A mixture of CH4( g) and C2 H6(g) has a total pressure of 0.53 atm. Just enough O2(g) is added t

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A mixture of CH4( g) and C2 H6(g) has a total pressure of...

A mixture of $\mathrm{CH}_{4}(\mathrm{~g})$ and $\mathrm{C}_{2} \mathrm{H}_{6}(g)$ has a total pressure of $0.53$ atm. Just enough $\mathrm{O}_{2}(g)$ is added to the mixture to bring about its complete combustion to $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g) .$ The total pressure of the two product gases is found to be $2.2 \mathrm{~atm}$. Assuming constant volume and temperature, find the mole fraction of $\mathrm{CH}_{4}$ in the mixture.

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Key Concepts

Partial Pressures in Gas Mixtures

Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the pressures of its individual components. This concept is instrumental in linking the changes in total pressure to the changes in the number of moles of gases before and after a reaction.

Mole Fraction

Mole fraction represents the ratio of the moles of one component to the total moles in a mixture. It is a key concept in calculating the composition of gas mixtures and is used to determine the proportion of individual gases relative to the whole system.

Chemical Stoichiometry of Combustion

Combustion reactions involve balanced equations where a hydrocarbon reacts with oxygen to produce carbon dioxide and water. Establishing the mole ratios from these balanced reactions is essential for determining both the amount of oxygen required for complete combustion and the resultant number of moles of products formed.

Ideal Gas Law

Under constant volume and temperature, the ideal gas law tells us that the pressure of a gas is directly proportional to the number of moles present. This concept is crucial because it allows one to deduce changes in the total moles of gas from changes in pressure during a chemical reaction.

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