An unknown sample with a molecular mass of 180.0g is analyzed to yield 40% C, 6.7% H, and 53.3% O. What is the empirical formula and the molecular formula of this compound?
Take a 100 g sample which will give you
40 g C
6.7 g H
53.3 g O.
Convert to mols.
40/12 = ? mols C.
6.7/1 = ? mols H
53.3/16 = ? mols O
Now find the ratio of the elements t each other with the smallest being 1.00. The easy way to do that is to divide the smallest number by itself (which makes it 1.00), then divide the other two numbers by the same small number. That will give you the empirical formula.
To find the molecular formula, do this
empirical formula mass = ?(add the atomic masses) and substitute into
empirical formula x n = molar mass, solve for n and the molecular formula is (CxHyOz)n
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To determine the empirical formula and molecular formula of the compound, we need to follow a few steps:
Step 1: Convert the mass percentages to grams.
Given that we have a 180.0g sample, we can convert the percentages to grams using these values:
- Carbon (C) = 40% of 180.0g = 72.0g
- Hydrogen (H) = 6.7% of 180.0g = 12.06g
- Oxygen (O) = 53.3% of 180.0g = 95.94g
Step 2: Calculate the number of moles of each element.
Using the atomic masses of the elements from the periodic table:
- Carbon (C) atomic mass = 12.01 g/mol. Therefore, the number of moles of C = 72.0g / 12.01 g/mol ≈ 5.996 moles.
- Hydrogen (H) atomic mass = 1.008 g/mol. Therefore, the number of moles of H = 12.06g / 1.008 g/mol ≈ 11.95 moles.
- Oxygen (O) atomic mass = 16.00 g/mol. Therefore, the number of moles of O = 95.94g / 16.00 g/mol ≈ 5.997 moles.
Step 3: Determine the simplest whole-number ratio of the elements.
Divide each number of moles by the smallest number of moles to get the simplest whole-number ratio:
- C: 5.996 moles / 5.996 ≈ 1
- H: 11.95 moles / 5.996 ≈ 2
- O: 5.997 moles / 5.996 ≈ 1
The empirical formula is C1H2O1, which can be simplified to CH2O.
Step 4: Calculate the empirical formula mass.
The empirical formula mass can be determined by adding the atomic masses of the elements in the empirical formula:
- Carbon (C) atomic mass = 12.01 g/mol
- Hydrogen (H) atomic mass = 1.008 g/mol
- Oxygen (O) atomic mass = 16.00 g/mol
Empirical formula mass = (1 * 12.01) + (2 * 1.008) + (1 * 16.00) = 30.03 g/mol.
Step 5: Calculate the molecular formula.
To determine the molecular formula, we need the molecular mass, which is given as 180.0g.
Molecular formula mass ÷ Empirical formula mass = n
180.0g ÷ 30.03 g/mol = 5.994
Round the value of n to the nearest whole number:
n ≈ 6
Multiply the empirical formula by n to get the molecular formula:
(C1H2O1) * 6 = C6H12O6
Therefore, the empirical formula is CH2O, and the molecular formula is C6H12O6.