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### Topic: Operating Line vs. Equilibrium line  (Read 23997 times)

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#### moleman1985

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##### Operating Line vs. Equilibrium line
« on: April 24, 2007, 09:10:16 AM »
Hello, I have constructed the following graph of an equilibrium line and operating line. The basic principle is the removal of water from a gas stream using H2SO4, I had to use partial pressures as equilibrium data, as no other were available.
The operating line is the, mole fraction of water (x) vs. partial pressure of water of H2SO4 (pa).
The equilibrium line is the, mole fraction of water (x) vs. partial pressure of water of H2SO4 (pa) / the mole fraction of water (x).
The graph is completely mine from scratch including all the annotations, I was wondering if someone could tell me if my annoatation are correct. Also I think that the x-axis, from 0.1-0.64 the range covered represents the column ie. half way inbetween 0.1-0.64, would mean half way through the column, if this is the case then this would tell me the ratios heights and separation of the trays and packing in the column, as I dont yet know the column height.

Is this correct?
« Last Edit: April 25, 2007, 11:25:01 AM by geodome »

#### Donaldson Tan

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##### Re: Operingtin Line vs. Equilibrium line
« Reply #1 on: April 24, 2007, 03:32:11 PM »
Why is your equilibrium line intersecting the x-axis at 0.1 and not 0?

http://en.wikipedia.org/wiki/McCabe-Thiele_method
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### moleman1985

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##### Re: Operingtin Line vs. Equilibrium line
« Reply #2 on: April 24, 2007, 04:32:36 PM »
I also found this a bit strange but the solvent starts off with a 0.1 precent mole fraction of the solute in it, does that explain it? I dont know if its a true equilibrium curve just the water vapour pressure thats in equilibrium with the water in the solvent.

thanks

#### moleman1985

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##### Re: Operingtin Line vs. Equilibrium line
« Reply #3 on: April 24, 2007, 04:40:09 PM »
the y-axis is the partial pressure of water vapour over the H2SO4 by the way, the data was from Perry's 6th Edition.

#### Donaldson Tan

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##### Re: Operingtin Line vs. Equilibrium line
« Reply #4 on: April 24, 2007, 06:50:09 PM »
Your graph suggests infinite number of stages - something is wrong.
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### moleman1985

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##### Re: Operingtin Line vs. Equilibrium line
« Reply #5 on: April 24, 2007, 09:11:26 PM »
Hi, thanks geodome for the interest, I actually realised a big flaw in my graph even though my process is an absorption, I have actually mis-labeled the operating line and equilibrium line the wrong way around (in the graph psoted above), this cannot be correct as the operating line should be above the equilibrium line, I'll try sort this out and get back, thankyou.

#### moleman1985

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##### Re: Operingtin Line vs. Equilibrium line
« Reply #6 on: April 24, 2007, 10:55:08 PM »
Hello, I have re-done I few calculation and approached the problem for a mole fraction point of view instead of a partial pressure point of view, a got exactly the same shape graph but obviously with different values.

Geodome, are you saying that there is something wrong just because the operating line and the equilibrium lines close together, because that graph I drew (the stepping) is very accurate I zoomed in about 1000% and the difference between the lines was large at this zoom so I know that the stepping is very accurate.

I definetly understand if my design is wrong because as the lines are coming together as I think your saying, using an equilibrium curve that goes to 0,0, does actually give a graph with about 2 steps in which seem more sensible.

Thankyou.

#### moleman1985

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##### Re: Operingtin Line vs. Equilibrium line
« Reply #7 on: April 25, 2007, 11:12:57 AM »
Hello, I'm going at it from now on from a mole fraction point view not partial pressures although they give exactly the same graphs, my new graph now is below, but I have forced this graph out from the data without understanding why is happens

To get y* the amount of solute (water) in the gas phase in equilibrium with the water in the solvent, I have multiplied the mole fraction of water in the vapour phase (y), by the mole fraction of water in the solvent (x), the curve is x vs. y*, and I will be using the operatin line and explapolating lines to the equilibrium curve to get the vales of y*, at y.

I dont understand why I have been forced to multiply y by x to get y*, I would have thought I should have done y divided by x, but this gives an equilibrium line above the operating line which would mean it was a stripping column but this is an absorption column.

Any help please or confirmation that the graph I have produced is correct and the value of y* (equilibrium curve) is, x mulitplied by y.

#### Donaldson Tan

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##### Re: Operating Line vs. Equilibrium line
« Reply #8 on: April 25, 2007, 11:33:01 AM »
To get y* the amount of solute (water) in the gas phase in equilibrium with the water in the solvent, I have multiplied the mole fraction of water in the vapour phase (y), by the mole fraction of water in the solvent (x), the curve is x vs. y*, and I will be using the operatin line and explapolating lines to the equilibrium curve to get the vales of y*, at y.

I dont understand why I have been forced to multiply y by x to get y*, I would have thought I should have done y divided by x, but this gives an equilibrium line above the operating line which would mean it was a stripping column but this is an absorption column.

Your equilibrium line looks dodgy. Where in Perry's did you get your H2SO4-Water data? I will need to take a further look into it. Why not attached your Excel worksheet here?
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### moleman1985

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##### Re: Operating Line vs. Equilibrium line
« Reply #9 on: April 25, 2007, 01:46:43 PM »
Hi, no I didnt get the data from perry's for the mole fraction point of view, I just assumed a constant mass transfer, I knew the y,x in and y,x out show changed them equally amoungst 10 evenly spaced points.
I have below the graph using data from perry's for the partial pressure point of view, I got data from perry's at 55oC, and drew a graph from the data I got and used that graph to get the partial pressure I actually needed at the 10 points, assuming that the acid dilutes from 98% to 75% at a constant rate.
Again to get pa* or the equilibrium data, I multiplied pa by x. The graph will give a two steps like the one I drew for mole fractions.
I am hoping this graph is correct as the equilibrium line clearly shows the system obeying to Henry's law for dilute streams at the top of the column (bottom half of the equilibrium curve) a low gradient, and obeying Raoult's law at the bottom of the column (top of the graph) for concentrated stream a high gradient.

The data for partial pressure is definetly correct I am just unsure about about how to get pa*. The only thing that seems to give any knid of appropiate graph is by multiplying pa by x, but this seems wrong as I am mixing partial pressures with mole fractions, but I hope that because the system is at 1 bar the mole fraction of water will represent the pressure of water in the solvent.

Let me know what you think thanks loads.

#### Donaldson Tan

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##### Re: Operating Line vs. Equilibrium line
« Reply #10 on: May 10, 2007, 08:14:35 PM »
Can you attach a file with numerical data instead of pictorial data?
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006