# Ideal gas law

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### Ideal Gas Law

The Ideal Gas Law was first written in 1834 by Emil Clapeyron.
Following relations can be expressed as constants (k_{1},
k_{2}...k_{6}) representing six different values.
** PV= k**_{1}

V/T = k_{2}

P/T = k_{3}

V/n = k_{4}

P/n = k_{5}

1/nT = 1/k_{6}

In order to make **one** equation that contain them all
i.e. **P,V,T** and **n**, we can multiply them all.
**P**^{3}V^{3} / n^{3}T^{3}
= k_{1}k_{2}k_{3} k_{4}k_{5} / k_{6}

Taking the cube root we get:

**PV/nT = (k**_{1}k_{2}k_{3}k_{4} k_{5}
/ k_{6})^{1/3}

An expression in which on the right side of the equation can be
presented as a single constant - **R** - the gas constant. Now we
have a single equation representing the relationship between
pressure(P), volume(V), mole(n) and temperature(T).
** PV/nT = R**

or as presented in CHEMIX

**PV = nRT**

The
ideal gas law.

Example : A 2 mol sample of oxygen gas O2 has a volume of 10.0 L at 300
Kelvin.
Calculate the pressure.

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