A solution contains 10.05 grams of an unknown covalent substance in 50.0
grams of water. The freezing point of this solution is (-) 3.16o C.
What is the formula weight of the unknown compound?
Below is what I tried, but don't know what to do next. Please explain step-by-step. Thanks
m=3.16/1.86=1.69 moles of solute/kg of water. 10.05 x 1000*50 g/kg of water is 200.4 g. So in l liter we have 1.69 moles = 200.4g. Mass of 1 mole =200.4/1.69 = 118.59
I don't follow all of you steps but you have essentially the right answer.
10.05 x 1000*50g/kg is not 200.4 and and kg is 50/1000 and not 50*1000. Anyway, here is the way to do it right.
dT = Kf*m
3.16/1.86 = m = 1.6989 (you threw the last 89 away and you should have rounded up to 1.70).
Tnen m = mols/kg solvent or
m x kg solvent = mols = 1.70 x 0.05 kg = 0.0849 mols.
Then mols = grams/molar mass or
molar mass = grams/mols = 10.05/0.0849 = 118.4.
To find the formula weight of the unknown compound, you can follow these steps:
Step 1: Calculate the moles of solute.
Using the formula for freezing point depression, m = ΔTf / Kf, where m is the molality of the solution, ΔTf is the freezing point depression, and Kf is the cryoscopic constant, solve for m:
m = (-3.16°C) / (-1.86°C/m)
m = 1.69 mol/kg
Step 2: Calculate the mass of the solute in grams.
Multiply the molality by the mass of the solvent:
mass of solute = m x mass of solvent
mass of solute = 1.69 mol/kg x 50.0 g = 84.5 g
Step 3: Calculate the molar mass (formula weight) of the unknown compound.
Divide the mass of the solute by the number of moles:
molar mass = mass of solute / number of moles
molar mass = 84.5 g / 1.69 mol
molar mass ≈ 50 g/mol
Therefore, the formula weight of the unknown compound is approximately 50 g/mol.
To find the formula weight of the unknown compound, you can use the concept of molality and freezing point depression.
Step 1: Calculate the molality (m) of the solution.
Molality is defined as the number of moles of solute per kilogram of solvent. In this case, the solvent is water. The molality (m) can be calculated using the formula:
m = (ΔTf / Kf) * i
where ΔTf is the freezing point depression (given as -3.16 °C), Kf is the cryoscopic constant for water (1.86 °C/kg·mol), and i is the van't Hoff factor, which is 1 for most covalent compounds (unless otherwise specified).
Using the given values, you can calculate the molality:
m = (-3.16 / 1.86) * 1
m = -1.70 mol/kg
Step 2: Calculate the mass of water in the solution.
You are given that the mass of water is 50.0 grams.
Step 3: Calculate the mass of the solute (unknown compound).
The mass of the solute can be calculated using the formula:
mass of solute = molality * mass of water * molar mass of water
In this case, the molar mass of water is 18.015 g/mol.
mass of solute = -1.70 mol/kg * 50.0 g * (18.015 g/mol / 1000 g/kg)
mass of solute = -1.53075 g
Note: The negative sign indicates that the freezing point of the solution is lower than the freezing point of pure water.
Step 4: Calculate the molar mass of the unknown compound.
The molar mass (formula weight) of the unknown compound can be calculated by dividing the mass of the solute by the number of moles of the solute.
molar mass = mass of solute / moles of solute
molar mass = -1.53075 g / -1.69 mol
molar mass ≈ 907.64 g/mol
Therefore, the formula weight of the unknown compound is approximately 907.64 g/mol.