When of a gaseous mixture containing only ethane () and propane () is burnt completely in an excess — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
When $2.96\text{ g}$ of a gaseous mixture containing only ethane ($C_2H_6$) and propane ($C_3H_8$) is burnt completely in an excess of $O_2$ gas, exactly $8.8\text{ g}$ of $CO_2$ and $5.04\text{ g}$ of $H_2O$ vapours are formed. Which of the following statements accurately describe the initial mixture?
💡 Solution & Explanation
Let moles of $C_2H_6 = a$, moles of $C_3H_8 = b$. Total mass = $30a + 44b = 2.96$. (Eq 1) Moles of $CO_2$ produced = $2a + 3b = 8.8 / 44 = 0.2$. (Eq 2) Solve equations: multiply Eq 2 by 15: $30a + 45b = 3.0$. Subtract Eq 1: $b = 0.04\text{ moles}$. Substitute $b=0.04$ into Eq 2: $2a + 0.12 = 0.2 \implies 2a = 0.08 \implies a = 0.04\text{ moles}$. Thus, $a = b = 0.04\text{ moles}$ (Statement A and D are true, B is false since masses are $1.2\text{ g}$ and $1.76\text{ g}$). Total C moles = $0.2$, mass = $2.4\text{ g}$. Total H moles = $(6 \times 0.04) + (8 \times 0.04) = 0.56\text{ moles}$, mass = $0.56\text{ g}$. C:H mass ratio = $2.4 / 0.56 = 240 / 56 = 30 / 7$ (Statement C is true).