# Ideal Gas (PV=nRT)

### Upon studying this section, you should be familiar with the following:

• Why (and when) we can use the ideal gas equation of state
• How to readily rearrange the ideal gas equation to find unknown properties of an ideal gas
• Temperature, pressure, volume, moles, mass, and density.
• what is mean by the specific molar volume and the standard molar volume of a gas

## Real and Ideal Gases

Explantion:

A Real Gas
Real, actual gases have attractions between themselves. That is, when one molecule zooms by another gas molecule in midair, they tend to attract or repel each other. Equations (called equations of state) that relate the properties (such as pressure, temperature and volume) of real gases are complex in order to take into account the unique attraction effects of individual molecules.

An Ideal Gas
If we let the volume that the gas fills go to infinity, that is, put the gas in an infinately big box, there are no longer attractive forces between the gas molecules because there is so much space between the individual gas molecules. The equation of state that describes a gas in this idealized situation is called the ideal gas equation of state. For us, the ideal gas equation of state gives a good approximation of gas properties near standard conditions (room temperature and pressure).

This table lists the ideal gas equation of state, along with subsequent relations that are just rearrangements of the equation.

Standard Form PV = nRT Vs = 22.4 m3

Example 1

A 100 grams of nitrogen gas (an ideal gas) is stored in a container at 23.0°C and 3.00 psig. What is the density and volume of the gas?

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Example 2

Ten cubic feet of air at 70°F and 1.00 atm is heated to 610°F and compressed to 2.50 atm. What volume does the gas occupy in its final state?

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