Problem 52 - Chemistry: The Central Science

Question

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{HCO}_{2}\), molar mass \(=90.0 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\), molar mass \(=88 \mathrm{~g} / \mathrm{mol}\)

Step-by-Step Solution

Answer

The molecular formulas for the given compounds are: (a) \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\) (b) \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{2}\)

Step 1: Calculate the molar mass of the empirical formula

The empirical formula is given as \(\mathrm{HCO}_{2}\). To find its molar mass, look up the molar masses of each individual element and add them together: - H: 1.01 g/mol - C: 12.01 g/mol - O: 16.00 g/mol Molar mass of \(\mathrm{HCO}_{2}\) = (1.01 + 12.01 + (2 × 16.00)) g/mol = 45.02 g/mol.

Step 2: Find the ratio between the molar masses of the molecular and empirical formulas

Divide the given molar mass of the molecular formula (90.0 g/mol) by the molar mass of the empirical formula (45.02 g/mol) to find the ratio: Ratio = \(\frac{90.0}{45.02} \approx 2\).

Step 3: Multiply the empirical formula by the ratio found in step 2

Since the ratio is 2, we need to multiply each element in the empirical formula by 2: Molecular formula = \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\). (b)

Step 1: Calculate the molar mass of the empirical formula

The empirical formula is given as \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\). To find its molar mass, look up the molar masses of each individual element and add them together: - C: 12.01 g/mol - H: 1.01 g/mol - O: 16.00 g/mol Molar mass of \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) = (2 × 12.01 + 4 × 1.01 + 16.00) g/mol = 44.06 g/mol.

Step 2: Find the ratio between the molar masses of the molecular and empirical formulas

Divide the given molar mass of the molecular formula (88 g/mol) by the molar mass of the empirical formula (44.06 g/mol) to find the ratio: Ratio = \(\frac{88}{44.06} \approx 2\).

Step 3: Multiply the empirical formula by the ratio found in step 2

Since the ratio is 2, we need to multiply each element in the empirical formula by 2: Molecular formula = \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{2}\).