Natural gas is a mixture of many substances, primarily CH4, C2H6, C3Hg, and C4H10. Assuming that the total pressure of the gases is 1.48 atm and that their mole ratio is 94:4.0:1.5:0.50, calculate the partial pressure in atmospheres of each gas.
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Identify the gases in the mixture: CH4, C2H6, C3Hg, and C4H10.
Note the total pressure of the gas mixture: 1.48 atm.
Understand the mole ratio of the gases: CH4:C2H6:C3Hg:C4H10 = 94:4.0:1.5:0.50.
Calculate the total number of moles in the ratio: 94 + 4.0 + 1.5 + 0.50.
Use the formula for partial pressure: P_i = (n_i / n_total) * P_total, where P_i is the partial pressure of gas i, n_i is the mole ratio of gas i, n_total is the total mole ratio, and P_total is the total pressure.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Dalton's Law of Partial Pressures
Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. Each gas's partial pressure is proportional to its mole fraction in the mixture. This principle is essential for calculating the contribution of each gas to the total pressure.
The mole fraction is a way of expressing the concentration of a component in a mixture. It is calculated by dividing the number of moles of a specific gas by the total number of moles of all gases in the mixture. Understanding mole fractions is crucial for determining the partial pressures of each gas using Dalton's Law.
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. While this question focuses on partial pressures, the Ideal Gas Law provides a foundational understanding of gas behavior under various conditions, which can be useful in broader applications of gas mixtures.
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