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Math  /  Algebra

Question12. An unknown compound contains 51.89%51.89 \% lead, 16.06%16.06 \% sulfur and 32.05%32.05 \% oxygen. Mass spec analysis shows that the unknown compound has a molar mass of 798.7 g/mol\mathrm{g} / \mathrm{mol}. Determine the empirical and molecular formulas of the compound.

Studdy Solution

STEP 1

1. The percentages given are by mass.
2. The molar mass of the compound is 798.7 g/mol.
3. We need to determine both the empirical and molecular formulas of the compound.

STEP 2

1. Convert percentage composition to grams assuming a 100 g sample.
2. Convert grams to moles for each element.
3. Determine the simplest whole number ratio of moles to find the empirical formula.
4. Calculate the empirical formula mass.
5. Determine the molecular formula using the empirical formula and the given molar mass.

STEP 3

Assume a 100 g sample of the compound. This means we have:
- 51.89 g 51.89 \, \text{g} of lead (Pb) - 16.06 g 16.06 \, \text{g} of sulfur (S) - 32.05 g 32.05 \, \text{g} of oxygen (O)

STEP 4

Convert grams to moles for each element using their atomic masses:
- Molar mass of Pb = 207.2 g/mol - Molar mass of S = 32.07 g/mol - Molar mass of O = 16.00 g/mol
Calculate moles of each:
Moles of Pb=51.89207.2≈0.250 mol \text{Moles of Pb} = \frac{51.89}{207.2} \approx 0.250 \, \text{mol}
Moles of S=16.0632.07≈0.500 mol \text{Moles of S} = \frac{16.06}{32.07} \approx 0.500 \, \text{mol}
Moles of O=32.0516.00≈2.003 mol \text{Moles of O} = \frac{32.05}{16.00} \approx 2.003 \, \text{mol}

STEP 5

Determine the simplest whole number ratio of moles:
Divide each by the smallest number of moles (0.250):
Ratio of Pb=0.2500.250=1 \text{Ratio of Pb} = \frac{0.250}{0.250} = 1
Ratio of S=0.5000.250=2 \text{Ratio of S} = \frac{0.500}{0.250} = 2
Ratio of O=2.0030.250≈8 \text{Ratio of O} = \frac{2.003}{0.250} \approx 8
The empirical formula is PbSO8 \text{PbSO}_8 .

STEP 6

Calculate the empirical formula mass:
Empirical formula mass=(1×207.2)+(1×32.07)+(8×16.00) \text{Empirical formula mass} = (1 \times 207.2) + (1 \times 32.07) + (8 \times 16.00)
=207.2+32.07+128.00 = 207.2 + 32.07 + 128.00
=367.27 g/mol = 367.27 \, \text{g/mol}

STEP 7

Determine the molecular formula using the empirical formula and the given molar mass:
Molar mass of compound=798.7 g/mol \text{Molar mass of compound} = 798.7 \, \text{g/mol}
Ratio=798.7367.27≈2.175 \text{Ratio} = \frac{798.7}{367.27} \approx 2.175
Since the ratio should be a whole number, round to the nearest whole number, which is 2.
Multiply the subscripts in the empirical formula by 2 to get the molecular formula:
Empirical formula: PbSO8 \text{PbSO}_8
Molecular formula: Pb2S2O16 \text{Pb}_2\text{S}_2\text{O}_{16}

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