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Chemistry Forums for Students => Inorganic Chemistry Forum => Topic started by: chehemi123 on November 30, 2012, 01:58:47 PM

Title: calculating partial pressures
Post by: chehemi123 on November 30, 2012, 01:58:47 PM
hey guys,

I have got the following problem:
I want to calculate the partial pressure of (SO3), (SO2) and (O2).
The reaction: SO2 + O2 --> SO3
The pressure p is 1,02bar. The temperature is 873K.
Kp is 65,1.

I came to this equations:

Kp= p2(SO3)/p2(SO2) · p(O2)
and
p=p(SO3) + p(SO2) + p(O2)

How can I calculate the partial pressure of SO2, SO3 and O2 ?
I think there must be another equation. Because there are 3 variables.
Maybe another condition by the temperature?

Can you help me?
Thanks in advance !
Title: Re: calculating partial pressures
Post by: fledarmus on November 30, 2012, 03:08:17 PM
Do you know the starting point of the system? All reactants or all products, perhaps?
Title: Re: calculating partial pressures
Post by: curiouscat on November 30, 2012, 03:11:03 PM
Do you know the starting point of the system? All reactants or all products, perhaps?

And further if all reactants than you need the ratio of SO2 : O2 that you start with.

As stated the problem is under-specified.
Title: Re: calculating partial pressures
Post by: chehemi123 on November 30, 2012, 04:08:56 PM
yes:

it is said: there is more or less no SO3 and the part by volume of SO2 is 10%.
Title: Re: calculating partial pressures
Post by: fledarmus on November 30, 2012, 04:12:19 PM
Ah - then you know the starting partial pressures of SO2 and O2, and that will let you write an equation relating the three concentrations at any point during the reaction.
Title: Re: calculating partial pressures
Post by: chehemi123 on November 30, 2012, 04:23:43 PM
how can i calculate the starting partial pressures?  ???
do i need the starting (total) pressure?
Title: Re: calculating partial pressures
Post by: fledarmus on November 30, 2012, 04:31:11 PM
I was assuming that the pressure and temperature you gave were constants during the reaction
Title: Re: calculating partial pressures
Post by: chehemi123 on November 30, 2012, 04:54:13 PM
I am not quite sure....

this is the task:

SO2 is produced by sulphur and O2. This gas mixture is more or less without SO3. The part by volume of SO2 is about 10%. This mixture is conducted through a kiln. There the equilibrium is maintained by the current pressure of 1,02 bar and 873K.

Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 05:46:26 AM
i hope you can understand me. I am from switzerland actually and studying in America!
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 06:17:33 AM
is the ratio of SO2 : O2 the same throughout the whole reaction? or is it changing? because 1mol O2 and 2mol SO2 react...so the ratio actually should change?!
Title: Re: calculating partial pressures
Post by: curiouscat on December 01, 2012, 07:26:02 AM
Assume  1 gmol feed basis
Let x be moles of O2 reacted

            2 SO2 +  O2 --> 2 SO3
Before:    0.1     0.9      0
IN:          0.1-2x  0.9-x    2x

Total moles 1-x

Mole frac.
[tex]
 x_{SO_2}=\frac{0.1-2x}{1-x}  \\

 x_{O_2}=\frac{0.9-x}{1-x} \\

  x_{SO_3}=\frac{2x}{1-x}  \\
[/tex]

[tex]
P_{SO_2}=\frac{(0.1-2x)}{(1-x)}P \\
P_{O_2}=\frac{(0.9-x)}{(1-x)}P  \\
P_{SO_3}=\frac{2x}{(1-x)}P   \\
[/tex]

[tex]
K_p= \frac{P^2_{SO_3}}{ P^2_{SO_2} · P_{O_2} } \\

K_p=\frac{ 4x^2 . (1-x) .P }{ (0.1-2x)^2 . (0.9-x)  } \\
[/tex]

P = 1.02bar. Kp = 65.1

Now you have only x as a variable. Solve.

[tex]
\frac{1.02}{65.1} = \frac{ 4x^2 . (1-x) }{ (0.1-2x)^2 . (0.9-x)  }
[/tex]
That's a cubic; you ought to get three solutions.

Use x = 0.005305; find a good reason to throw the rest away..[x seems a bit too small; Only 5% of the SO2 reacting away; makes me a bit suspicious I've some bug in my solution. ]

Leave it to you to calculate the partial pressures.

Now, you can hope that I've not messed up my arithmetic.....But I'm pretty sure I have (especially since I already found and corrected 3 mistakes; there's probably more). So redo it yourself!  ;D
Title: Re: calculating partial pressures
Post by: curiouscat on December 01, 2012, 07:58:20 AM
i hope you can understand me. I am from switzerland actually and studying in America!

Quote
The pressure p is 1,02bar.  Kp is 65,1.

Now that you've Americanized yourself, might as well  get rid of the habit of using swapped punctuation.  ;D

OK, I'm KIDDING. But it might confuse a few people on this side of the bathtub.  ;)
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 11:40:21 AM
you're a legend !  :)  Thanks a lot! I am going to redo it and will tell you if there´s a mistake  ;)

Quote

Now that you've Americanized yourself, might as well  get rid of the habit of using swapped punctuation.  ;D

OK, I'm KIDDING. But it might confuse a few people on this side of the bathtub.  ;)

I will do my best and try to get rid of it  ;D
Title: Re: calculating partial pressures
Post by: curiouscat on December 01, 2012, 12:04:45 PM
I was assuming that the pressure and temperature you gave were constants during the reaction

It would be nice if they were indeed constant. But I don't think that assumption is needed.

In fact, I'm still confused why the T was provided at all. Unless I am making a mistake in my solution?
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 12:25:18 PM
maybe the temperature is only there for confusing? :P
but i am not quite sure really...
And there is no pressure and temperature ( at the start ) provided...

I was just redoing the calculation:

is it:

Quote
[tex]
K_p= \frac{P^2_{SO_3}}{ P^2_{SO_2} · P_{O_2} } \\

K_p=\frac{ 4x^2 . (1-x) .P }{ (0.1-2x)^2 . (0.9-x)  } \\
[/tex]
 

my solution was:
K_p=\frac{ 4x^2 . (1-x) }{ (0.1-2x)^2 . (0.9-x) .P  } \\
[/tex]
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 12:27:14 PM
ah sorry...I meant that P is in the denominator ?
Title: Re: calculating partial pressures
Post by: curiouscat on December 01, 2012, 12:42:20 PM
ah sorry...I meant that P is in the denominator ?

You are right.

[tex]
1.02*65.1 = \frac{ 4x^2 . (1-x) }{ (0.1-2x)^2 . (0.9-x)  }
[/tex]

What does that give; x=0.044?

 It'd mean ~88% conversion on SO2.  That sounds like a way more reasonable answer.
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 01:18:20 PM
I am not that good in solving these cubics...

I might find a program which can calculate x  :P
Title: Re: calculating partial pressures
Post by: curiouscat on December 01, 2012, 01:51:59 PM
I am not that good in solving these cubics...

I might find a program which can calculate x  :P

Use Brute Force and Bisection. 0<x<0.05 is not a big range.
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 01:55:45 PM
I got

x1= 0,0442599
x2= 0,0574578
x3= 0,898282

x2 and x3 are thrown away ( cause X(So2) would be negative...) ;)

wooop  :D
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 02:08:57 PM
oh, by the way there is another little problem.

If I have the parts by substance amount of SO2, O2 and SO3 at the equilibrium at 1000K and 1,013*10^5 Pa.

Can I calculate Kp?

Kx= x2(SO3)/x2(SO2)*x(O2)

I found:
Kx= Kp · (p/pt)2

with p/pt as a pressure factor?

is this way right?
Title: Re: calculating partial pressures
Post by: curiouscat on December 01, 2012, 02:19:55 PM
What's p and pt
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 02:25:46 PM
I don´t really know  ;D
I read it somewhere in the internet...
but shouldn´t be right..

Do you know any relation between Kp and Kx ? o0
Title: Re: calculating partial pressures
Post by: chehemi123 on December 01, 2012, 03:12:41 PM
found it:

https://docs.google.com/viewer?a=v&q=cache:7g96HWjj1RIJ:www.psci305.utep.edu/ch1305/Chapter12/gc12.pdf+relation+Kx+Kp&hl=de&gl=de&pid=bl&srcid=ADGEESjpvGVc4ZUnGO_SQ99s13qurl5o3svtmwFTLjMNgfyHgJaNvGUbHi67awMB7G28-nKq_HwB6sDnWGY8PYeqYEAN0IsBE5bBjYeHJUvEq0dxIPfqK09jjNaxdApHGUF05iIhwnKG&sig=AHIEtbS8pBDI7-qGLKYOUUg06vUSHZXSNQ
(page 7)

should be:

Kp=Kx · ptotΔn

hope so  :P