Math Is Fun Forum

yonski

Member

Registered: 2005-12-14

Posts: 67

Gas flow problem!

Hi there,
this one is bugging me. I've written everything down methodically but i seem to end up with 3 equations and 4 unknowns. I can't see what i'm missing   Any help appreciated!!

"Two containers of volumes VA = 6.4x10^-2 m³ and VB = 2.7x10^-2 m³ contain 7 and 3 moles of the same gas, respectively. The containers are communicating via a tube with a valve which is initially shut. The voume of the connecting tube is negligible. The temperatures in the two containers are initially TA = 400k and TB = 600K respectively. The valve then opens and after gas transfers from one container to the other, the two gases reach equilibrium (i.e. the two containers are at the same temperature and pressure).

Find the number of moles in each of the containers and also the pressure and temperature of the gas."

Thanks!

Last edited by yonski (2007-10-01 09:32:01)

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Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

Hunt

Member

Registered: 2007-09-29

Posts: 9

Re: Gas flow problem!

I assume you are dealing with ideal gases. Our system is closed and no chemical reaction occurs so n = constant. The equation of state obeyed is :

Isolate each container and work on it. First we calculate the initial pressures.

'i' = initial state
'f' = final state

Hence, intial P , V , and T for both A and B are known. ( check the given )

After the two gases mix , they form a single gase of certain pressure, temperature, and volume. Each ideal gase occupies all the volume available as if they were alone. Since our gas is ideal, then the total pressure of this mixture of gases is the summation of the two gases. This is known as Dalton's law of partial pressures.

For each of the containers, the following holds true for a closed system :

Take the ratio :

I do this to form a relation bettween the partial pressures of A and B since the "ratio" is known.

We have to uknowns and a single equation, so we need another.

Again from Dalton's law,

Again, take the ratios :

We have a system of 2 equations 2 unknowns, Solve using eq(1) and eq(2) to find partial pressures of A and B. Once determined, the total pressure is determined as well by simply addition of partial pressures.

To find the final temp , apply :

Finally to find the number of moles in each container, it is simple. Each container has some unknown number of particles , but in both containers the pressure and tempreaure is the same. ( Eq is established ).

In container A , the number of particles is :

In container B, the number of particles is :

I am sorry for not doing the calculation, but I think that should no problem to you.

Incase of doubt, do return.

yonski

Member

Registered: 2005-12-14

Posts: 67

Re: Gas flow problem!

I'm a bit confused. You talk about

and

but what are these? From the naming convention you've used it suggests they're the final pressures in conatiners A and B, but I thought these were equal?

---

Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

Hunt

Member

Registered: 2007-09-29

Posts: 9

Re: Gas flow problem!

yonski , this is how it goes:

Initially , we have two containers each of certain initial pressure , temp, and volume. After the valve is open, the gases mix to form a single gas. However, this 'gaseous mixture' is formed of two gases , one coming from container A and another from B. The partial pressures of A and B ( which r not equal ) form the total final pressure of the entire system ( 2 containers ). This pressure is the same thoughout.

Last edited by Hunt (2007-10-01 11:32:07)

Hunt

Member

Registered: 2007-09-29

Posts: 9

Re: Gas flow problem!

To understand you have to review dalton's law on partial pressures:

Take the simple case. Gas A of initial pressure p_a mixes with Gas B of initial pressure p_b.

What is the total pressure ?

Chi is a mole fraction. I think u r familiar with this from ur general / highschool chemistry literature.

Now take the case above where each gas is in its own container, and each gas has its own pressure, temp , and volume. You cannot use the same argument to find the total pressure. As I said, isolate each container.

What happens to the gas in container A after the valve is open? Its pressure, temp, and volume should change. How do they change ? according to the ideal gas equation.

PV=nRT for initial case
P'V' = nRT' for final case

but n is constant ( closed system )

so PV / T = P'V'/T'

this way you find the new partial pressure of A ( assume T is known here , V' = V_a + V_b ).

Same argument holds for container B. Next you add both new partial pressures p_a + p_b to get the total pressure of the gaseous mixture formed.

I hope this makes thing clearer.

Last edited by Hunt (2007-10-02 10:34:43)

yonski

Member

Registered: 2005-12-14

Posts: 67

Re: Gas flow problem!

Yeah thanks, I understand it now i think   We have not even discussed Dalton's law of partial pressures in our lessons yet so that's why it confused me a bit. I wish my teacher would teach things first before asking questions on them lol!

Thanks for your help. It's getting late here now so i'll return in the morning to calculate the answers.

---

Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

Hunt

Member

Registered: 2007-09-29

Posts: 9

Re: Gas flow problem!

It's ok if u dont get it for the 1st time. Once you've gone over and fully understood the basic laws of ideal gases, a problem like this one can be tackled easily and understood better. Incase there's something wrong with the answers ( assuming u have a solution manual ) or you have a specific question, do come back.