When 15.0 g of ethyl alcohol, C2H5OH, is dissolved in 750 g of formic acid, the freezing point of the solution is 7.20 C. The freezing point of the pure formic acid is 8.40 C. Evaluate Kf for fomic acid.
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To calculate the freezing point depression constant (Kf) for formic acid, we can use the formula:
ΔT = Kf * m
where:
ΔT is the freezing point depression (in Celsius),
Kf is the freezing point depression constant (in °C⋅kg/mol),
m is the molality of the solution (in mol/kg).
In this case, we are given the following information:
mass of ethyl alcohol (C2H5OH) = 15.0 g
mass of formic acid = 750 g
freezing point of solution = 7.20 °C
freezing point of pure formic acid = 8.40 °C
First, we need to calculate the molality (m) using the formula:
m = moles of solute / mass of solvent (in kg)
To find the moles of solute (C2H5OH), we can use the molar mass:
molar mass of C2H5OH = (2 * atomic mass of C) + (6 * atomic mass of H) + atomic mass of O
= (2 * 12.01 g/mol) + (6 * 1.01 g/mol) + 16.00 g/mol
= 46.07 g/mol
moles of C2H5OH = mass of C2H5OH / molar mass of C2H5OH
= 15.0 g / 46.07 g/mol
= 0.325 mol
Next, we convert the mass of formic acid to kg:
mass of formic acid = 750 g / 1000
= 0.750 kg
Now, we can calculate the molality (m):
m = moles of solute / mass of solvent
= 0.325 mol / 0.750 kg
= 0.4333 mol/kg
Finally, we can calculate the freezing point depression constant (Kf) using the given freezing point depression (ΔT) and the molality (m):
ΔT = Kf * m
Rearranging the formula, we have:
Kf = ΔT / m
= (8.40 °C - 7.20 °C) / 0.4333 mol/kg
= 1.20 °C / 0.4333 mol/kg
= 2.769 °C⋅kg/mol
Therefore, the freezing point depression constant (Kf) for formic acid is approximately 2.769 °C⋅kg/mol.
To evaluate the freezing point depression constant (Kf) for formic acid, we can use the formula:
ΔT = Kf * m * i
Where:
- ΔT is the change in freezing point (fp) of the solution (in Celsius)
- Kf is the freezing point depression constant (in Celsius/mol)
- m is the molality of the solution (in mol/kg)
- i is the van't Hoff factor (number of ions or particles formed in the solution)
First, we need to calculate the ΔT (the change in freezing point) using the given information. We can find this by subtracting the freezing point of the solution from the freezing point of pure formic acid:
ΔT = fp (pure formic acid) - fp (solution)
= 8.40 °C - 7.20 °C
= 1.20 °C
Next, we need to find the molality (m) of the solution. Molality is defined as the moles of solute per kilogram of solvent. Given that 15.0 g of ethyl alcohol (C2H5OH) is dissolved in 750 g of formic acid, we need to convert the masses to moles:
Molar mass of C2H5OH:
C: 12.01 g/mol
H: 1.01 g/mol (x 6)
O: 16.00 g/mol
Total: 46.07 g/mol
Moles of C2H5OH = mass / molar mass
= 15.0 g / 46.07 g/mol
= 0.325 mol
Molality (m) = moles of solute / kg of solvent
= 0.325 mol / 0.750 kg
= 0.433 mol/kg
Now, we need to calculate the van't Hoff factor (i). For formic acid, i is equal to 1 because it does not ionize or dissociate in solution.
Plugging all the values into the formula, we have:
1.20 °C = Kf * 0.433 mol/kg * 1
To solve for Kf, we rearrange the equation:
Kf = ΔT / (m * i)
= 1.20 °C / (0.433 mol/kg * 1)
≈ 2.77 °C/mol
Therefore, the freezing point depression constant (Kf) for formic acid is approximately 2.77 °C/mol.