Question

How would you derive the ideal gas equation?

Answer 1

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.

`"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).

`"V"propcolor(white)(.)"T"`

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

`"V"propcolor(white)(.)"n"`

From these three laws we get:

`V=(nT)/P` `color(white)(..)` or`color(white)(..)` `PV=(nRT)/T`

A gas constant, `R`, is multiplied by `nT` so the equation becomes:

`PV=nRT`

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: `"22.710980 L/mol"` https://en.wikipedia.org/wiki/Molar_volume ; `1xx10^5` `"Pa"`; and `"273.15 K"`.

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

`R="8314.47 L Pa K"^(-1) "mol"^(-1)`