# How would you derive the ideal gas equation?

Jul 26, 2018

Refer to the explanation.

#### Explanation:

Boyle's law states that the volume of a fixed mass of a gas is inversely proportional to the pressure.

$\text{V"prop1/"P}$

Charles' law states that the volume of a fixed mass of a gas held at constant pressure is directly proportional to its absolute temperature (Kelvins).

$\text{V"propcolor(white)(.)"T}$

Avogadro's law states that If the amount (moles) of gas in a container is directly proportional to the volume.

$\text{V"propcolor(white)(.)"n}$

From these three laws we get:

$V = \frac{n T}{P}$$\textcolor{w h i t e}{. .}$ or$\textcolor{w h i t e}{. .}$$P V = \frac{n R T}{T}$

A gas constant, $R$, is multiplied by $n T$ so the equation becomes:

$P V = n R T$

The units of the gas constant depend on the units used for volume, pressure, moles, and temperature. It can be calculated using the molar volume, pressure, and temperature of a gas at STP: $\text{22.710980 L/mol}$ https://en.wikipedia.org/wiki/Molar_volume ; $1 \times {10}^{5}$ $\text{Pa}$; and $\text{273.15 K}$.

R=((22.710980 "L"/"mol")xx(1xx10^5"Pa"))/(273.15"K")

$R = {\text{8314.47 L Pa K"^(-1) "mol}}^{- 1}$