Average molecular weight?

Borek

Do the calculations for each bulb separately.

Yes, now I see you have calculated masses of water earlier. Trick is, in some posts you write things that are half right and half wrong, it is hard to keep track of what was already correct and what was not. Besides, you have not listed the V value earlier, and when I asked what it was you suggested it was 250 mL, which was incorrect.

tag16

I just assumed what I originally thought the volume was must be wrong or you wouldn't asked about the volume so I just came up with something random because I didn't know what else it could be, hence the 250 cm^3.

So I have to do the calculations for each of the three bulbs seperately as well as for each temperature, correct?

Borek

To quote the document you have read:

tag16

So the volume of the bulbs using V= mass (w/water)/ water density

bulb 1: 397.122
bulb 2: 362.841
bulb 3: 398.928

Which brings me back to my problem of finding the average molecular weight of the gas mixture at each temperature. I originally thought I was suppose to use this equation: M(mix)=x(NO2)M(NO2)+x(N2O4)M(N2O4), is that right?

Borek

These are not volumes, volumes should be much closer to 250. You forgot to subtract mass of empty bulb.

Calculate volumes, calculate masses of gas mixtures. Knowing mass, volume, temperature and pressure you should be able to calculate average molar mass, later you can use this number to calculate molar fractions of both gases.

tag16

opps thats what I did originally but I also averaged them all together which was wrong. This is minus the mass of the bulb:

bulb1:254.882
bulb2:263.277
bulb3:284.049

tag16

I'm not really sure what to do next, I think I'm suppose to use this equation: M(mix)=x(NO2)M(NO2)+x(N2O4)M(N2O4), if so I'm not sure how to get the mole fractions from the data I have or the degree of dissociation.

Borek

Calculate volumes, calculate masses of gas mixtures. Knowing mass, volume, temperature and pressure you should be able to calculate average molar mass, later you can use this number to calculate molar fractions of both gases.

tag16

so I used M=DRT/P to find the average molecular mass and got this:

For bulb 1: P=717.41 Torr= 0.94396 atm
V= 254.882 cm^3
T=303.15 K
mass= 141.9780 g


M=(141.9780 g/254.882 cm^3)(0.0821)(303.15 K)/(0.94396 atm)
ave. molecular mass of bulb 1: 14.686

Am I going about this the right way or am I completely off?

Borek

You are off. Perhaps not completely, but seriously.

First - 141.8780 g can't be mass of the gas. I guess you forgot to subtract bulb mass again.

Second - your volume units are inconsistent with R units.

tag16

For bulb 1: P=717.41 Torr= 0.94396 atm
V= 254.882 cm^3
T=303.15 K
mass= 141.9780 g(bulb w/gas)-141.229 g(bulb empty)= 0.749 g


M=(0.749g/254.882 cm^3)(8.314)(303.15 K)/(0.94396 atm)
ave. molecular mass of bulb 1: 7.846g

tag16

opps I think I used the wrong gas constant again:

M=(0.749g/254.882 cm^3)(82.057)(303.15 K)/(0.94396 atm)
ave. molecular mass of bulb 1: 77.4395 g

Borek

That looks OK.

Now, write the equation for average molar mass using x & y for molar fractions of both gases. You know that x+y=1, that means you have two equations and two unknowns. Solve and you will know how much of each gas is present.

tag16

x + y = 1
92.011 x + 46.0055 y = 77.4395

x= -y + 1
92.011 (-y +1) + 46.0055 y = 77.4395
-92.011 y + 92.011 + 46.0055 y = 77.4395
-46.0055 y + 92.011= 77.4395
-46.0055 y = -14.5715
y = 0.316734
1- y = x
x = 0.683266

To find the degree of dissociation I did this:

n(N2O4)=77.4395/92=0.841 mol

degree dissociation: x(N2O4)/n(N2O4)= 0.683266/0.841= 0.812445= 81.24%


To find Kp I did:

n(N2O4)=77.4395/92=0.841 mol
n(NO2)= 77.4395/46=1.683 mol

Kp= n(N2O4)/(n(NO2))^2= 0.841/(1.683)^2= 0.296912

I think to find delta G standard I'd want to use this equation: delta G= -RTlnKp

and for delta S: delta S= delta G/T

Did I go about any of that right or is that not what I'm suppose to do?

Borek

Looks OK.

So you have calculated composition of the mixture only to ignore it now and not use the information in following calculations?

tag16

Is this right? If not I don't know how to find it.

PV = nRT --> n =PV/RT--> n = (1 − α)n + 2αn = PV/RT

α = (PV/nRT)− 1

Borek

You have two different n in this equation - on the left, total number of moles after reaction took place, on the right - initial number of moles.

You know molar fractions of both gases present. Calculate numbers of moles of both. Use stoichiometry of the reaction to calculate initial number of moles of gas. Use definition of dissociation degree.