Problem 51 - Chemistry: The Central Science

Question

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{CH}_{2}\), molar mass \(=84 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{NH}_{2} \mathrm{Cl}\), molar mass \(=51.5 \mathrm{~g} / \mathrm{mol}\)

Step-by-Step Solution

Answer

The molecular formulas of the two compounds are: (a) \(\mathrm{C}_{6}\mathrm{H}_{12}\) (b) \(\mathrm{NH}_{2}\mathrm{Cl}\)

Step 1: Calculate the molar mass of the empirical formula

We will find the molar mass of the empirical formula \(\mathrm{CH}_{2}\): C: 1 atom × 12.01 g/mol = 12.01 g/mol H: 2 atoms × 1.01 g/mol = 2.02 g/mol ----------------------------------------- Total: 14.03 g/mol The molar mass of \(\mathrm{CH}_{2}\) is 14.03 g/mol.

Step 2: Calculate the multiple

To find the multiple, we will divide the molar mass of the molecular formula (84 g/mol) by the molar mass of the empirical formula (14.03 g/mol): Multiple = \(\frac{84}{14.03}\) ≈ 6

Step 3: Determine the molecular formula

Now, multiply the empirical formula by the multiple: \(\mathrm{CH}_{2}\) × 6 = \(\mathrm{C}_{6}\mathrm{H}_{12}\) The molecular formula of the compound is \(\mathrm{C}_{6}\mathrm{H}_{12}\). (b) empirical formula \(\mathrm{NH}_{2} \mathrm{Cl}\), molar mass \(=51.5 \mathrm{~g} / \mathrm{mol}\)

Step 1: Calculate the molar mass of the empirical formula

We will find the molar mass of the empirical formula \(\mathrm{NH}_{2} \mathrm{Cl}\): N: 1 atom × 14.01 g/mol = 14.01 g/mol H: 2 atoms × 1.01 g/mol = 2.02 g/mol Cl: 1 atom × 35.45 g/mol = 35.45 g/mol ----------------------------------------- Total: 51.48 g/mol The molar mass of \(\mathrm{NH}_{2} \mathrm{Cl}\) is 51.48 g/mol.

Step 2: Calculate the multiple

To find the multiple, we will divide the molar mass of the molecular formula (51.5 g/mol) by the molar mass of the empirical formula (51.48 g/mol): Multiple = \(\frac{51.5}{51.48}\) ≈ 1

Step 3: Determine the molecular formula

Now, multiply the empirical formula by the multiple: \(\mathrm{NH}_{2} \mathrm{Cl}\) × 1 = \(\mathrm{NH}_{2}\mathrm{Cl}\) The molecular formula of the compound is \(\mathrm{NH}_{2}\mathrm{Cl}\).