The Ideal Gas Equation For Moles

If you are just looking for the equation, it is: $pV = nRT$.

Quick Recap:

Ideal gasses are theoretical gasses which follow the following three laws:

• Boyle’s Law: $pV\space =\space constant$
• Charles’ Law: $\frac{V}{T} = constant$
• The Pressure Law: $\frac{p}{T} = constant$

These can all be combined into the equation:

$$\large{\frac{pV}{T}\space =\space constant}$$

…Applying This:

If you use this equation, subbing in the value for one mole of an ideal gas at a room temperature and atmospheric pressure (so as if we have taken 1 mole of Oxygen from the room in which you are most likely sat in) we get a constant which we call the Molar Gas Constant.

The Molar Gas Constant has a value of:

$$ \LARGE{8.31\space JK^{-1}mol^{-1}} $$

Notice that the units show this is for one mole. Therefore, to adapt this constant so that it can be used when there is a sample of more than one mole, we must times the Molar Gas Constant, $R$, by the number of moles, $n$.

Therefore,

$$\LARGE{\frac{pV}{T} = nR} $$

Rearranging gives the more widely used format of:

$$\LARGE{pV = nRT} $$

Where,

$p$ - pressure of / exerted by the gas

$V$ - volume occupied by the gas

$n$ - number of moles of gas in sample

$R$ - Molar Gas Constant ($8.31\space JK^{-1}mol^{-1}$)

$T$ - Absolute temperature of the gas

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