In an experiment, 3.545 grams of an unknown nonelectrolyte is dissolved in 15.0 grams of water. The extrapolated freezing point is -.56 degrees C. What is the molecular weight of the unknown material?
delta T = Kf*molality
Solve for molality.
m = moles/kg solvent
Solve for moles. You have m and 0.15 kg solvent)
moles = grams/molar mass
You have moles and grams, solve for molar mass.
Ok so when I solved for molality I got 0.30108. Then I plugged in and solved for moles and I got .0045 moles. So when I solved for molar mass I got 784.96 g/mol. Does that sound right? Thank you so much!!
That looks ok to me. I think you are allowed only three significant figures so I would round to 785.
To determine the molecular weight of the unknown material, we can use the concept of freezing point depression. Freezing point depression occurs when a solute is added to a solvent, and the freezing point of the solvent decreases as a result.
The formula to calculate the molecular weight using freezing point depression is:
\( \text{Molecular weight} = \frac{{(\Delta T_f) \times (K_f)}}{{\text{molality}}} \)
Where:
- \(\Delta T_f\) is the freezing point depression, which is the difference between the freezing point of the pure solvent and the freezing point of the solution.
- \(K_f\) is the cryoscopic constant, which is specific to the solvent.
- Molality is the amount of solute (in moles) divided by the mass of the solvent (in kg).
For water, the cryoscopic constant \(K_f\) is 1.86 °C/m.
First, we need to calculate the molality of the solution:
\( \text{molality} = \frac{{\text{moles of solute}}}{{\text{mass of water (in kg)}}} \)
To find the moles of solute, we use the formula:
\( \text{moles of solute} = \frac{{\text{mass of solute}}}{{\text{molar mass of solute}}} \)
Now, let's apply these calculations to the given information:
Given:
Mass of solute = 3.545 g
Mass of water = 15.0 g
Freezing point depression (\(\Delta T_f\)) = -0.56 °C
Cryoscopic constant (\(K_f\)) = 1.86 °C/m
1. Calculate moles of solute:
\(\text{moles of solute} = \frac{{3.545 \, \text{g}}}{{\text{molar mass of solute}}}\)
2. Calculate molality:
\(\text{molality} = \frac{{\text{moles of solute}}}{{\text{mass of water (in kg)}}}\)
3. Rearrange the formula to find the molar mass (molecular weight):
\(\text{Molar mass of solute} = \frac{{(\Delta T_f) \times (K_f)}}{{\text{molality}}}\)
By substituting the given values and solving this equation, you will find the molecular weight of the unknown material.