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Chapter 5: Problem 56

A sample of air contains only nitrogen and oxygen gases whose partial pressures are 0.80 atm and 0.20 atm, respectively. Calculate the total pressure and the mole fractions of the gases.

Short Answer

Expert verified
The total pressure of the gas mixture is 1.0 atm. The mole fraction of nitrogen is 0.80 and the mole fraction of oxygen is 0.20.

Step by step solution

01

Calculate the total pressure

The total pressure of a gas mixture is the sum of the partial pressures of each individual gas. In this case, the total pressure \( P_{total} \) can be calculated by adding the partial pressure of nitrogen \( P_{N2} \) and the partial pressure of oxygen \( P_{O2} \). So, we have: \[\ P_{total} = P_{N2} + P_{O2} = 0.80\ atm + 0.20\ atm = 1.0\ atm\].
02

Calculate the mole fractions of the gases

In this step, the mole fraction of each gas is calculated. The mole fraction \( X \) of a gas is the ratio of the number of moles of that gas to the total number of moles of all gases in a mixture. Here, since the gases are in a mixture and the total number of moles is not given, we use the ratio of the individual pressure of the gas to the total pressure as the mole fraction. Thus, the mole fraction of nitrogen \( X_{N2} \) is \[\ X_{N2} = \dfrac{P_{N2}}{P_{total}}\ = \dfrac{0.80\ atm}{1.00\ atm} = 0.80\] And the mole fraction of oxygen \( X_{O2} \) is \[\ X_{O2} = \dfrac{P_{O2}}{P_{total}}\ = \dfrac{0.20\ atm}{1.00\ atm} = 0.20\].

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