The empirical formula of an organic liquid hydrocarbon is XY. If the relative molar masses of X and Y are 72…

1. Analyze the Question

We are given the empirical formula of a hydrocarbon as $XY$. We are provided with the relative molar masses of the individual components $X$ and $Y$. We need to find the vapour density of the compound.

2. Explain the Concept

• Empirical Formula: This represents the simplest whole-number ratio of atoms of each element in a compound.
• Molar Mass of the Compound: The molar mass of the compound is the sum of the molar masses of its constituent parts based on the empirical formula.
• Vapour Density: Vapour density is defined as the ratio of the mass of a certain volume of a gas or vapour to the mass of an equal volume of hydrogen gas at the same temperature and pressure. The relationship between molar mass ($M$) and vapour density ($VD$) is: $$M = 2 \times VD$$Therefore,$VD = \frac{M}{2}$

3. Show the Solution

Step 1: Calculate the molar mass ($M$) of the hydrocarbon. The empirical formula is $XY$. Given:

• Molar mass of $X = 72$
• Molar mass of $Y = 6$

Total molar mass ($M$) = $72 + 6 = 78\text{ g/mol}$

Step 2: Calculate the vapour density ($VD$). Using the formula $VD = \frac{M}{2}$:

4. Identify the Answer

Comparing our result to the options provided: A. 33 B. 66 C. 39 D. 78

The calculated value matches option C.

5. Tip

Always remember the relationship $M = 2 \times VD$. A common mistake students make is to multiply the molar mass by 2 instead of dividing it. If you ever forget the formula, just remember that the molar mass of a gas is always twice its vapour density because the molar mass of hydrogen gas ($H_2$) is approximately 2.