In this section we recall a couple of definitions and introduce a new one. These definitions will then get us ready to discuss the topic of the ideal gas.

Pressure

Recall also that the atmospheric pressure at the earth’s surface is given by p_atm = 1.01 x 10⁵ Pa.

Absolute Temperature

The temperature of a substance measured in Kelvin is called the absolute temperature of the substance. It will be important to keep in mind that, whenever a temperature occurs in an equation and is not part of a expression for a change in temperature, then that temperature reading must be put in Kelvin before being used in the equation.  (This is because the temperature of a substance can never reach 0 K, which means that we will never have to worry about dividing by zero when solving for a quantity in an  equation with temperature if that temperature is expressed in Kelvin!) Such will be the case with our equation for ideal gases.

Mole

A mole is a small mammal which tunnels underground and has been known  to resemble certain professors of mathematics. It is also a measure of the number of objects under consideration (atoms, molecules, mathematics professors, etc.). In this respect, a mole is just like a dozen.  However,  whereas a dozen is a useful measure for the number of objects we might want to sit down and count, the mole is a measure that is extremely large, and certainly a number that we would not want to have to count.  It is a  number that is characteristic of, for example, the number of atoms in a glass of water.  The number of objects in one dozen is 12.  The number of objects in one mole is called Avogadro’s number, and is denoted N_A:

N_A = 6.02 x 10 ²³ .

Thus, two moles of atoms contains 12.04 x 10 ²³ atoms.  A gas of 0.057 moles of water molecules contains 0.057 N_A = 3.4 x 10 ²² molecules.  We  usually use the unit of moles when speaking of the number of atoms or molecules in a macroscopic sample of such atoms or molecules (like a glass of water, or the number of gas atoms in the room...).