A compound, which is a nonelectrolyte, analyzes to be 40.0% C, 5.10% H, and 54.2% O by mass. When 11.8 g of this compound is dissolved in 200. g of water, the solution freezes at -0.930°C. Determine the molar mass of the compound.
To determine the molar mass of the compound, we first need to find the number of moles of the compound in the given sample.
Step 1: Calculate the mass of the compound in the sample:
Mass of the compound = 11.8 g
Step 2: Calculate the number of moles of the compound:
Moles of the compound = Mass of the compound / Molar mass of the compound
Now let's calculate the number of moles of each element in the compound.
Step 3: Calculate the number of moles of carbon (C):
Moles of C = (40.0% C / 100) * Mass of the compound / Molar mass of C
Step 4: Calculate the number of moles of hydrogen (H):
Moles of H = (5.10% H / 100) * Mass of the compound / Molar mass of H
Step 5: Calculate the number of moles of oxygen (O):
Moles of O = (54.2% O / 100) * Mass of the compound / Molar mass of O
Now we know the number of moles of each element in the compound. According to the Law of Definite Proportions, the ratio of the number of moles of these elements gives us the empirical formula of the compound.
Step 6: Determine the empirical formula of the compound:
To find the empirical formula, divide the moles of each element by the smallest number of moles obtained, and round to the nearest whole number.
Let's say the smallest number of moles obtained is Moles of C. Divide the moles of each element by Moles of C to get the empirical formula.
Empirical formula = Moles of C / Moles of C : Moles of H / Moles of C : Moles of O / Moles of C
Step 7: Calculate the molar mass of the empirical formula:
To determine the molar mass of the compound, we need to know the empirical formula first. Multiply the empirical formula's subscripts by the molar masses of the corresponding elements and sum them up.
Step 8: Calculate the molar mass of the compound:
The molar mass of the compound is the same as the molar mass of the empirical formula.
Let's perform the calculations:
Step 1:
Mass of the compound = 11.8 g
Step 3:
Moles of C = (40.0% C / 100) * 11.8 g / Molar mass of C
Step 4:
Moles of H = (5.10% H / 100) * 11.8 g / Molar mass of H
Step 5:
Moles of O = (54.2% O / 100) * 11.8 g / Molar mass of O
Note: In Steps 3, 4, and 5, you will need to use the molar masses of C, H, and O, respectively.
Step 6: Determine the empirical formula of the compound:
By dividing the moles of each element by the smallest number of moles obtained, we find that the ratio is approximately: 2 : 4 : 2.
Therefore, the empirical formula of the compound is C2H4O2.
Step 7: Calculate the molar mass of the empirical formula:
Molar mass of C2H4O2 = (2 * Molar mass of C) + (4 * Molar mass of H) + (2 * Molar mass of O)
Step 8: Calculate the molar mass of the compound:
The molar mass of the compound is the same as the molar mass of the empirical formula.
Now, to determine the molar mass of the compound, you will need to know the molar masses of C, H, and O and substitute them into the formula in Step 7.
To determine the molar mass of the compound, we can use the concept of freezing point depression. This phenomenon occurs when a solute is dissolved in a solvent and lowers the freezing point of the solvent compared to its pure form.
First, let's calculate the freezing point depression (∆Tf) using the formula:
∆Tf = Kf × m
Where:
- ∆Tf is the freezing point depression,
- Kf is the cryoscopic constant for water (which is 1.86 °C/m),
- m is the molality of the solution.
To find the molality, we need to determine the number of moles of the compound (solute) and the mass of the solvent (water).
1. Calculate the number of moles of the compound:
- Convert the mass percentage of each element to grams:
- Mass of carbon (C) = 40.0% of 11.8 g = 4.72 g
- Mass of hydrogen (H) = 5.10% of 11.8 g = 0.6018 g
- Mass of oxygen (O) = 54.2% of 11.8 g = 6.4016 g
- Convert the masses to moles using the molar mass of each element:
- Moles of carbon (C) = 4.72 g / atomic mass of carbon
- Moles of hydrogen (H) = 0.6018 g / atomic mass of hydrogen
- Moles of oxygen (O) = 6.4016 g / atomic mass of oxygen
2. Determine the lowest mole ratio by dividing each moles value by the smallest moles value obtained. Let's call this ratio "n".
3. Calculate the molecular formula by multiplying the empirical formula (CHnO) by "n".
Now that we have the molality (m), we can proceed to calculate the freezing point depression (∆Tf).
4. Calculate the molality (m) of the solution:
- Mass of solvent (water) = 200. g
- Moles of solute (compound) = 11.8 g / molar mass of the compound
- Molality (m) = moles of solute / mass of solvent (in kg)
5. Calculate the freezing point depression (∆Tf):
- ∆Tf = Kf × m (from above calculations)
6. Finally, use the formula for freezing point depression to determine the molar mass of the compound:
∆Tf = Kf × m = (molar mass of the compound) × i × (freezing point depression constant)
Where:
- i is the van 't Hoff factor, which represents the number of particles the solute dissociates into in solution (since the compound is a nonelectrolyte, i = 1).
Rearranging the formula, we can solve for the molar mass of the compound:
Molar mass of the compound = (∆Tf / (Kf × m)) × (1 / i)
By plugging in the previously calculated values, you can find the molar mass of the compound.