A solution was prepared by dissolving 0.834 g of sulfur, S8, in 100.0 g of acetic acid, HC2H3O2. Calculate the freezing point and boiling point of the solution. (Use the table from the textbook.)
mols S8 = grams/molar mass
Solve for mols.
molality = m = mols/kg solvent
Solve for m
delta T = Kf*m
Find delta T and subtract delta T from normal freezing point to find new freezing point.
delta T = Kb*m
Find delta T and add to normal boiling point to find new boiling point.
To calculate the freezing point and boiling point of the solution, we need to use the formula:
∆T = Kf * m * i
Where:
∆T = change in temperature
Kf = cryoscopic constant (given in the table)
m = molality of the solution
i = van't Hoff factor (the number of particles formed after dissociation)
1. Calculate the molality (m) of the solution:
Molar mass of sulfur (S8) = 8 * atomic mass of sulfur (S)
Molar mass of sulfur (S8) = 8 * 32.06 g/mol = 256.48 g/mol
molality (m) = (mass of solute / molar mass of solute) / (mass of solvent / molar mass of solvent)
molality (m) = (0.834 g / 256.48 g/mol) / (100.0 g / 60.052 g/mol)
molality (m) = (0.003254 mol / 0.083286 mol/kg) = 0.03914 mol/kg
2. Determine the van't Hoff factor (i):
For sulfur, S8, the i value is 1 because it does not dissociate or ionize in solution.
3. Use the cryoscopic constant (Kf) to calculate the change in temperature (∆T):
Looking at the table in the textbook, the Kf value for acetic acid (HC2H3O2) is 3.90 °C/m.
∆T = Kf * m * i
∆T = 3.90 °C/m * 0.03914 mol/kg * 1
∆T = 0.15246 °C
4. Calculate the freezing point of the solution:
The freezing point depression equation is:
Freezing point of solution = Freezing point of solvent - ∆T
From the table in the textbook, the freezing point of acetic acid is 16.6 °C.
Freezing point of solution = 16.6 °C - 0.15246 °C
Freezing point of solution ≈ 16.4 °C
5. Calculate the boiling point of the solution:
The boiling point elevation equation is:
Boiling point of solution = Boiling point of solvent + ∆T
From the table in the textbook, the boiling point of pure acetic acid is 118.1 °C.
Boiling point of solution = 118.1 °C + 0.15246 °C
Boiling point of solution ≈ 118.3 °C
Therefore, the freezing point of the solution is approximately 16.4 °C, and the boiling point of the solution is approximately 118.3 °C.
To determine the freezing point and boiling point of the solution, we need to calculate the molality and use the colligative properties equations.
Step 1: Calculate the molality (m) of the solution.
Molality (m) is the amount of solute (in moles) per kilogram of solvent. To calculate the molality, we need to find the moles of solute (sulfur) and the mass of the solvent (acetic acid).
Given:
Mass of sulfur (S8) = 0.834 g
Molar mass of sulfur (S8) = 256.52 g/mol
Moles of sulfur = mass of sulfur / molar mass of sulfur
= 0.834 g / 256.52 g/mol
Now, we need to calculate the mass of acetic acid, which will act as the solvent.
Given:
Mass of acetic acid = 100.0 g
The molality (m) can be calculated using the formula:
m = moles of solute / mass of solvent (in kg)
To convert grams to kilograms, divide by 1000:
Mass of solvent (in kg) = 100.0 g / 1000
Now substitute the known values to calculate the molality.
Step 2: Use the colligative properties equations to find the freezing point depression and boiling point elevation.
The freezing point depression (ΔTf) can be calculated using the equation:
ΔTf = Kf * m
The boiling point elevation (ΔTb) can be calculated using the equation:
ΔTb = Kb * m
Kf and Kb are the cryoscopic and ebullioscopic constants, respectively. These constants can be found in a table from your textbook or other reliable sources. Substitute the correct values into the equations.
Step 3: Calculate the freezing point and boiling point of the solution.
The freezing point (Tf) of the solution can be calculated using the equation:
Tf = Tf° - ΔTf
The boiling point (Tb) of the solution can be calculated using the equation:
Tb = Tb° + ΔTb
Tf° and Tb° are the freezing and boiling points of the pure solvent, respectively. These values can also be found in a table from your textbook or other reliable sources. Substitute the correct values into the equations.
By following these steps, you should be able to calculate the freezing point and boiling point of the solution.