A pure gas that is hydrogen and carbon by mass has an absolute density of measured at and pressure. — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
A pure gas that is $14.3\%$ hydrogen and $85.7\%$ carbon by mass has an absolute density of $2.5\text{ g/L}$ measured at $0^\circ\text{C}$ and $1\text{ atm}$ pressure. What is the true molecular formula of the gas?
💡 Solution & Explanation
Step 1: Find the empirical formula from mass percentages. Moles of C = $85.7 / 12 = 7.14$. Moles of H = $14.3 / 1 = 14.3$. Ratio C:H is $1:2$. The empirical formula is $CH_2$ (Mass = $14\text{ g/mol}$). Step 2: Find the molar mass using density. Molar volume at $0^\circ\text{C}$ and $1\text{ atm}$ (STP) is approximately $22.4\text{ L/mol}$. Molar Mass = Density $\times$ Molar Volume = $2.5\text{ g/L} \times 22.4\text{ L/mol} = 56\text{ g/mol}$. Step 3: Find the n-factor. $n = 56 / 14 = 4$. Molecular formula = $(CH_2)_4 = C_4H_8$.