# Ideal Gas Law : Pv = Nrt – Derivation Of The Equation Pv = Rt

I know this will sound dumb for the people who are here but I need to learn eventuallywhen can I use $pv=RT$ and when to use $pV=nRT$

If you write $pv = RT$ then $v$ is the molar volume i.e. the volume occupied by one mole of the gas. We often do this because we don”t know or aren”t interested in exactly how much gas is present. For example if you were calculating the properties of air you don”t need to know the total amount of air in the whole atmosphere.

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If you write $pV = nRT$ then $V$ is the total volume of the gas and $n$ is the number of moles of gas present. The two equations are equivalent because the molar volume is the total volume divided by the number of moles present:

$$v = frac{V}{n}$$

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answered Nov 23 “20 at 5:57

John RennieJohn Rennie
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Both of these equations are completely the same. But let’s just make sure of one thing first.

Assuming both equations are the same in that both $v$ and $V$ represent volume, then the difference is that in the equation where you don’t have $n$, then the number of mole $n$ is taken to be one.

If you are looking at system where the number of mole is $n eq 1$ then you would use

$$pv = nRT$$

However, if $v$ and $V$ represent molar volume and normal volume respectively, then note that

$$v = V/n$$

where $v$ represents the volume per mole of gas and you will know which equation to use since the problem should refer to $v$ as molar volume as oppose to standard volume. In that case you would use your first equation

$$pv = RT$$

Note that $n$ is dimensionless so that sometimes $v$ and $V$ will both be expressed in the same units $m^3$ (or $cm^3$ etc). But it should usually be expressed as $m^3 mol^{-1}$.

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edited Nov 23 “20 at 6:54
answered Nov 23 “20 at 5:37

joseph hjoseph h
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