# chemistry ideal gas question

Discussion in 'DAT Discussions' started by arpitpatel86, May 14, 2008.

1. ### arpitpatel86 2+ Year Member

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from what i understand D=m/v= P(MM)/RT

the question on kaplan book is: what is the density of HCL gas at 2 atm and 45C

they give the answer in this fromula: V2= (22.4L/mol)(1atm/2atm)(318k/273K)= 13.0L/mol

d= (36g/mol/ 13.0L/mol) = 2.77 g/L

I was wondering why can u just plug it into P(MM)/RT? and when would use this equation if u cant use it in this question?

2. ### alanan84 D1 5+ Year Member

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It's just an algebraic manipulation of the ideal gas law. You start with PV=nRT. The n and R are constants so they fall out leaving you with PV=T. Bring the T over and set it equal to zero and you've got P1V1/T1=P2V2/T2. Now isolate the equation for V2. You multiple by T2 and get P2V2=P1V1T2/T1, now just divide by P2 and you end up with V2=P1V1T2/T1P2 which when you plug in the numbers gives you the answer that they have. Hope that helps!

3. ### arpitpatel86 2+ Year Member

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so u dont really ever use P(MM)/RT
to find the density

u just use find it through doing V2= blah blah blah and then divide by the MMis that right?

4. ### alanan84 D1 5+ Year Member

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Exactly

5. ### bigstix808 Mac Daddy Member 10+ Year Member

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you can't just plug and play numbers in these problems. all the formulas you have are for IDEAL gases at standard conditions (hence the IDEAL GAS constant). when they use V2= (22.4L/mol)(1atm/2atm)(318k/273K)= 13.0L/mol all they are doing is converting the gas at non-standard conditions (which does not fit into the ideal gas equations) to a gas AT standard conditions. this way you CAN actually use the P(MW)/RT = D equation.

Alanan - careful, if that was all that was neccessary, then all the OP would find is the volume of the gas at ideal conditions. the P(MW)/RT = D equation must be used in order to find the density once the ideal volume has been calculated.

clear things up??

6. ### alanan84 D1 5+ Year Member

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Correct, I was mainly explaining how kaplan came up with their answer. I think the OP understood that after finding the volume you would have to divide to get the density.

7. ### bigstix808 Mac Daddy Member 10+ Year Member

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yea, i didn't mean to sound like i'm correcting you, i just didn't want anyone else reading this to think that.

8. ### la brat 2+ Year Member

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I was under the impression that we assume a gas behaves ideally unless otherwise told, even if the pressure is 2 atm. You're saying, you can't use P(MW) = dRT unless conditions are at STP? What's the point of this equation then?

9. ### bigstix808 Mac Daddy Member 10+ Year Member

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because a simple calculation will give you the numbers that will tell you how that gas WOULD act at ideal conditions. most formulas derived for use with gases are only accurate at STP, or at least standardized at STP (ex: P(MW) = DRT).

oh yea, because density is an intensive property, and also because density is temp dependent, there must be a set standard of densities to compare with in which the original density (HCL for this problem i think) was calculated - that standard is STP.

would you rather use:

PV=nRT

or

<-- to be used if you don't feel like converting your numbers to ideal conditions. this accounts for attractive forces between molecules when ideal conditions cannot be met (such as at 2 atm, etc)

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