Matter
Kinetic Particle Theory
All matter is formed by tiny particles - atoms. These particles are in constant erratic motion due to their internal kinetic energy.
Temperature correlates to the average energy of molecules within a substance. Higher temperatures will increase their internal kinetic energy, causing them to move faster, and possibly change states. It is often measured in degrees Celsius or Fahrenheit, but astronomers and physicists use Kelvin (K). To convert from Kelvin to degrees Celsius, simply add $273.15$ to the value.
Particles in matter that are in the solid state will vibrate about at fixed positions. Their movements are restricted due to the stronger intermolecular or van der Waals forces holding them together. This causes them to have a definite volume and shape.
Those in the liquid state would be closely packed in a disorderly manner. Particles would slide over each other, which explains why liquids do not have a definite shape. However, liquids still have a definite volume.
As for gaseous matter, the forces between particles are extremely weak, and hence they move very fast in random directions and are extremely spread out. They have no definite shape or volume.
Thus, the density of solid matter is usually higher than that of a liquid, which is in turn higher than that of a gas, of the same material. The density of matter of mass $m$, and volume $v$ is given by $\rho = \frac{m}{v}$.
Ideal Gas Law
An equation of state relates the temperature of a material to other measurable variables like density.
Low-density gases have particularly simple equations of state because individual molecules have little influence on others. If we imagine a box of gas, the molecules bounce off the walls creating an outward gas pressure $P$ but do not apply forces to each other. This simplified system is called an ideal gas. The ideal gas law relates the gas pressure $P$ to the density $\rho$ and temperature $T$ and is given by:
where $m$ is the mass of one gas molecule, which can be found from the $A_r$ (relative atomic mass) of each of its elements. $k_B$ is the Boltzmann constant $k_b = 1.381 \times 10^{-23} J/K$ calibrates the Kelvin temperature scale to energy in Joules.
Use the ideal gas law to estimate the density of diatomic nitrogen in $kg/m^3$ at Earth's surface. Assume that the pressure at sea level is $1.01 \times 10^5 Pa$, the average temperature of gas at sea level is $288K$, $A_r$ of Nitrogen to be $14.0$, and Avogadro's constant $N_A = 6.022 \times 10^{26}$
To find the mass of one molecule of diatomic nitrogen
Then changing the subject of the formula and applying the ideal gas law equation
$$ \rho = \frac{4.65 \times 10^{-26} \cdot 1.01 \times 10^5}{1.381 \times 10^{-23} \cdot 288} = 1.18 \; kg/m^3 \; (3 sf) $`