Consider a homogeneous gaseous mixture containing exclusively oxygen () and ozone (). If the measure — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
Consider a homogeneous gaseous mixture containing exclusively oxygen ($O_2$) and ozone ($O_3$). If the measured vapour density of this mixture is exactly $18.4$, which of the following statements describe the system accurately?
💡 Solution & Explanation
Step 1: Average Molar Mass = $2 \times V.D. = 2 \times 18.4 = 36.8\text{ g/mol}$ (Option A is true). Step 2: Let mole fraction of $O_2$ be $x$. Then $O_3$ is $(1-x)$. $M_{\text{avg}} = 32x + 48(1-x) = 36.8 \implies 32x + 48 - 48x = 36.8 \implies 16x = 11.2 \implies x = 0.7$. So mole fraction of $O_2 = 0.70$ (Option B is true). Step 3: Volume % is identical to mole % for ideal gases. Mole % of $O_3 = (1 - 0.7) \times 100 = 30\%$, so Volume % = $30\%$ (Option C is true). Step 4: Mass fraction of $O_2$ = $\frac{\text{Mass of } O_2}{\text{Total Mass}} = \frac{0.7 \times 32}{36.8} = \frac{22.4}{36.8} = 0.6086 \approx 60.8\%$ (Option D is true).