Final answer:
The volume of CH4 in the mixture is 25 L, as calculated by analyzing the stoichiometry of the combustion reaction and considering the total volumes of the initial mixture and final CO2.
Step-by-step explanation:
To calculate the volume of CH4 in the mixture, we can use stoichiometry. When CH4 burns, it reacts with O2 to produce CO2 and H2O. The balanced chemical equation is:
CH4 + 2O2 → CO2 + 2H2O
From this equation, we see that 1 volume of CH4 produces 1 volume of CO2. If the combustion of the mixture resulted in 80 L of CO2, knowing that CO2 could have also come from the initial CO2 in the mixture, we can conclude that the CH4 volume must be less than or equal to 80 L. Since the initial mixture was 50 L and completely turned into CO2, we have:
- Total initial volume of gases = CH4 volume + CO2 volume = 50 L
- Total volume of CO2 after combustion = 80 L
- Thus, the CH4 volume must be the increase in CO2 volume after combustion, which is 80 L - initial CO2 volume.
If we let x be the initial volume of CH4, then initial CO2 volume is (50 L - x).
Therefore, x = 80 L - (50 L - x) => x = 80 L - 50 L + x => x = 30 L.
Since the initial mixture cannot have more CH4 than the total mixture volume, the only option that is less than 30 L but also satisfies the condition is D) 25 L.