okay let's take a look at a problem regarding the density of a gas
the question is very simple it simply asks calculate the density of ammonia at
30 degrees Celsius and 5 atmospheres so you may want to review some information
on ideal gases I have several tutorials on this concept
if you need some review and when you're ready give it a try
so we have a very
handy equation that relates all of these variables associated with a gas and that
is the ideal gas law PV equals NRT now the thing is that we want to talk about
density density is not present in this equation but we do have moles and moles
is going to correlate with density because from moles we can be talking
about mass and from mass and volume we can be talking about density and so the
relationship we want to utilize here is that the molar mass equals mass over
moles right it's a grams per mole value so molar mass equals the grams of the
gas over the moles of the gas that will be the molar mass therefore if we
rearrange we can solve for moles and say that moles is equal to grams over molar
mass so because that is the case let's go ahead and plug that in for n so
instead of n we're gonna rewrite this but we're gonna say PV equals little M
over Big M times RT so now we've gotten rid of moles and we have mass and volume
in there that's going to be important because as we said density is mass per
volume so that means we should be able to rearrange this equation in order to
get mass and volume together so let's multiply both sides by Big M and divide
both sides by viii and that is going to give us p.m.
equals little M over V times RT now this is very important because we have put M
over V right here where we want it and that means we can change that to density
because mass over volume is density and so now we have density in our equation
and we can solve for it so D is going to be equal to PM over RT now we just plug
in what we know for pressure we are given five atmospheres for molar mass
that's going to be the molar mass of ammonia which is 17 because nitrogen has
a mass of 14 and each hydrogen is 1 so 17 grams per mole then we have the gas
constant which as always in this context is going to be 0.0821 liters atmospheres
per mole Kelvin and then the temperature is given to us but remember we always
need to convert from Celsius to Kelvin that is our absolute temperature scale
so we're gonna add 273 and that gives us 303 Kelvin then we just do the
arithmetic and we end up with a density of 3.42 grams per liter so this was
fairly straightforward we just had to do this clever algebraic manipulation to
get the ideal gas law in terms of density