Question

interactive example molecular formula
vinegar contains carbon, hydrogen, and oxygen with percent masses of 40.01% c, 6.70% h, and 53.29% o, respectively. determine the molecular formula of the compound, with a molar mass of 60.052 g/mol
question
convert to moles.
c. mol c/mol vinegar
h. mol h/mol vinegar
d. mol o/mol vinegar
check (2 of 3)

Explanation:

Step1: Assume 100g of vinegar

We assume a 100g sample to simplify percentage mass calculations. So, mass of C = 40.01g, H = 6.70g, O = 53.29g.

Step2: Calculate moles of each element

Moles of C: $n_C = \frac{40.01\,\text{g}}{12.01\,\text{g/mol}} \approx 3.33\,\text{mol}$
Moles of H: $n_H = \frac{6.70\,\text{g}}{1.008\,\text{g/mol}} \approx 6.65\,\text{mol}$
Moles of O: $n_O = \frac{53.29\,\text{g}}{16.00\,\text{g/mol}} \approx 3.33\,\text{mol}$

Step3: Find mole ratio (divide by smallest moles)

Smallest moles is ~3.33.
Ratio of C: $\frac{3.33}{3.33} = 1$
Ratio of H: $\frac{6.65}{3.33} \approx 2$
Ratio of O: $\frac{3.33}{3.33} = 1$
Empirical formula: $\text{CH}_2\text{O}$ (molar mass of empirical formula: $12.01 + 2(1.008) + 16.00 = 30.03\,\text{g/mol}$)

Step4: Determine molecular formula multiplier

Molar mass of compound is 60.052 g/mol. Multiplier $n = \frac{60.052}{30.03} \approx 2$

Step5: Calculate moles per mole of vinegar (molecular formula $\text{C}_2\text{H}_4\text{O}_2$)

• mol C/mol vinegar: 2 (since 2 C atoms per molecule)
• mol H/mol vinegar: 4 (4 H atoms per molecule)
• mol O/mol vinegar: 2 (2 O atoms per molecule)

Answer:

• mol C/mol vinegar: $\boldsymbol{2}$
• mol H/mol vinegar: $\boldsymbol{4}$
• mol O/mol vinegar: $\boldsymbol{2}$