Calculating Average Molecular Weight and Equilibrium Constants for Gas Mixtures

[tag16]

Homework Statement

I'm trying to figure out how to compute the average molecular weight of a gas mixture (nitrogen dioxide and dinitrogen tetroxide). I think I'm suppose to use this equation: M(mix)=X(NO2)M(NO2)+ X(N2O4)M(N2O4) , where I would just need to calculate the mole fractions and the molecular weight of the individual gases. Is this correct? If not assistance would be appreciated.

Also I need to determine the equilibrium constant, delta G standard and delta S standard. I think to find the equilibrium constant I need to use this equation: K= n(N2O4)/((2)n(NO2)) ? To find delta G I could then use this equation: detla G= -RTlnK ? and I have no idea how to find delta S standard.

Known: Pressure, Temp, Volume and three different weights of gas mixture.

Homework Equations

M(mix)=X(NO2)M(NO2)+ X(N2O4)M(N2O4)
K= n(N2O4)/((2)n(NO2))
detla G= -RTlnK

The Attempt at a Solution

Ok I'm trying to get the mole fraction and ran into a little bit of a problem:
nf= PV/RT= 0.95646 x105cm3x267.403 x10-6bar/ 8.31 x 303.15 K
= 0.010153 mol

ni+x=119.283g/(92 g/mol)
= 1.29655 ?

ni+x cannot equal nf when ni alone is larger. What am I doing wrong?

 

[Borek]

Ok I'm trying to get the mole fraction and ran into a little bit of a problem:
nf= PV/RT= 0.95646 x105cm3x267.403 x10-6bar/ 8.31 x 303.15 K
= 0.010153 mol

ni+x=119.283g/(92 g/mol)
= 1.29655 ?

What is what of what? We are not a bunch of seers.

 

[tag16]

I'm not sure what is unclear. I'm try to get the average molecular by using this equation:M(mix)=X(NO2)M(NO2)+ X(N2O4)M(N2O4) (unless this not the equation I should be using?)

To do that I need the mole fractions, which is what I was trying to do here: nf= PV/RT= 0.95646 x105cm3x267.403 x10-6bar/ 8.31 x 303.15 K
= 0.010153 mol

ni+x=119.283g/(92 g/mol)
= 1.29655 ?

ni+x cannot equal nf when ni alone is larger. What am I doing wrong?


If you need more information I would be happy to oblige, especially since your helping me, I'm just not sure what other information you need.

 

[Borek]

I have no idea what is 0.95646, 105cm3 is probably volume, but I have no idea of what, then comes pressure (of what?), R (that I know) and temperature (of what?), and finally 0.010153 mol is not a mole fraction, although you wrote that's what you are trying to calculate.

I have no idea what is ni and nf, I have no idea what is x (that is - it is probably molar fraction, but of what?)

What is 119.283g? Mass, but of what?

So - to quote Piglet once again - what is what of what?

 

[tag16]

0.95646 cm^3 is the volume of the dinitrogen textroxide and nitrogen dioxide gas mixture, the pressure is the pressure in the lab at the time of the experiment, temperature of the gas mixture.

119.283g in the mass of the gas mixture

x is the mole fraction, ni is the number of moles of the components

To get the mole fractions of both gases I need to do this:

N2O4= 2(NO2)

n(N2O4)= ni -x
n(NO2)= 2x

but first I need to find ni and x, hence this:

n= PV/RT= 0.95646 x105cm3x267.403 x10-6bar/ 8.31 x 303.15 K
= 0.010153 mol

ni+x=119.283g/(92 g/mol) + x
119.283g/(92 g/mol)= 1.29655

or I'm going about this in completely the wrong way, which is definitely possible.

 

[Borek]

Am I right guessing that the volume is in fact 0.65646x10⁵cm³? If not, your gas has density over 120 g/mL, this is about five times more than the most dense metals.

N2O4= 2(NO2)

n(N2O4)= ni -x
n(NO2)= 2x

I guess you are trying to use some information about reaction stoichiometry, but - sorry - it won't get you anywhere. I am almost sure this is wrong, but you have still not gave full information about the problem and known data, so I still have no idea what you are doing. Sorry to say that, but you are wasting my time. Please explain the question in full. Don't repeat for the fourth time the same calculation, describe PROBLEM and DATA.

 

[tag16]

PROBLEM: Assume an ideal mixture of ideal gases. From your data, compute the average molecular weight
of the gas mixture at each temperature. Using these values, determine the degree of dissociation
and the equilibrium constant, Kp, ΔG^o and ΔS^o for the dissociation at each temperature.
http://homepages.wmich.edu/~dschreib/Courses/Chem436/I-4 N2O4 Dissociation.pdf

experimental data: bulb 1: 141.97 g
bulb 2: 99.9668g
bulb 3: 115.9037g

T=30C^o
P= 717.41 Torr= 0.956468003 bar

 

[Borek]

Now we are getting somewhere.

115.9037g is not mass of the gas, it is mass of the bulb and gas inside. You should also know mass of the empty bulb (point 2, week two).

0.95646cm³ is not volume of the bulb - bulb volume is around 250 mL. No idea what 0.95646 is. Perhaps mass of the gass?

 

[tag16]

Oh sorry, that is week 2 data, weighing the bulbs with the gas inside, this is week 1:

bulb 1: 141.82g
w/water:395.95g
bulb 2: 99.27g
w/water: 361.77g
bulb 3: 143.79g
w/water: 397.75g

To get the volume I did V= mass/ water density , don't know if that's what I should have done but that's what I did.

 

[Borek]

So, what is volume of the bulb, and what is mass of the gas inside? Can you use these two information to calculate density and average molar mass?

Let's stick to bulb number 1.

 

[tag16]

Well the mass of the gas would just be the mass of the bulb filled with the gas minus the mass of the bulb itself, correct?

Do you mean just the volume of the bulb by itself? 250 cm^3 ?

 

[Borek]

Well the mass of the gas would just be the mass of the bulb filled with the gas minus the mass of the bulb itself, correct?

Yes.

Do you mean just the volume of the bulb by itself? 250 cm^3 ?

No, you have determined the volume experimentally on the first week of the lab. Have you actually read the document you have linked to?

 

[tag16]

Yes, it was necessary in order to perform the experiment.

So the volume would be the mass w/ water minus w/o?

 

[Borek]

No, that will be mass of water, not the volume.

Have you read the document you have linked to? It contains plenty of hints.

Accurately measure the water temperature so that you may look up the correct water density.

 

[tag16]

yes, that is what I did. Then I did V= mass/ water density, which must have been wrong.

 

[Borek]

yes, that is what I did. Then I did V= mass/ water density, which must have been wrong.

What was the result and why do you think it was wrong?

 

[tag16]

In a previous post I wrote this:

To get the volume I did V= mass/ water density , don't know if that's what I should have done but that's what I did.

Since in a later post you asked me how to get the volume, I just assumed that what I had already posted must have been wrong.

When I calculated it I got V=267.403 cm^3. To get the mass to use in this equation would I want to take the average of the three bulbs w/water?

 

[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:

Treat each bulb separately, do not average the values from the two bulbs.

 

[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 that's 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]

ave. molecular mass of bulb 1: 77.4395 g

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]

y = 0.316734
1- y = x
x = 0.683266

Looks OK.

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%

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]

n = (1 − α)n + 2αn

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.