A 0.01205 mg sample of an unknown compound was found to contain 0.0001 mg of H, 0.0043 mg of Cl, and 0.0077 mg of O. It was also determined that the unknown compound had a molecular weight of 100.46 g/mol. What is the molecular formula for this compound?
Convert grams of each element into mols. mols = grams/atomic mass.
Then take the ratio of the elements. The easiest way to do this is to divide the smallest # mols by itself (thus making it 1.00), then divide the other mol values by the same smallest number. That will get you the mole ratios and the empirical (simplest) formula. To find the molecular formula, divide the molecular weight of 100.46 by the formula weight of the empirical formula, round to the nearest whole number, then multiply the empirical formula by this whole number. Post your work if you get stuck and I can help you through it.
thanks a million for the help.
To find the molecular formula of the unknown compound, we first need to determine the number of moles of each element present in the sample.
Step 1: Determine the number of moles of hydrogen (H):
- Mass of H in the sample = 0.0001 mg = 1 × 10^-7 g
- Molar mass of H = 1.00784 g/mol
- Number of moles of H = mass of H / molar mass of H = (1 × 10^-7 g) / (1.00784 g/mol) = 9.918 × 10^-8 mol
Step 2: Determine the number of moles of chlorine (Cl):
- Mass of Cl in the sample = 0.0043 mg = 4.3 × 10^-6 g
- Molar mass of Cl = 35.453 g/mol
- Number of moles of Cl = mass of Cl / molar mass of Cl = (4.3 × 10^-6 g) / (35.453 g/mol) = 1.214 × 10^-7 mol
Step 3: Determine the number of moles of oxygen (O):
- Mass of O in the sample = 0.0077 mg = 7.7 × 10^-6 g
- Molar mass of O = 15.999 g/mol
- Number of moles of O = mass of O / molar mass of O = (7.7 × 10^-6 g) / (15.999 g/mol) = 4.813 × 10^-7 mol
Step 4: Determine the empirical formula:
The empirical formula represents the simplest, whole-number ratio of atoms in a compound. To find the empirical formula, divide the number of moles of each element by the smallest number of moles.
- H: (9.918 × 10^-8 mol) / (9.918 × 10^-8 mol) ≈ 1
- Cl: (1.214 × 10^-7 mol) / (9.918 × 10^-8 mol) ≈ 1.225
- O: (4.813 × 10^-7 mol) / (9.918 × 10^-8 mol) ≈ 4.854
Rounded to the nearest whole number, the empirical formula is HClO5.
Step 5: Determine the molecular formula:
To find the molecular formula, we need to know the molecular weight.
- Molecular weight = 100.46 g/mol
- Empirical formula weight = (1.00784 g/mol × 1) + (35.453 g/mol × 1.225) + (15.999 g/mol × 4.854) ≈ 98.998 g/mol
The molecular formula can be calculated by dividing the molecular weight by the empirical formula weight:
- Molecular formula = Molecular weight / Empirical formula weight = 100.46 g/mol / 98.998 g/mol
Rounded to the nearest whole number, the molecular formula is H2Cl2O10.
To determine the molecular formula of the compound, we need to find the empirical formula first.
Step 1: Calculate the number of moles for each element.
- Moles of H: 0.0001 mg / molar mass of H
- Moles of Cl: 0.0043 mg / molar mass of Cl
- Moles of O: 0.0077 mg / molar mass of O
Step 2: Determine the mole ratio.
Divide the number of moles of each element by the smallest value. Since the smallest value is in moles, we don't need to convert the others to moles.
Step 3: Round the mole ratio to the nearest whole number.
The molecular formula will be an integer multiple of the empirical formula, so round the mole ratio to the nearest whole number.
Step 4: Calculate the empirical formula mass.
Multiply the atomic masses of each element by the rounded mole ratio and sum them up.
Step 5: Determine the empirical formula.
Divide the molecular weight (100.46 g/mol) by the empirical formula mass to find the number of empirical formula units in the molecular formula.
Step 6: Multiply the empirical formula by the number of empirical formula units to get the molecular formula.
Now, let's calculate the molecular formula:
Step 1: Calculate the number of moles for each element.
- Moles of H: 0.0001 mg / 1.008 g/mol = 9.92 × 10^-5 mol
- Moles of Cl: 0.0043 mg / 35.453 g/mol = 1.21 × 10^-4 mol
- Moles of O: 0.0077 mg / 16.00 g/mol = 4.81 × 10^-4 mol
Step 2: Determine the mole ratio.
Divide the number of moles of each element by the smallest value, which is 9.92 × 10^-5 mol (H).
- Moles of H: (9.92 × 10^-5 mol) / (9.92 × 10^-5 mol) = 1.00
- Moles of Cl: (1.21 × 10^-4 mol) / (9.92 × 10^-5 mol) ≈ 1.22
- Moles of O: (4.81 × 10^-4 mol) / (9.92 × 10^-5 mol) ≈ 4.85
Step 3: Round the mole ratio to the nearest whole number.
- H: 1.00
- Cl: 1.22 (approximately 1)
- O: 4.85 (approximately 5)
Step 4: Calculate the empirical formula mass.
- H: 1.008 g/mol × 1 = 1.008 g/mol
- Cl: 35.453 g/mol × 1 = 35.453 g/mol
- O: 16.00 g/mol × 5 = 80.00 g/mol
Empirical formula mass = 1.008 g/mol + 35.453 g/mol + 80.00 g/mol = 116.461 g/mol
Step 5: Determine the empirical formula.
The molecular weight is given as 100.46 g/mol. Divide the molecular weight by the empirical formula mass to find the number of empirical formula units:
- (100.46 g/mol) / (116.461 g/mol) ≈ 0.863
Step 6: Multiply the empirical formula by the number of empirical formula units to get the molecular formula.
- Empirical formula: HClO
- Molecular formula: (HClO) × 0.863 ≈ H0.863Cl0.863O0.863
Since we can't have fractional subscripts in a molecular formula, we need to round off the subscripts to the nearest whole number:
- Molecular formula: HClO