An oxide XO2 has a vapour density of 32. What is the atomic mass of X?

1. Analyze the Question

We are given an oxide with the formula $XO_2$ and its vapour density ($VD = 32$). We need to find the relative atomic mass of the element $X$.

2. Explain the Concept

• Vapour Density and Molar Mass: There is a fundamental relationship between the vapour density of a gas and its molar mass: $$\text{Molar Mass} = 2 \times \text{Vapour Density}$$
• Molar Mass of a Compound: The molar mass of a compound is the sum of the atomic masses of all the atoms in its formula. For $XO_2$, the molar mass is: $$\text{Molar Mass} = (\text{Atomic mass of } X) + 2 \times (\text{Atomic mass of } O)$$(Note: The atomic mass of Oxygen ($O$) is$16.00\text{ g/mol}$).

3. Show the Solution

Step 1: Calculate the molar mass of $XO_2$

Step 2: Set up the equation for the atomic mass of $X$ Let $A_x$ be the atomic mass of $X$.

Step 3: Solve for $A_x$

The atomic mass of $X$ is 32. Looking at the periodic table, this corresponds to the element Sulfur ($S$).

4. Identify the Answer

Comparing our result to the given options: A. 20 B. 32 C. 14 D. 12

The correct option is B.

5. Exam Tip

Always remember the "Double Vapour Density" rule: Whenever you see "Vapour Density" in a chemistry problem, immediately multiply it by 2 to get the Molar Mass. It is a common trap in JAMB questions to give you the vapour density when you actually need the molar mass to proceed with your calculations.