To solve the problem of determining the total volume of the residual gases after the reaction between hydrogen and oxygen, we need to follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understand the Reaction The reaction between hydrogen (H₂) and oxygen (O₂) can be represented by the balanced chemical equation: \[ 2H_2 + O_2 \rightarrow 2H_2O \] This equation tells us that 2 volumes of hydrogen react with 1 volume of oxygen to produce water vapor. ### Step 2: Identify the Initial Volumes From the problem, we have: - Volume of hydrogen (H₂) = \(50 \, cm^3\) - Volume of oxygen (O₂) = \(20 \, cm^3\) ### Step 3: Determine the Stoichiometry of the Reaction According to the balanced equation: - 2 volumes of H₂ react with 1 volume of O₂. - Therefore, for every 2 volumes of H₂, we need 1 volume of O₂. ### Step 4: Calculate the Required Volumes To find out how much of each gas will react, we can set up a ratio based on the stoichiometry: - For \(50 \, cm^3\) of H₂, the amount of O₂ required is: \[ \text{Required O}_2 = \frac{50 \, cm^3}{2} = 25 \, cm^3 \] ### Step 5: Compare Available O₂ with Required O₂ We have \(20 \, cm^3\) of O₂ available, but we need \(25 \, cm^3\) to completely react with \(50 \, cm^3\) of H₂. This means that O₂ is the limiting reactant because we do not have enough O₂ to react with all the H₂. ### Step 6: Calculate the Amount of H₂ that Reacts Since we only have \(20 \, cm^3\) of O₂, we can calculate how much H₂ will react with this amount of O₂: - According to the stoichiometry, \(1 \, cm^3\) of O₂ reacts with \(2 \, cm^3\) of H₂. Therefore, \(20 \, cm^3\) of O₂ will react with: \[ \text{Reacting H}_2 = 20 \, cm^3 \times 2 = 40 \, cm^3 \] ### Step 7: Determine the Residual Gases Now we can find out how much of each gas remains after the reaction: - Initial H₂ = \(50 \, cm^3\) - H₂ that reacted = \(40 \, cm^3\) - Residual H₂ = \(50 \, cm^3 - 40 \, cm^3 = 10 \, cm^3\) - Initial O₂ = \(20 \, cm^3\) - O₂ that reacted = \(20 \, cm^3\) - Residual O₂ = \(20 \, cm^3 - 20 \, cm^3 = 0 \, cm^3\) ### Step 8: Calculate Total Volume of Residual Gases The total volume of the residual gases is the sum of the remaining volumes of H₂ and O₂: \[ \text{Total residual volume} = \text{Residual H}_2 + \text{Residual O}_2 = 10 \, cm^3 + 0 \, cm^3 = 10 \, cm^3 \] ### Conclusion The total volume of the residual gases after the reaction is \(10 \, cm^3\). Therefore, the correct answer is: **B. 10 cm³** ### Explanation of Other Options - **A. 50 cm³**: This option assumes that no reaction occurred, which is incorrect because the gases do react. - **C. 40 cm³**: This option incorrectly assumes that all of the H₂ remains unreacted, which is not the case. - **D. 30 cm³**: This option does not account for the correct stoichiometry of the reaction and miscalculates the residual gases. ### Revision Summary - The reaction between H₂ and O₂ produces water vapor in a 2:1 volume ratio. - O₂ is the limiting reactant in this scenario. - After the reaction, \(10 \, cm^3\) of H₂ remains unreacted, and all O₂ is consumed. - The total volume of residual gases is \(10 \, cm^3\).