Ch.6 - Gases

Problem 73

Chapter 6, Problem 73

A gas mixture contains 1.05 g N2 and 1.35 g O2 in a 1.35-L container at 15°C. Calculate the mole fraction and partial pressure of each component in the gas mixture.

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Convert the mass of each gas to moles using their molar masses: \( \text{N}_2 \) has a molar mass of 28.02 g/mol and \( \text{O}_2 \) has a molar mass of 32.00 g/mol.

Calculate the total number of moles in the gas mixture by adding the moles of \( \text{N}_2 \) and \( \text{O}_2 \).

Determine the mole fraction of each gas by dividing the moles of each gas by the total moles of the gas mixture.

Use the ideal gas law \( PV = nRT \) to calculate the total pressure of the gas mixture, where \( R = 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \) and temperature \( T \) is in Kelvin.

Calculate the partial pressure of each gas by multiplying its mole fraction by the total pressure.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mole Fraction

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 component by the total number of moles of all components in the mixture. This dimensionless quantity helps in understanding the composition of the gas mixture and is crucial for calculating partial pressures.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the partial pressures of gases in a mixture, as it allows us to determine how the gases behave under specific conditions. Understanding this relationship is key to solving problems involving gas mixtures.

Partial Pressure

Partial pressure is the pressure that a single component of a gas mixture would exert if it occupied the entire volume alone at the same temperature. It can be calculated using the mole fraction of the component and the total pressure of the gas mixture. This concept is vital for analyzing the behavior of individual gases within a mixture and is directly linked to the Ideal Gas Law.

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Textbook Question

A gas mixture with a total pressure of 745 mmHg contains each of the following gases at the indicated partial pressures: CO2, 112 mmHg; Ar, 225 mmHg; and O2, 114 mmHg. The mixture also contains helium gas. What is the partial pressure of the helium gas? What mass of helium gas is present in a 12.0-L sample of this mixture at 273 K?

Textbook Question

A 1.20-g sample of dry ice is added to a 755 mL flask containing nitrogen gas at a temperature of 25.0 °C and a pressure of 725 mmHg. The dry ice sublimes (converts from solid to gas), and the mixture returns to 25.0 °C. What is the total pressure in the flask?

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Textbook Question

A 275-mL flask contains pure helium at a pressure of 752 torr. A second flask with a volume of 475 mL contains pure argon at a pressure of 722 torr. If we connect the two flasks through a stopcock and we open the stopcock, what is the partial pressure of argon?

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Textbook Question

What is the mole fraction of oxygen gas in air (see Table 6.3)? What volume of air contains 20.0 g of oxygen gas at 273 K and 1.00 atm?

Textbook Question

The hydrogen gas formed in a chemical reaction is collected over water at 30.0 °C at a total pressure of 732 mmHg. What is the partial pressure of the hydrogen gas collected in this way? If the total volume of gas collected is 722 mL, what mass of hydrogen gas is collected?

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