Register to reply 
Finding the concentration of a gas (thermodynamics) 
Share this thread: 
#1
Jan1607, 09:29 AM

P: 105

Hi.
1. The problem statement, all variables and given/known data The root mean square velocity of oxygen molecules is 480m/s while the pressure is 20kPa. What is the concentration (particles/volume) of oxygen? 2. Relevant equations PV=nRT [tex] E_{kin}=\frac{m \overline{v}^2}{2}=\frac{3}{2}kT [/tex] 3. The attempt at a solution [tex] m \overline{v}^2=3kT \Rightarrow T= \frac{m \overline{v}^2}{3k} [/tex] [tex] PV=nR \frac{m \overline{v}^2}{3k} \Rightarrow n=\frac{3kPV}{Rm \overline{v}^2} [/tex] where [tex] m=2 \times 16 \times 1.66 \times 10^{27} kg [/tex] I set V=1m^3 and get n=8.137mol and therefore [tex] \frac{n \times n_{a}}{V}=4.899 m^{3} [/tex] where [tex] n_{a}=6.02 \times 10^{23} [/tex] Is this correct? I'm sure there's a simpler way to do this. 


#2
Jan1607, 07:54 PM

Sci Advisor
HW Helper
P: 1,769

Note that the mass refers to an individual oxygen molecule (from what I recall at the moment), (16 grams of Oxygen/mole of Oxygen)(1 mole/6.022 x 10^23 atoms)(1 kilogram/1000 grams)(2 atoms of Oxygen/1 diatomic molecule)=____.......the setup should be solved for n/V, this means that you need to incorporate a particular value of R, choose from the list on the page that can be linked to through the below text so that the final units for n/V is respect to moles/liter.
http://en.wikipedia.org/wiki/Gas_constant 


#3
Jan1707, 04:01 AM

P: 105

Actually, since this is one of my physics class problems (not chemistry) concentration really does mean particles/volume in this case. Which means that I have chosen the right value for R, I think.



#4
Jan1707, 04:12 AM

Emeritus
Sci Advisor
PF Gold
P: 11,155

Finding the concentration of a gas (thermodynamics)
As for a simpler way, I think this is as simple as it gets. Only, notice that since R=k*Na, and M=m*Na, your final expression simplifies to n=3PV/Mv^2 (in moles). 


#5
Jan1707, 07:01 PM

Sci Advisor
HW Helper
P: 1,769

(n/v)=20 kPa(1000 Pa/1 kPa)(1.3806503 × 1023 m2 kg s2 K1)3/[8.314472 m^3 · Pa · K1 · mol1(16 grams of Oxygen/mole of Oxygen)(1 mole/6.022 x 10^23 atoms)(1 kilogram/1000 grams)(2 atoms of Oxygen/1 diatomic molecule)(480 m/s)^2]= 0.00813782909722 moles/m^3
(0.00813782909722 moles Oxygen/L)(6.022x10^23 molecules Oxygen/mole)= 4.900600682 x 10^24 molecules/m^3 So there's everything done in a perfunctory fashion for ya, I wanted to see what answer would result with the "chemist" method. I'm going to need to see if the units cancel out exactly....... 


Register to reply 
Related Discussions  
Finding out the concentration of an acid or base  Chemistry  3  
ThermodynamicsFinding Internal energy  Introductory Physics Homework  1  
Finding Free Electrons and Hole Concentration  Engineering, Comp Sci, & Technology Homework  1  
Finding the iodide ion concentration  Biology, Chemistry & Other Homework  1  
Chemical Equilibrium, finding concentration  Chemistry  2 