a compound containing only boron, nitrogen and hydrogen was found to be 40.3% B, 52.2%N, and 7.5% H by mass. If 3.301g of this compound is dissolved in 50.00g of benzene, the solution produced freezes at 1.30 degrees celsius. If Kf(freezing point depression constant) for benzene is 5.12 degrees celsius per metre and the freezing point of benzene is 5.48 degrees celsius, what is the molecular weight of this compound?
You can use the percents to determine the empirical formula.
Take 100 g sample which will give you
40.3 g C, 52.2 g N and 7.5 g H. Now divide each by the atomic mass of C, N, and H respectively, find the ratio in small whole numbers and you have the empirical formula.
Now use delta T = kf*molality to determine molality. Finally, knowing molality = # mols/kg solvent, you can determine the molar mass and from that the molecular formula and from that the molar mass.
Post your work if you get stuck.
80.9g/mol
To find the molecular weight of the compound, we need to first calculate the molecular formula using the given percentages of boron (B), nitrogen (N), and hydrogen (H).
1. Convert the mass percentages to grams:
- B: 40.3% -> 40.3g
- N: 52.2% -> 52.2g
- H: 7.5% -> 7.5g
2. Determine the moles of each element:
- Moles of B = Mass of B / Molar mass of B = 40.3g / molar mass of B
- Moles of N = Mass of N / Molar mass of N = 52.2g / molar mass of N
- Moles of H = Mass of H / Molar mass of H = 7.5g / molar mass of H
3. Find the empirical formula:
- Divide the moles of each element by the smallest number of moles to get the ratio of the elements. Round the ratio to the nearest whole number.
- The ratio will give us the empirical formula.
4. Calculate the molar mass:
- Multiply the subscripts in the empirical formula obtained in step 3 by the molar masses of the respective elements.
- The sum of these masses will give us the molecular weight of the compound.
Now, let's calculate the molecular weight of the compound.
Step 1: Find the moles of each element.
We need the molar masses of B, N, and H to calculate the moles. The molar mass of boron (B) is 10.81 g/mol, nitrogen (N) is 14.01 g/mol, and hydrogen (H) is 1.01 g/mol.
Moles of B = 40.3g / 10.81 g/mol = 3.72 mol
Moles of N = 52.2g / 14.01 g/mol = 3.72 mol
Moles of H = 7.5g / 1.01 g/mol = 7.43 mol
Step 2: Determine the empirical formula.
Since the ratio of moles is approximately 1:1:2 (3.72:3.72:7.43), the empirical formula is B(NH)₂.
Step 3: Calculate the molar mass of the compound.
The molar mass of B(NH)₂ can be calculated by adding the molar masses of each element.
Molar mass of B(NH)₂ = (molar mass of B) + 2 * (molar mass of N) + 4 * (molar mass of H)
= (10.81 g/mol) + 2 * (14.01 g/mol) + 4 * (1.01 g/mol)
= 37.84 g/mol
Therefore, the molecular weight of the compound B(NH)₂ is 37.84 g/mol.