which should be -2.46 °C.