Physical Chemistry-Gas Laws (Find R and M)

[bluegreen]

Thanks ahead of time for any help!

Homework Statement

From Atkins Physical Chemistry text, 9th Edition:
1.7b) The following data has been obtained for oxygen gas at 273.15 K. Calculate the best value of the gas constant R from them and the best value of the molar mass of O2 (oxygen).

p(in atm)
P1=0.750 000
P2= 0.500 000
P3=0.250 000

Vm [molar volume] (in dm^3/mol)
Vm1= 29.8649
Vm2=44.8090
Vm3=89.6384

Homework Equations

The Attempt at a Solution

To find R, I used R= (Vm P)/ T to find the different Rs for each set of data, then used y=mx+b (using data points [P, R]) to extrapolate back to when p=0 (when ideal gas is most accurate; so that means the y intercept which was equivalent to R).

I know you can just graph it and get the same result. Either way, I got R= 0.0820614 dm^3 atm/K mol.

Now I'm lost. How do I set it up to find molar mass? Do I extrapolate using a graph again? I'm not given density, so it throws a wrench in a lot of the equations I tried using, like:
Vm= M/ density = RT/P= V/n

 

[Borek]

No idea - I can't think of any approach that will let calculate molar mass from the given data.

That's to let you know someone actually read your post and spend a moment thinking how to help.

It can always be an error in the book. I can be also missing something.

 

[bluegreen]

Thanks. I know that in the old editions, density is given, but density was omitted for the 9th edition. Not sure if it was a mistake or if it was to make the question trickier!

 

[Borek]

Must be mistake then.

--

 

[DeeNos]

RT.

Hello,

To find the molar mass (M) of oxygen, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. We can rearrange this equation to solve for the molar mass M:

M = (mRT)/PV, where m is the mass of the gas in grams.

To find m, we can use the density equation d = m/V, where d is the density, m is the mass, and V is the volume. We can rearrange this equation to solve for m:

m = dV.

Substituting this into the equation for M, we get:

M = (dVRT)/PV.

Now, we can use the data given to solve for M:

P1 = 0.750 atm, V1 = 29.8649 dm^3/mol
P2 = 0.500 atm, V2 = 44.8090 dm^3/mol
P3 = 0.250 atm, V3 = 89.6384 dm^3/mol
T = 273.15 K

Substituting these values into the equation for M, we get:

M = [(d)(29.8649 dm^3/mol)(0.0820614 dm^3 atm/K mol)(273.15 K)]/[(0.750 atm)(29.8649 dm^3/mol) + (0.500 atm)(44.8090 dm^3/mol) + (0.250 atm)(89.6384 dm^3/mol)]

Simplifying, we get:

M = [(d)(7.7737 dm^3 atm K mol)]/[(22.3987 dm^3/mol) + (22.4045 dm^3/mol) + (22.4096 dm^3/mol)]

M = (d)(0.3462 dm^3 atm K mol)

Now, we need to find the density (d) of oxygen at 273.15 K. We can use the ideal gas law equation again, but this time for a single set of data (P1 = 0.750 atm, V1 = 29.8649 dm^3/mol):

d = (P1M)/(RT) = [(0.750 atm)(0.0820614