Ch 18: Thermal Properties of Matter

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 18: Thermal Properties of Matter

문제 23b

18장, 문제 23b

Modern vacuum pumps make it easy to attain pressures of the order of $10^{-13}$ 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 $1.00$ atm instead?

검증된 단계별 안내

Start by recalling the ideal gas law, which is given by the equation:

P V = n R T

, 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 = \frac{P V}{R T}

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 \times 10^{23}

molecules/mol. Multiply the moles by Avogadro's number to find the total number of molecules.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.