We are going to picture a container of gas, such as the box shown in Figure 20.4. There are four properties of this gas that we might measure: pressure, temperature, volume and mass. In this chapter, you will learn how these quantities are related to one another.
Figure 20.4: A gas has four measurable properties, which are all related to one another: pressure, temperature, volume and mass.

Pressure

This is the normal force exerted per unit area by the gas on the walls of the container. We saw in Chapter 7 that molecular collisions with the walls of the container produce a force and thus create a pressure.
Pressure is measured in pascals, Pa $(1\,Pa = 1N\,{m^{ - 2}})$.

Temperature

This might be measured in $^ \circ C$, but in practice it is more useful to use the thermodynamic (Kelvin) scale of temperature. You should recall how these two scales are related:

$T(K) = \theta {(^ \circ }C) + 273.15$

Volume

This is a measure of the space occupied by the gas. Volume is measured in ${m^3}$.

Mass

This is measured in g or kg. In practice, it is more useful to consider the amount of gas, measured in moles. The mole is the SI unit of substance, not a unit of mass.
We have seen in Chapter 15 that each atom or molecule has a mass in unified atomic mass units (u), approximately equal to the number of nucleons (protons and neutrons) it contains.
We have also seen that $1\,u\, = 1.66 \times {10^{ - 27}}\,kg$.
Thus, each atom of carbon-12 has a mass:

$\begin{array}{l}
12u = 12 \times 1.66 \times {10^{ - 27}}\,kg\\
 = 1.99 \times {10^{ - 26}}\,kg
\end{array}$

So, $0.012 kg$ of carbon-12 contains $\frac{{0.012}}{{1.99 \times {{10}^{ - 26}}}} = 6.02 \times {10^{23}}$ molecules.
A mole of any substance (solid, liquid or gas) contains a standard number of particles (molecules or atoms). This number is known as the Avogadro constant, ${N_A}$. The value for ${N_A}$ is $6.02 \times {10^{23}}\,mo{l^{ - 1}}$. We can easily determine the number of atoms in a sample if we know how many moles it contains. For example:
$2.0 mol$ of helium contains

$2.0 \times 6.02 \times {10^{23}} = 1.20 \times {10^{24}}\,atoms$

$10 mol$ of carbon contains

$10 \times 6.02 \times {10^{23}} = 6.02 \times {10^{24}}\,atoms$

We will see later that, if we consider equal numbers of moles of two different gases under the same conditions, their physical properties are the same.