A 115 mL sample of a 10.0 M ethylene glycol (C2H6O2) solution is diluted to 1.30 L. What is the freezing point of the final solution? (Assume a density of 1.06 g/mL for the final solution.) What is the boiling point of the final solution?
How would I go about setting this up? thanks!
10.0 M x (115 mL/1300) = 0.885 M.
That's 0.883 mols/L soln.
1000 mL x 1.06 g/mL = 1060g soln is the mass of 1000 mL soln.
0.883 mols ethylene glycol x molar mass = 0.883 x 62.07 = 54.8 g is the mass of ethylene glycol in a liter (1060 g) of soln.
1060 - 54.8 = 1005.2 g is the solvent or 1.005 kg for the solvent and 0.883 mols solute or 0.883/1.005 = molality ethylene glycol.
Then delta T = Kf*m and subtract from zero to obtain freezing point.
delta T = Kb*m and add to 100 to obtain boiling point.
To solve this problem, you can use the equation:
ΔT = kf × m × i
where ΔT represents the change in temperature, kf is the freezing point depression constant, m is the molality of the solution, and i is the van't Hoff factor.
Step 1: Calculate the molality (m) of the final solution.
Molality is defined as the moles of solute per kilogram of solvent. In this case, the solute is ethylene glycol (C2H6O2), and the solvent is the final solution.
Given:
Volume of ethylene glycol solution (V1) = 115 mL = 0.115 L
Concentration of ethylene glycol solution (C1) = 10.0 M
Final solution volume (V2) = 1.30 L
Density of final solution = 1.06 g/mL
First, convert the volume of the ethylene glycol solution to mass using density:
Mass of ethylene glycol solution = Density × Volume
Mass of ethylene glycol solution = 1.06 g/mL × 0.115 L
Next, calculate the moles of ethylene glycol using the given concentration:
Moles of ethylene glycol = Concentration × Volume of ethylene glycol solution
Moles of ethylene glycol = 10.0 M × 0.115 L
Finally, divide the moles of ethylene glycol by the mass of the final solution:
Molality (m) = Moles of ethylene glycol / Mass of final solution
Step 2: Calculate the freezing point depression (ΔT) of the final solution using the molality (m) and van't Hoff factor (i).
The van't Hoff factor for ethylene glycol is 2, since it dissociates into two particles in solution.
Step 3: Calculate the freezing point of the final solution by adding the freezing point depression (ΔT) to the freezing point of the pure solvent.
Step 4: Repeat steps 1-3 to calculate the boiling point of the final solution using the boiling point elevation equation:
ΔT = kb × m × i
where ΔT represents the change in temperature, kb is the boiling point elevation constant, m is the molality of the solution, and i is the van't Hoff factor.
To find the freezing point of the final solution, you can make use of the formula for freezing point depression. It is given by:
∆Tf = Kf * m
where:
∆Tf = freezing point depression (in degrees Celsius)
Kf = cryoscopic constant (specific to the solvent, in this case, ethylene glycol)
m = molality of the solute (ethylene glycol)
To find the boiling point of the final solution, you can use the formula for boiling point elevation:
∆Tb = Kb * m
where:
∆Tb = boiling point elevation (in degrees Celsius)
Kb = ebullioscopic constant (specific to the solvent, in this case, ethylene glycol)
m = molality of the solute (ethylene glycol)
To set up these equations, you need to determine the molality of the solute in the final solution. Molality (m) is the amount of solute (in moles) divided by the mass of the solvent (in kilograms).
Here are the steps you can follow to set up the equations:
Step 1: Calculate the number of moles of ethylene glycol in the original 115 mL solution.
moles = concentration (in M) x volume (in L) = 10.0 M x (115 mL / 1000 mL/L)
Step 2: Determine the mass of the ethylene glycol in the original 115 mL solution.
mass = moles x molar mass = moles x (24 g/mol + 6 g/mol + 16 g/mol + 16 g/mol)
Step 3: Calculate the final mass of the solution after dilution.
mass_final = volume_final x density_final = 1.30 L x 1.06 g/mL
Step 4: Calculate the mass of the solute (ethylene glycol) in the final solution.
mass_solute_final = (mass_final / volume_final) x volume_solute_initial
(Note: Since volume_solute_initial and volume_final are given in mL, they need to be converted to L before using them in the equation.)
Step 5: Calculate the molality of the solute in the final solution by dividing the moles of solute by the mass of the solvent (in kilograms).
Step 6: Substitute the values you calculated into the freezing point depression and boiling point elevation formulas to find the respective temperature changes (∆Tf and ∆Tb).
Step 7: Finally, add or subtract the temperature changes (∆Tf and ∆Tb) to or from the normal freezing point (-1.86°C) and boiling point (100.0°C) of pure ethylene glycol to find the freezing point and boiling point of the final solution.
Please note that to find the cryoscopic constant (Kf) and ebullioscopic constant (Kb) specific to ethylene glycol, you may need to refer to a reference book or the literature.