Explain the relationship between pressure,volume,and density of gases.

(N/A) Boyle's Law states that at constant temperature,the pressure $(p)$ of a fixed amount of gas is inversely proportional to its volume $(V)$.
Mathematically: $p \propto \frac{1}{V}$ (at constant $T$ and $n$)
$p = k_1 \frac{1}{V} \implies pV = k_1$
Since density $(d)$ is defined as mass $(m)$ divided by volume $(V)$,we have $d = \frac{m}{V}$,which means $V = \frac{m}{d}$.
Substituting this into Boyle's law $(pV = k_1)$:
$p \left( \frac{m}{d} \right) = k_1$
$p = \left( \frac{k_1}{m} \right) d$
Since $k_1$ and $m$ are constants for a fixed amount of gas at a constant temperature,we can write $\frac{k_1}{m} = k'$ (another constant).
Therefore,$p = k' d$,which means $p \propto d$.
This shows that at a constant temperature,the pressure of a fixed amount of gas is directly proportional to its density.