Ch.10 - Gases

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.10 - Gases

Problem 69

Chapter 10, Problem 69

A rigid vessel containing a 3:1 mol ratio of carbon dioxide and water vapor is held at 200°C where it has a total pressure of 2.00 atm. If the vessel is cooled to 10°C so that all of the water vapor condenses, what is the pressure of carbon dioxide? Neglect the volume of the liquid water that forms on cooling.

Verified step by step guidance

Identify the initial conditions: The vessel contains a 3:1 mol ratio of CO₂ to H₂O vapor at 200°C with a total pressure of 2.00 atm.

Use the ideal gas law to express the initial partial pressures: Let P_CO2 and P_H2O be the partial pressures of CO₂ and H₂O, respectively. Since the mol ratio is 3:1, P_CO2 = 3x and P_H2O = x, where 3x + x = 2.00 atm.

Solve for x to find the initial partial pressures: 4x = 2.00 atm, so x = 0.50 atm. Therefore, P_CO2 = 1.50 atm and P_H2O = 0.50 atm.

Consider the cooling process: When the vessel is cooled to 10°C, all the water vapor condenses, meaning P_H2O becomes 0 atm.

Determine the final pressure of CO₂: Since the volume of the vessel is constant and the temperature changes, use the ideal gas law to find the new pressure of CO₂ at 10°C, considering only the CO₂ gas remains.

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Key Concepts

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

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 understanding how gases behave under varying conditions of temperature and pressure, particularly in rigid vessels where volume remains constant.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of its individual components. This concept is crucial for determining the pressure of carbon dioxide after the water vapor condenses.

Phase Changes and Vapor Pressure

Phase changes, such as the condensation of water vapor, occur when a substance transitions between solid, liquid, and gas states. The vapor pressure of a liquid at a given temperature indicates the pressure exerted by its vapor in equilibrium with its liquid. Understanding this helps in calculating the remaining pressure of carbon dioxide after the water vapor has condensed.

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Textbook Question

A sample of 5.00 mL of diethyl ether (C2H5OC2H5,density=0.7134 g/mL) is introduced into a 6.00-L vessel that already contains a mixture of N2 and O2, whose partial pressures are 𝑃N2=0.751atm and 𝑃O2=0.208atm. The temperature is held at 35.0°C, and the diethyl ether totally evaporates. b. Calculate the total pressure in the container.

Textbook Question

At an underwater depth of 250 ft, the pressure is 8.38 atm. What should the mole percent of oxygen be in the diving gas for the partial pressure of oxygen in the mixture to be 0.21 atm, the same as in air at 1 atm?

Textbook Question

(a) What are the mole fractions of H₂ in a mixture of 15.08 g of O₂, 8.17 g of N₂, and 2.64 g of H₂?

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Textbook Question

The atmospheric concentration of CO2 gas is presently 407 ppm (parts per million, by volume; that is, 407 L of every 106 L of the atmosphere are CO2). What is the mole fraction of CO2 in the atmosphere?.

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Textbook Question

(a) What are the mole fractions of N₂ in a mixture of 15.08 g of O₂, 8.17 g of N₂, and 2.64 g of H₂?

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Textbook Question

A piece of dry ice (solid carbon dioxide) with a mass of 5.50 g is placed in a 10.0-L vessel that already contains air at 705 torr and 24°C. After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant CO2 gas, and the total pressure in the container, at 24°C?