The molecular formular of a hydrocarbon with an empirical formula of CH$_3$  and a molar mass of 30 is

Analysis

To find the molecular formula of a hydrocarbon when given the empirical formula and the molar mass, we need to determine the ratio between the molar mass of the compound and the molar mass of the empirical formula.

Concept

The relationship between the molecular formula and the empirical formula is given by the formula: Molecular Formula = (Empirical Formula)$_n$

Where $n$ is a whole number calculated as: $n = \frac{\text{Molar Mass of the compound}}{\text{Empirical Formula Mass}}$

Step-by-Step Solution

1. Calculate the Empirical Formula Mass: The empirical formula is $\text{CH}_3$. • Atomic mass of Carbon (C) = 12 • Atomic mass of Hydrogen (H) = 1 • Empirical Formula Mass = $12 + (3 \times 1) = 12 + 3 = 15\text{ g/mol}$

2. Calculate the value of $n$: We are given that the molar mass of the hydrocarbon is 30. • $n = \frac{30}{15} = 2$

3. Determine the Molecular Formula: Multiply the subscripts in the empirical formula ($\text{CH}_3$) by $n$ (which is 2): • Molecular Formula = $(\text{CH}_3)_2$ • Molecular Formula = $\text{C}_{(1 \times 2)}\text{H}_{(3 \times 2)}$ • Molecular Formula = $\text{C}_2\text{H}_6$

Conclusion

Comparing our result ($\text{C}_2\text{H}_6$) with the given options, it matches option C.

Exam Tip

Whenever you see a question asking for a molecular formula, always calculate the "Empirical Formula Mass" first. If your calculated $n$ is not a whole number, double-check your addition of the atomic masses—it is almost always a small integer like 1, 2, or 3!