density of gasoues mixture

[crazziekid82]

ok im doing this question and i am totally lost. once again got the Q&A but no working out so i cant follow the steps to HOW they got the answer.

So here it is

 

Ammonia is produced in the Harber Process under conditions of high pressure and moderate temperture. If 13.05L of an equilibrium mix at 550'C (823K) and 200kPa presurre consists of 3.00 L of nitrogen and 9.00L of hydrogen and 1.50L of ammonia calculate teh density of (g) mixture..

 

im not sure where to start or what formulas to use.

[big314mp]

Well, density is mass per unit volume. You are given a volume, and you need to find the mass.

 

To find the mass you will need to find the moles of each gas present, and then convert that into a mass.

[CaptainPanic]

Do you know the "Ideal gas law"? That's what I would use to calculate the density.

[pioneer]

What you do is PV=nRT for each of the components and solve for n. The T and P are the same for all, only V is different. We calculate n or the number of moles for each. Once we now the n for each, we can calculate the mass of each, which is molecular weight times the number of moles of each.

 

Density is the total mass/volume. We add all the masses and divide by the total volume to get density at those conditions of T and P.

[hermanntrude]

it's easier than that. The ideal gas equation can be re-written to include density:

 

PV = nRT

 

PV = [math]\frac{m}{M}[/math]RT

 

PV = [math]\frac{mRT}{M}[/math]

 

P = [math]\frac{mRT}{VM}[/math]

 

P= [math]\frac{mRT}{VM}[/math]

 

PM = [math]\frac{mRT}{V}[/math]

 

[math]\frac{PM}{RT}[/math] = [math]\frac{m}{V}[/math] = d

 

the question is, though... which "M" should you use?

[crazziekid82]

can u add all the M values together then substitute into the EQN?

[hermanntrude]

i'm not sure if that would work.

 

I would use P(a)V = [math]\frac{mRT}{M}[/math] three times to get the masses of the three gases and then use the version I already posted to get the density. This might not be the quickest route but it's the only one I can see. you'd have to first calculate the partial pressures of the gases using the volume ratio