10cm^3 of aa hydrocarbon was completely combusted in 200cm^3 of O2. It was found that there was 20cm^3 of O2 remaining and the volume of CO2 produced was 120cm^3. Determine the formula of the hydrocarbon.
To determine the formula of the hydrocarbon, we need to use the principles of stoichiometry and the concept of the ideal gas law.
1. Start by calculating the volume of gas consumed during combustion:
Initial volume of O2 - Remaining volume of O2 = Volume of O2 consumed
200 cm^3 - 20 cm^3 = 180 cm^3 of O2 consumed
2. Use stoichiometry to relate the volume of O2 consumed to the volume of CO2 produced. Based on the balanced chemical equation for the complete combustion of a hydrocarbon, we know that 1 mole of hydrocarbon consumes 5 moles of O2 and produces 4 moles of CO2.
Moles of O2 consumed = Volume of O2 consumed / Molar volume of O2
Moles of CO2 produced = Volume of CO2 produced / Molar volume of CO2
3. Based on the given volumes, we can calculate the moles of O2 consumed and the moles of CO2 produced:
Moles of O2 consumed = 180 cm^3 / 22.7 L/mol = 7.92 × 10^-3 mol
Moles of CO2 produced = 120 cm^3 / 22.4 L/mol = 5.36 × 10^-3 mol
4. Now, let's determine the ratio of moles of O2 consumed to moles of hydrocarbon combusted. Since we know that 1 mole of hydrocarbon consumes 5 moles of O2, we can set up the following proportion:
5 moles of O2 / 1 mole of hydrocarbon = 7.92 × 10^-3 mol / x moles of hydrocarbon
Solving for "x," we find that x ≈ 1.584 × 10^-3 mol of hydrocarbon.
5. Finally, to determine the formula of the hydrocarbon, we need to find the empirical formula. The empirical formula represents the simplest, most reduced ratio of atoms present in a compound. Since we know the ratio of moles of carbon and oxygen in carbon dioxide is 1:2, we can deduce that the empirical formula of the hydrocarbon is C1H2.
Therefore, the formula of the hydrocarbon is CH2.