This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the moles of carbon dioxide (CO_2) produced. At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 dm^3. Given volume of CO_2 = 89.6 dm^3. n_CO_2 = Volume of CO_2Molar volume at STP n_CO_2 = 89.6 dm^322.4 dm^3/mol = 4 mol Step 2: Calculate the moles of water (H_2O) produced. The molar mass of H_2O is 2 × 1.008 g/mol (H) + 16.00 g/mol (O) = 18.016 g/mol ≈ 18 g/mol. Given mass of H_2O = 54 g. n_H_2O = Mass of H_2OMolar mass of H_2O n_H_2O = 54 g18 g/mol = 3 mol Step 3: Determine the moles of carbon (C) and hydrogen (H) atoms in the hydrocarbon. From the complete combustion of a hydrocarbon, all carbon atoms form CO_2 and all hydrogen atoms form H_2O. Each mole of CO_2 contains 1 mole of C atoms. Moles of C atoms = n_CO_2 = 4 mol Each mole of H_2O contains 2 moles of H atoms. Moles of H atoms = 2 × n_H_2O = 2 × 3 mol = 6 mol Step 4: Determine the molecular formula of the hydrocarbon. The ratio of carbon atoms to hydrogen atoms in the hydrocarbon is 4:6. This simplifies to 2:3. So, the empirical formula is C_2H_3. Let the general formula of the hydrocarbon be C_xH_y. From the moles of C and H atoms, we have x=4 and y=6. Therefore, the molecular formula of the hydrocarbon is C_4H_6. Step 5: Classify the hydrocarbon. The general formula for alkanes is C_nH_2n+2. For n=4, this would be C_4H_10. The general formula for alkenes is C_nH_2n. For n=4, this would be C_4H_8. The general formula for alkynes or dienes is C_nH_2n-2. For n=4, this would be C_4H_2(4)-2 = C_4H_6. Thus, the hydrocarbon is an alkyne or a diene. The final answer is C_4H_6.