A hydrocarbon has an empirical formula CH and a vapour density of 39. Determine its molecular formula. [C = 12, H = 1]

To determine the molecular formula of the hydrocarbon, we follow these steps:

1. Analyze the Question

We are given:

• Empirical formula = $\text{CH}$
• Vapour density = $39$
• Atomic masses: $\text{C} = 12, \text{H} = 1$
• Goal: Find the molecular formula.

2. Explain the Concept

• Molecular Mass: The molecular mass of a substance is twice its vapour density. $$\text{Molecular Mass} = 2 \times \text{Vapour Density}$$
• Relationship: The molecular formula is a multiple of the empirical formula. If $n$ is the multiplier, then: $$\text{Molecular Formula} = (\text{Empirical Formula})_n$$ $$\text{Molecular Mass} = n \times (\text{Empirical Formula Mass})$$

3. Show the Solution

Step 1: Calculate the molecular mass.

Step 2: Calculate the empirical formula mass.

Step 3: Find the value of $n$.

Step 4: Determine the molecular formula. Multiply the empirical formula ($\text{CH}$) by $n = 6$:

4. Identify the Answer

Comparing our result with the given options, $\text{C}_6\text{H}_6$ corresponds to option D.

5. Exam Tip

Always remember the relationship Molecular Mass = 2 × Vapour Density. This is a classic JAMB question pattern. If you ever forget the formula, just remember that the molecular mass of Hydrogen gas ($\text{H}_2$) is 2, and its vapour density is 1, which confirms the "times 2" rule!