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?
To find the formula weight of the unknown compound, you can use the concept of freezing point depression. This concept states that the freezing point of a solution is lower than the freezing point of the pure solvent (in this case, water) and is directly proportional to the concentration of solute particles in the solution.
The formula for freezing point depression is:
ΔT = Kf * molality
Where:
- ΔT is the change in freezing point (in degrees Celsius)
- Kf is the cryoscopic constant (a constant value for each solvent)
- molality is the concentration of solute particles in the solution, expressed in moles per kilogram (mol/kg)
Now, let's calculate the molality of the solution.
First, we need to calculate the number of moles of the unknown substance. We can use the given mass of the compound and the molar mass to find this.
To do that, we'll first need to convert the given mass of the unknown compound to moles. We divide the mass by the molar mass.
Given mass: 10.05 grams
Now, we need the molar mass of the unknown compound, which will allow us to convert grams to moles. Since the compound is covalent, its molar mass is the sum of the atomic masses of its constituent elements.
Since we don't have information about the type of compound, we can't calculate the exact molar mass. However, based on the given data, we'll use a hypothetical value of 50 g/mol as the molar mass of the unknown compound for illustration purposes.
Using this hypothetical molar mass, we can calculate the number of moles of the unknown compound:
moles of unknown compound = given mass / molar mass
moles of unknown compound = 10.05 g / 50 g/mol
moles of unknown compound = 0.201 mol
Next, we calculate the molality of the solution:
molality = moles of solute / mass of solvent (in kg)
mass of solvent = 50.0 g = 0.050 kg
molality = 0.201 mol / 0.050 kg
molality = 4.02 mol/kg
Now, let's calculate the change in freezing point (ΔT) using the given freezing point depression (-3.16 °C) and the cryoscopic constant for water (1.86 °C/m).
ΔT = -3.16 °C
Now, we can rearrange the freezing point depression equation to find the formula weight of the unknown compound:
Formula weight = ΔT / (Kf * molality)
Since we are given the freezing point depression (-3.16 °C), and the cryoscopic constant for water (1.86 °C/m), and we calculated the molality (4.02 mol/kg), we can now substitute these values into the equation:
Formula weight = -3.16 °C / (1.86 °C/m * 4.02 mol/kg)
Calculating this expression will give us the formula weight of the unknown compound.