# Ideal Gas

Recall our constant-volume gas thermometer:

Under a wide range of conditions -- for various gasses -- we found the same temperature measured by different gasses. A gas for which this is exactly true is called an ideal gas. These ideas can be summarized in the Ideal Gas Law:

# P V = n R T

where P is the pressure, V is the volume, n is the number of moles, R is the "universal gas constant" and depends upon the units used, and T is the absolute temperature.

A mole of anything is Avagadro's number of those things; NA = 6.022 x 1023

The number of moles, n, of a substance (like a gas) is given by

## n = m / M

where m is the mass of the substance and M is its molar mass.

If we measure pressure in pascals (1 Pa = 1 N/m2) and volume in m3 -- regular, standard SI units -- then the universal gas constant is

## R = 8.315 J / mole-K

It is also common to measure pressure in atmospheres and volume in liters. With these units, the universal gas constant is

## R = 0.082 L-atm / mol-K

It is sometimes useful to describe a system in terms of the actual number of molecules present, N. The number of moles n, then is

n = N / NA

so that the ideal gas law becomes

# PV = N kB T

where

## kB = R / NA

is known as Boltzmann's constant, kB = 1.38 x 10 - 23 J / K

How many moles of gas are present if the volume is 1.3 L at 1.0 atm when the temperature is 25oC?