C6H6 freezes at 5.5°C. At what temperature will a solution of 10 g of C4h10 in 200g of C6H6 freeze? The molal freezing point depression constant of C6H6 is 5.16°C/m?
To calculate the freezing point of a solution, we need to use the concept of freezing point depression. The formula for freezing point depression is given by:
ΔT = Kf * m
Where:
ΔT = freezing point depression
Kf = molal freezing point depression constant
m = molality of the solution (moles of solute per kilogram of solvent)
First, we need to calculate the molality (m) of the solution. Molality is calculated using the following formula:
m = moles of solute / mass of solvent in kg
Given:
Mass of C4H10 = 10g
Mass of C6H6 = 200g
Molar mass of C4H10 = 58.12 g/mol
Molar mass of C6H6 = 78.11 g/mol
Step 1: Calculate the moles of solute (C4H10)
moles of C4H10 = mass / molar mass
moles of C4H10 = 10g / 58.12 g/mol
Step 2: Calculate the mass of solvent (C6H6) in kg
mass of C6H6 = 200g / 1000
mass of C6H6 = 0.2kg
Step 3: Calculate the molality (m) of the solution
m = moles of solute / mass of solvent in kg
m = (10g / 58.12 g/mol) / 0.2kg
Step 4: Calculate the freezing point depression (ΔT)
ΔT = Kf * m
Given Kf = 5.16 °C/m
ΔT = 5.16 °C/m * (10g / 58.12 g/mol) / 0.2kg
Step 5: Calculate the freezing point of the solution
Freezing point of the solution = Freezing point of pure C6H6 - ΔT
Freezing point of the solution = 5.5 °C - (5.16 °C/m * (10g / 58.12 g/mol) / 0.2kg)
Now, plug in the values and calculate the freezing point of the solution.
To find the freezing point of a solution of C4H10 in C6H6, we can use the formula for freezing point depression:
∆T = Kf * m
where ∆T is the freezing point depression, Kf is the molal freezing point depression constant, and m is the molality of the solute.
To calculate the molality (m) of C4H10 in the solution, we first need to determine the number of moles of C4H10 and the mass of the solvent C6H6.
The molecular weight of C4H10 is 58.12 g/mol, so the number of moles of C4H10 can be calculated as:
moles of C4H10 = mass of C4H10 / molecular weight of C4H10
= 10 g / 58.12 g/mol
= 0.172 mol
The molality (m) is calculated by dividing the moles of solute by the mass of the solvent in kg:
molality (m) = moles of solute / mass of solvent (in kg)
= 0.172 mol / (200 g / 1000)
= 0.86 mol/kg
Now, we can calculate the freezing point depression:
∆T = Kf * m
= 5.16°C/m * 0.86 mol/kg
= 4.45°C
Finally, to find the freezing point of the solution, subtract the freezing point depression from the freezing point of pure C6H6:
Freezing point of solution = Freezing point of pure C6H6 - ∆T
= 5.5°C - 4.45°C
= 1.05°C
Therefore, the solution of 10 g of C4H10 in 200 g of C6H6 will freeze at approximately 1.05°C.
moles = gram/molar mass
calculate moles C4H10.
molality = moles/kg solvent.
calculate molality.
delta T = Kf*m
calculate delta T and from there freezing point.