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If 20 cc of methane in burnt using 50 cc...

If 20 cc of methane in burnt using 50 cc of oxygen, the volume of the gases left after cooling to room temperature is

A

60 cc

B

70 cc

C

30 cc

D

50 cc

Text Solution

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The correct Answer is:
To solve the problem of determining the volume of gases left after burning 20 cc of methane with 50 cc of oxygen, we can follow these steps: ### Step 1: Write the balanced chemical equation for the combustion of methane. The combustion of methane (CH₄) in the presence of oxygen (O₂) can be represented by the following balanced equation: \[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \] ### Step 2: Determine the stoichiometry of the reaction. From the balanced equation, we see that: - 1 volume of methane (CH₄) reacts with 2 volumes of oxygen (O₂). - This means that for every 1 volume of CH₄, 2 volumes of O₂ are required to completely combust it. ### Step 3: Calculate the amount of oxygen required for 20 cc of methane. Given that we have 20 cc of methane, we can calculate the required amount of oxygen: - Required oxygen = 2 × 20 cc = 40 cc ### Step 4: Compare the available oxygen with the required oxygen. We have 50 cc of oxygen available, but only 40 cc is needed to completely react with 20 cc of methane. Therefore, there will be some excess oxygen left after the reaction. ### Step 5: Calculate the volume of oxygen left after the reaction. - Oxygen used = 40 cc (to react with 20 cc of methane) - Oxygen available = 50 cc - Oxygen left = 50 cc - 40 cc = 10 cc ### Step 6: Determine the volume of gases after the reaction. After the combustion, the products are carbon dioxide (CO₂) and water (H₂O). However, water will condense into liquid form at room temperature, so it does not contribute to the gas volume. The volume of gas left after the reaction will be the volume of carbon dioxide produced plus any excess oxygen left: - Volume of carbon dioxide produced = 20 cc (from the balanced equation, 1 volume of CH₄ produces 1 volume of CO₂) - Volume of excess oxygen left = 10 cc ### Step 7: Calculate the total volume of gases left. Total volume of gases left = Volume of CO₂ + Volume of excess O₂ \[ \text{Total volume} = 20 \text{ cc} + 10 \text{ cc} = 30 \text{ cc} \] ### Conclusion The volume of gases left after cooling to room temperature is **30 cc**.
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