How would you derive the ideal gas equation?

1 Answer
Jul 26, 2018

Answer:

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)#