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Ch.5 - Gases
Chapter 5, Problem 118

A quantity of N2 occupies a volume of 1.0 L at 300 K and 1.0 atm. The gas expands to a volume of 3.0 L as the result of a change in both temperature and pressure. Find the density of the gas at these new conditions.

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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 fundamental for understanding gas behavior under varying conditions and allows for the calculation of one variable when the others are known.
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Density of a Gas

Density is defined as mass per unit volume. For gases, density can be calculated using the formula ρ = PM/RT, where ρ is density, P is pressure, M is molar mass, R is the ideal gas constant, and T is temperature. Understanding this relationship is crucial for determining the density of gases under different conditions.
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Gas Density Example

Changes in State Variables

When a gas undergoes changes in volume, temperature, or pressure, its state variables are interrelated. Understanding how these variables affect each other is essential for solving problems involving gas expansion or compression, as it allows for the application of the Ideal Gas Law to find unknown quantities.
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Related Practice
Textbook Question

A scuba diver creates a spherical bubble with a radius of 2.5 cm at a depth of 30.0 m where the total pressure (including atmospheric pressure) is 4.00 atm. What is the radius of the bubble when it reaches the surface of the water? (Assume that the atmospheric pressure is 1.00 atm and the temperature is 298 K.)

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Open Question
A particular balloon can be stretched to a maximum surface area of 1257 cm². The balloon is filled with 3.0 L of helium gas at a pressure of 755 torr and a temperature of 298 K. The balloon is then allowed to rise in the atmosphere. If the atmospheric temperature is 273 K, what pressure will the balloon burst at? (Assume the balloon is the shape of a sphere.)
Textbook Question

A catalytic converter in an automobile uses a palladium or platinum catalyst (a substance that increases the rate of a reaction without being consumed by the reaction) to convert carbon monoxide gas to carbon dioxide according to the reaction: 2 CO(g) + O2(g) → 2 CO2(g) A chemist researching the effectiveness of a new catalyst combines a 2.0:1.0 mole ratio mixture of carbon monoxide and oxygen gas (respectively) over the catalyst in a 2.45-L flask at a total pressure of 745 torr and a temperature of 552 °C. When the reaction is complete, the pressure in the flask has dropped to 552 torr. What percentage of the carbon monoxide was converted to carbon dioxide?

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Textbook Question

A mixture of CO(g) and O2(g) in a 1.0-L container at 1.0×103 K has a total pressure of 2.2 atm. After some time, the total pressure falls to 1.9 atm as the result of the formation of CO2. Determine the mass (in grams) of CO2 that forms.

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Textbook Question

The radius of a xenon atom is 1.3×10– 8 cm. A 100-mL flask is filled with Xe at a pressure of 1.0 atm and a temperature of 273 K. Calculate the fraction of the volume that is occupied by Xe atoms. (Hint: The atoms are spheres.)

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Open Question
Determine the temperature on the second day, assuming that the pressure and amount of gas in a natural gas storage tank have not changed, where the tank is a cylinder with a moveable top and a fixed radius. The height of the cylinder is 22.6 m at 22 °C, and the next day the height increases to 23.8 m due to a heat wave.