Chemisty states of matter

Question

The two bulb of volume 5L n 10L contai an ideal gas at 9atm and 6atm respectively r connected. What is d final pressure in d two bulbs if d temperature remains constant...???

Answer 1

The Pressure and Volume of any gas is directly related to the number of moles of gas (times R and T).  PV=nRT for any gas sample.  We can do this the long way (and be sure) or use a short cut.  I like certainty over uncertain short cuts, but we would have to work in abstracts (algebra!) since we aren't given T. 

 

Let's call the left hand bulb Gas 1, and the right hand bulb Gas 2, and after they mix it is Total Gas.

How many moles of Gas 1 do we have? n = PV/RT, so we have (9 atm)(5L)/RT or we can say 45/RT moles of gas

Gas 2 we have (6atm)(10L)/RT = 60/RT moles

So the total moles of gas in the container is 45/RT + 60/RT = 105/RT

If I want the final Pressure, I need to again use PV = nRT and solve for P.  P = nRT/V

 

We have "defined" the total moles of gas as 105/RT, and our total V = 15 L

By substitution we have (105/RT)• (RT/15) = 105/15  atm = 7 atm   

Note that the units for everything should work out/cancel out as needed as long as we are using P in atm and V in L.  ;)

 

The "short way" is a formula for mixing gases of different pressures and volumes: 

P₁V₁ + P₂V₂ + P₃V₃... etc = P_totV_tot    

 

But unless you can at least sort of follow what we already did, then you are just memorizing a formula and might not understand why it works...  :(  That's why I don't like formulas that aren't easy to remember, because you might not know when to apply them.  But hopefully since you have seen the origins of this one now you know. 

 

Using this formula, we have  (9atm)(5L) + (6 atm)(10 L) = (?? atm)(15L)

45 L-atm + 60 L-atm = 15x L-atm

105 L-atm = 15x L-atm       divide both sides by 15 L-atm and you get

7 = x  

Therefore the final Pressure is 7 atm (ta-da!)  :D

 

Hope that helps!