The best laboratory vacuum has a pressure of about 1.00 ×10^-18 atm, or 1.01 ×10^-13 Pa . How ma

step 1 So in the given vacuum that we are looking at, the pressure is 1 times 10 par minus 18 atmospher

The best laboratory vacuum has a pressure of about 1.00...

The best laboratory vacuum has a pressure of about $1.00 \times$ $10^{-18}$ atm, or $1.01 \times 10^{-13} \mathrm{Pa}$ . How many gas molecules are there
per cubic centimeter in such a vacuum at 293 $\mathrm{K} ?$

Key Concepts

Ideal Gas Law

The ideal gas law is a fundamental principle that relates the pressure, volume, temperature, and number of particles (or moles) of a gas. It is usually expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. This law provides a framework for calculating any one of these variables when the others are known, making it essential for determining the molecular density in gases under various conditions.

Avogadro's Number

Avogadro's number is a fundamental constant that represents the number of constituent particles, usually atoms or molecules, in one mole of a substance. It is approximately 6.022 x 10^23 particles per mole. This constant is crucial for converting between the number of moles derived from the ideal gas law and the actual count of individual gas molecules in a given volume.

Unit Conversions in Gas Problems

Accurate problem solving in gas dynamics often requires converting between different units of pressure, volume, and temperature to maintain consistency. For instance, pressure might be given in atmospheres, Pascals, or torr, and volumes might need to be converted from cubic centimeters to liters or cubic meters. Mastering these conversions is vital for correctly applying the ideal gas law and other gas-related calculations.

Molecular Density

Molecular density refers to the number of gas molecules contained within a specific volume. In the context of vacuum physics and gas dynamics, determining the molecular density involves using the ideal gas law to find the mole number per unit volume and then converting that to the number of molecules using Avogadro's number. This concept is essential for understanding how sparsely gas molecules can be distributed in a high-vacuum environment.

Transcript

Please give Ace some feedback