A solution containing 0.750g of an unknown substance in 30.0g of cyclohexane was found to freeze at 3.1 degree Celsius. What is the molar mass of the unknown substance?
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To determine the molar mass of the unknown substance, you will need to use the freezing point depression equation. This equation relates the change in freezing point to the molality of the solution.
The equation for freezing point depression is:
ΔT = Kf × m
Where:
- ΔT is the change in freezing point, which is equal to the freezing point of the pure solvent minus the freezing point of the solution.
- Kf is the cryoscopic constant for the solvent.
- m is the molality of the solution in mol solute / kg solvent.
In this case, the freezing point depression, ΔT, is given as 3.1 °C. The molality, m, is calculated by dividing the moles of solute by the mass of the solvent.
Step 1: Calculate the moles of the unknown substance
To calculate the moles of the unknown substance, we need to know the mass of the unknown substance.
Given:
Mass of the unknown substance = 0.750 g
To convert the mass of the unknown substance into moles, we need to divide it by the molar mass of the unknown substance.
Step 2: Calculate the moles of cyclohexane
Since we know the mass of the cyclohexane, we can calculate the moles of cyclohexane using its molar mass.
Given:
Mass of cyclohexane = 30.0 g
Molar mass of cyclohexane = 84.16 g/mol
Using the formula: moles = mass / molar mass
Step 3: Calculate the molality of the solution
The molality, m, is calculated by dividing the moles of solute by the mass of the solvent in kilograms.
Given:
Mass of the solvent (cyclohexane) = 30.0 g = 0.030 kg
Using the formula: molality = moles of solute / mass of solvent (in kg)
Step 4: Calculate the molar mass of the unknown substance
Now that we have the molality, we can rearrange the freezing point depression equation and solve for the molar mass of the unknown substance.
Given:
Freezing point depression, ΔT = 3.1 °C
Cryoscopic constant for cyclohexane, Kf = 20.2 °C/molal (or K kg/mol)
Using the formula: molar mass = (ΔT / (Kf × m))
Plug in the values and calculate the molar mass of the unknown substance.
To determine the molar mass of the unknown substance, we need to use the concept of freezing point depression. Freezing point depression occurs when a solute is added to a solvent, causing the freezing point of the solvent to decrease.
The freezing point depression can be calculated using the equation:
ΔT = Kf * m * i
Where:
ΔT is the change in freezing point
Kf is the cryoscopic constant (a constant value depending on the solvent, in this case, cyclohexane)
m is the molality of the solution (moles of solute per kilogram of solvent)
i is the van't Hoff factor (the number of particles the solute dissociates into)
In this case, we are given the change in freezing point (ΔT) as 3.1 degrees Celsius, and the mass of cyclohexane (solvent) as 30.0g. To find the molality (m), we need to calculate the moles of solute (unknown substance).
Moles of unknown substance = Mass of unknown substance / Molar mass of unknown substance
Given the mass of the unknown substance as 0.750g, we can use this information to calculate the moles of the unknown substance.
Now we can proceed to find the molality of the solution:
m = moles of solute / mass of solvent (in kg)
Given the mass of cyclohexane as 30.0g, we convert it to kilograms by dividing by 1000.
Finally, with the freezing point depression (ΔT), the molality (m), and the cryoscopic constant (Kf), we can solve for the molar mass of the unknown substance using the equation:
Molar mass of unknown substance = (ΔT / (Kf * m)) * 1000
Plug in the given values and solve the equation to find the molar mass of the unknown substance.
I assume this is a non-polar substance where i = 1
delta T = i*Kf*m
Substitute and solve for molality.
molality = mols/L
Substitute and solve for mols.
mols = grams/molar mass
Subtitute and solve for molar mass.