Ch.5 - Gases

Problem 49

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Chapter 5, Problem 49

Which gas sample has the greatest pressure? Assume that all the samples are at the same temperature. Explain.

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Identify that pressure is directly related to the number of gas particles in a given volume, according to the ideal gas law (PV = nRT).

Observe the four flasks labeled a, b, c, and d, and note the number of gas particles in each flask.

Compare the density of gas particles in each flask visually.

Determine that the flask with the highest density of gas particles will have the greatest pressure, assuming all other conditions (temperature and volume) are constant.

Conclude which flask has the greatest pressure based on the visual comparison of particle density.

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Key Concepts

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

Gas Pressure

Gas pressure is defined as the force exerted by gas particles colliding with the walls of their container. It is influenced by the number of particles, their speed, and the volume of the container. According to the ideal gas law, pressure increases with more gas particles in a given volume, assuming temperature remains constant.

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry represented as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. This law helps predict the behavior of gases under various conditions and indicates that at constant temperature, pressure is directly proportional to the number of gas particles.

Density of Gas

The density of a gas is defined as its mass per unit volume. In the context of gas samples, a higher density often indicates a greater number of gas particles in a given volume, which can lead to higher pressure. When comparing gas samples at the same temperature, the sample with the highest density will typically exert the greatest pressure.

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Related Practice

A 1.0-L container of liquid nitrogen is kept in a closet measuring 1.0 m by 1.0 m by 2.0 m. Assuming that the container is completely full, that the temperature is 25.0 °C, and that the atmospheric pressure is 1.0 atm, calculate the percent (by volume) of air that is displaced if all of the liquid nitrogen evaporates. (Liquid nitrogen has a density of 0.807 g/mL.)

A wine-dispensing system uses argon canisters to pressurize and preserve wine in the bottle. An argon canister for the system has a volume of 55.0 mL and contains 26.0 g of argon. When the argon is released from the canister, it expands to fill the wine bottle. How many 750.0-mL wine bottles can be purged with the argon in the canister at a pressure of 1.20 atm and a temperature of 295 K? Assuming ideal gas behavior, what is the pressure in the canister at 295 K?

Open Question

Cyclists sometimes use pressurized carbon dioxide inflators to inflate a bicycle tire in the event of a flat. These inflators use metal cartridges that contain 16.0 g of carbon dioxide. At 298 K, to what pressure (in psi) can the carbon dioxide in the cartridge inflate a 3.45-L mountain bike tire? (Note: Assume that atmospheric pressure is 14.7 psi; the gauge pressure is the total pressure minus the atmospheric pressure.)

Textbook Question

This picture represents a sample of gas at a pressure of 1 atm, a volume of 1 L, and a temperature of 25 °C. Draw a similar picture showing what would happen to the sample if the volume were reduced to 0.5 L and the temperature were increased to 250 °C. What would happen to the pressure?

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Textbook Question

Aerosol cans carry clear warnings against incineration because of the high pressures that can develop upon heating. Suppose that a can contains a residual amount of gas at a pressure of 755 mmHg and a temperature of 25 °C. What would the pressure be if the can were heated to 1155 °C?

A sample of nitrogen gas in a 1.75-L container exerts a pressure of 1.35 atm at 25 °C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 355 °C?

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