An organic compound has the empirical formula $CH_{2}$. If its molar mass is 42$gmol^{-1}$, what is its molecular formula?  (C = 12.0, H = 1.0)

Step 1: Analyze the question We are given the empirical formula (CH₂) and the molar mass (42 g/mol), and we must find the molecular formula.

Step 2: The concept The molecular formula is a whole-number multiple of the empirical formula:

Molecular formula = (Empirical formula)ₙ, where n = molar mass ÷ empirical formula mass

Step 3: Solution

Empirical formula mass of CH₂: = 12.0 + (2 × 1.0) = 14.0 g/mol

Find n: n = 42 ÷ 14 = 3

Molecular formula: (CH₂)₃ = C₃H₆

Check: C₃H₆ has a mass of (3 × 12) + (6 × 1) = 36 + 6 = 42 g/mol ✔

Checking the other options:

• A. C₂H₄ = 28 g/mol ✘
• B. C₃H₄ = 40 g/mol (and not a multiple of CH₂) ✘
• D. C₄H₈ = 56 g/mol ✘

Step 4: Answer The correct option is **C.

Exam tip: Always compute the empirical formula mass first, then divide the molar mass by it. If the result is a whole number, multiply every subscript by it. You can also quickly eliminate options that are not in the ratio 1:2 (C:H), as with option B.