\(V_{1} \mathrm{ml}\) of unknown gas (A) \(+V_{2} \mathrm{ml}\) of \(\mathrm{O}_{2}\) \(\rightarrow\left(V_{1}+V_{2}\right) \mathrm{ml}\) of \(\mathrm{CO}_{2} .\) Gas 'A' may be (a) \(\mathrm{CO}\) (b) \(\left(\mathrm{CO}+\mathrm{CO}_{2}\right)\) in equal proportion (c) \(\mathrm{C}_{12} \mathrm{O}_{9}\) (d) \(\mathrm{C}_{3} \mathrm{O}_{2}\)

We will analyze the given options for the unknown gas and write down the possible balanced chemical equations for each option. (a) If gas A is CO, the balanced equation is: \(\mathrm{2CO} + \mathrm{O}_{2} \rightarrow \mathrm{2CO}_{2}\) (b) If gas A is a mixture of equal parts CO and CO2, then the balanced equation for the CO part is: \(\mathrm{2CO} + \mathrm{O}_{2} \rightarrow \mathrm{ 2CO}_{2}\). However, CO2 does not react with O2, so there will be no additional reaction in this case. (c) If gas A is C12O9, the balanced equation is: \(\mathrm{4C}_{12} \mathrm{O}_{9} + \mathrm{15O}_{2} \rightarrow \mathrm{24CO}_{2}\) (d) If gas A is C3O2, the balanced equation is: \(\mathrm{2C}_{3} \mathrm{O}_{2} + \mathrm{3O}_{2} \rightarrow \mathrm{6CO}_{2}\)

We will now calculate the relationship between the initial volume and the final volume for each option. (a) For CO: When 2 moles of CO react with 1 mole of O2, they produce 2 moles of CO2. So the initial volume is V1 (CO) + V2 (O2) and the final volume is 2 * V1 (since 2 moles of CO2 are produced for each mole of CO reacted). The final volume, as given in the problem, is (V1 + V2). To satisfy this condition, we find that V1 = V2. (b) For the CO+CO2 mixture: When 2 moles of CO react with 1 mole of O2, they produce 2 moles of CO2. CO2 does not react with O2, so it does not contribute to the volume change. In this case, the final volume should be less than (V1 + V2) since some CO2 does not participate in the reaction. This option does not satisfy the problem conditions. (c) For C12O9: The reaction produces 24 moles of CO2 from a combination of 4 moles of C12O9 and 15 moles of O2. The relationship between initial and final volumes is not satisfied in this option, as it does not match V1 + V2. (d) For C3O2: The reaction produces 6 moles of CO2 from a combination of 2 moles of C3O2 and 3 moles of O2. Here, the initial volume is V1 (C3O2) + V2 (O2), and the final volume is 6 * V1/2 (since 6 moles of CO2 are produced for every 2 moles of C3O2 reacted). This leads to the final volume being 3 * V1, which does not satisfy the problem conditions.

According to the analysis in steps 1 and 2, option (a) is the correct answer. The unknown gas A must be CO as it is the only option that satisfies the relationship between initial and final volumes given in the problem statement.