How would you derive the ideal gas equation?

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How would you derive the ideal gas equation?

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Answer 1 · 2018-07-26T22:18:16

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.

$V \propto \frac{1}{P}$ $"V"prop1/"P"$

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).

$V \propto . T$ $"V"propcolor(white)(.)"T"$

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

$V \propto . n$ $"V"propcolor(white)(.)"n"$

From these three laws we get:

$V = \frac{n T}{P}$ $V=(nT)/P$ $. .$ $color(white)(..)$ or $. .$ $color(white)(..)$ $P V = \frac{n R T}{T}$ $PV=(nRT)/T$

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

$P V = n R T$ $PV=nRT$

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: $22.710980 L/mol$ $"22.710980 L/mol"$ https://en.wikipedia.org/wiki/Molar_volume ; $1 \times 10^{5}$ $1xx10^5$ $Pa$ $"Pa"$ ; and $273.15 K$ $"273.15 K"$ .

$R = \frac{(22.710980 \frac{L}{mol}) \times (1 \times 10^{5} Pa)}{273.15 K}$ $R=((22.710980 "L"/"mol")xx(1xx10^5"Pa"))/(273.15"K")$

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

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How would you derive the ideal gas equation?

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