Mass fraction and volume of a gas in a cylinder

[Sabra_a]

Homework Statement

Three 60-litre high-pressure gas cylinders contain gaseous fire suppressants. The suppressants are:
1) IG-100 (which is 100% N2),
2) Carbon dioxide (CO2),
3) IG-55 (50% vol. N2 and 50% vol. Ar).
The suppressants are stored in gaseous form under the pressure 170 atm (1 atm=101325 Pa) and at normal temperature (T=293K).
(i) Calculate the mass fraction of nitrogen and argon in gas mixture IG-55.
(ii) Assume ideal gas behaviour of the suppressants. What is the mass of the gas contained in each cylinder?
(iii) The suppressants are to be released in an environment at normal conditions of pressure and temperature (p=1atm, T=293K). What volume will be occupied by each suppressant after their release into the environment? Assume isothermal expansion in your calculation.
Note: atomic masses: M(N)=14 kg/kmol, M(Ar)=40 kg/kmol, M(C)
=12 kg/kmol, M(O)=16 kg/kmol.

Relevant Equations

mass fraction
atomic mass
molecular mass
ideal gas equation

I have attached the full answer in PDF file. I'm not sure about the answers. will really appreciate if they get checked

 

[Chestermiller]

Part (i) is done correctly. Before we get to part iii, part ii is done incorrectly. The pressure is equal to 170 atm, not 1 atm. Try again, and be careful of units.

 

[mjc123]

At 170 atm and 293 K, CO₂ will liquefy. The vapour pressure of CO₂ at 293 K is about 55 atm. However, you can still do what the question asks, i.e. assume ideal gas behaviour, to get a hypothetical answer.

 

[Sabra_a]

is it correct?

 

[Chestermiller]

What are the units of the R value you used? I don't think the value you used is correct.

 

[Sabra_a]

R = 83145 J/kmol.K

 

[Chestermiller]

R = 83145 J/kmol.K

That should be 8314.5 J/kmol.K

$$n=\frac{(170)(101325)(0.06)}{(8.314)(293)}=424\ moles$$

 

[Sabra_a]

I have changed the value of n

 

[Chestermiller]

View attachment 252446
I have changed the value of n

That completes part ii. Now, continue with part iii.

 

[Sabra_a]

for part iii I will use PV=nRT, then rearranging it to calculate the volume of each cylinder!

but should I include 101325 in the denominator?

 

[Chestermiller]

for part iii I will use PV=nRT, then rearranging it to calculate the volume of each cylinder!View attachment 252464
but should I include 101325 in the denominator?

You are not being careful about units. You should not have to ask this question if you are canceling units properly.

 

[Sabra_a]

 

[mjc123]

Part iii can be answered more simply, just using Boyle's law: PV = constant at constant T.
60*170 = 1*V
V = 10200 L