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Ch 18: Thermal Properties of Matter
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 18: Thermal Properties of MatterProblem 23b
Chapter 18, Problem 23b

Modern vacuum pumps make it easy to attain pressures of the order of 10−1310^{-13} atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. How many molecules would be present at the same temperature but at 1.001.00 atm instead?

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1
Start by recalling the ideal gas law, which is given by the equation: PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
To find the number of molecules, we need to determine the number of moles first. Rearrange the ideal gas law to solve for n: n=PVRT.
Assume the volume V and temperature T remain constant. Substitute P with 1.00 atm, and use the ideal gas constant R in appropriate units (e.g., 0.0821 L atm/mol K).
Calculate the number of moles n using the rearranged equation. This will give you the moles of gas at 1.00 atm.
Finally, convert the number of moles to molecules using Avogadro's number, which is approximately 6.022×1023 molecules/mol. Multiply the moles by Avogadro's number to find the total number of molecules.

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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 is a fundamental equation in physics that relates the pressure, volume, and temperature of an ideal gas with the number of molecules. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. This law helps in calculating the number of molecules when conditions such as pressure change.
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Mole Concept

The mole concept is essential for quantifying the amount of substance in chemistry and physics. One mole corresponds to Avogadro's number, approximately 6.022 x 10^23 molecules. Understanding this concept allows us to convert between the number of molecules and moles, which is crucial when using the Ideal Gas Law to find the number of molecules at different pressures.
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Pressure

Pressure is the force exerted by gas molecules per unit area on the walls of a container. It is measured in units such as atmospheres (atm). In the context of the question, understanding how pressure changes affect the number of molecules in a given volume is key, as the pressure is directly proportional to the number of molecules in the Ideal Gas Law.
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Related Practice
Textbook Question

Modern vacuum pumps make it easy to attain pressures of the order of 10−1310^{-13} atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. At a pressure of 9.00×10−149.00\(\times\)10^{-14} atm and an ordinary temperature of 300.0300.0 K, how many molecules are present in a volume of 1.001.00 cm3?

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Textbook Question

What is the total translational kinetic energy of the air in an empty room that has dimensions 8.008.00 m×12.00\(\times\)12.00 m×4.00\(\times\)4.00 m if the air is treated as an ideal gas at 1.001.00 atm?

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Textbook Question

A large organic molecule has a mass of 1.41×10−211.41\(\times\)10^{-21} kg. What is the molar mass of this compound?

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Textbook Question

How many moles are in a 1.001.00-kg bottle of water? How many molecules? The molar mass of water is 18.018.0 g/mol.

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Textbook Question

Consider an ideal gas at 2727°C and 1.001.00 atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. What is the length of an edge of each cube if adjacent cubes touch but do not overlap?

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Textbook Question

In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 7×1097\(\times\)10^9 people)?