Volume Change in Phase Transitions

[Minihoudini]

Homework Statement

It's not so much an exact question. One of the things I need to figure out to answer my question is if there is a formula of some sort that helps me calculate volume change through a phase change. The final volume of a liquid that vaporizes into a gas, if the temperature and pressure is constant in an inclosed space.

Homework Equations

The Attempt at a Solution

I was thinking maybe w=-nRTln (Vfinal)/(Vinitial)

any help would be fantastic.

 

[BvU]

Well, small Harry,

Depending on how accurate you want your formula, anything between zero extra information and a lot of physical property information is needed to determine this volume change.

I start with the simplest possible formula:
1 mol of liquid has volume zero (or: negligible volume)
1 mol of ideal gas at standard T and p has volume 22.4 dm³

Example:
liquid water 18 grams, 18 *10^-6 m³
water vapour 18 grams 22.4 *10^-3 m³
The difference is equal to the water vapour volume to a very good approximation, isn't it ?

 

[Minihoudini]

alright, well I suppose to clarify I'm attempting to figure out a simple 1cc of liquid glycerol to gas. From what I calculated was 214.9cc with a (2.961 atm).

Edit: I just realized you called me small Harry. Gave me a large smile! and thank you for your help.

 

[BvU]

From what I calculated was 214.9cc with a (2.961 atm).

Looks as if the cat walked on the rubout key. Can you show your calculation ? Is it for 1 g or for 1 mole ?

In the mean time I found a mol wt of 92 and a density of 1261 kg/m³ for the liquid, so 0.116 dm³/mol.

And glycerol has a boiling point of 290 $^\circ$C at 1 Atm.

So ideal gas law has at least V/n = RT/p, i.e. 15.6 dm³/mol at 3 Bar for the vapour.
(I used T = 563 K, should have used the boiling temperature at 3 Bar. Need e.g. coefficients for the Antoine equation to do that. Not now, bedtime. )

If using pV = nRT (i.e. treating the vapour as an ideal gas) really isn't good enough, you can step up to an equation of state (e.g. de Van der Waals, Peng Robinson, Redlich Kwong Soave).

 

[Minihoudini]

I used 1 mole. Here is my calculation

n= (1.26g)(1mol/92.093892g)= 0.013682267

[(0.013682267)(0.0826)(563.15k)]/(2.961) = 0.2149L
1cm3= 214.9cc

2.961 pressure was used as opposed to straight 1 atm since it's in a vessel that places pressure on liquid in addition of heating the glycerol into a gas. My general knowledge of chemistry is pretty rusty, but in more realistic situation maybe I should use an equation of state formula. Again thank you so much for helping me!

 

[BvU]

My mistake: I should have started with so 0.073 dm3/mol (92 g/mol / (1.261 g/cm3) * .001 dm3/cm3)

Your last post is confusing with all the = = = but I see you let 1 cm3 of liquid go to 215 cm3 vapour. Same ratio.

 

[Minihoudini]

Sorry about that, I just fixed it so I hope that makes it more clear. So by same ratio are you saying it's similar if not the same of what you got with it scaling for pressure? it's been a long day so I might be a little dense.

 

[BvU]

You calculate 1 cm3 to 214 , I calculate .073 dm3 to 15.6. Same calculation, same ratio.
Late here too (02:30), have a course tomorrow: bedtime .

 

[Gene Climer]

I have a different question related to volumetric expansion of air and fuel. The air (N2, O2) is moved over a temperature delta of 230F from 70F to 300F. 1^3 foot of air at 70F will expand to some new volume when it is heated to 300F. Next, a small amount of gasoline fuel is introduced to the air at 70F with a Stoichiometric Air/Fuel Ratio of about 14:1 AFR. The fuel is mixed, atomized/sprayed, at 70F. As the liquid gasoline goes through the phase change to 300F, it should become much larger. My question is what is the ratio of volumes at 70F and 300F? I have no idea how to arrive at this, not being a chemist, and having long forgotten, if I ever even knew, any of the formulas you have discussed so far. Thanks for any insight you can offer. Keep it simple, in other words, please explain every symbol used so I can follow the logic and calculations. Thanks. Gene

 

[BvU]

@Chestermiller : do you want to take this on ? and perhaps gently steer this newcomer towards decent PF culture ?

Gene !

 

[Chestermiller]

@Chestermiller : do you want to take this on ? and perhaps gently steer this newcomer towards decent PF culture ?

Gene !

I'll give it a shot.

 

[Chestermiller]

I have a different question related to volumetric expansion of air and fuel. The air (N2, O2) is moved over a temperature delta of 230F from 70F to 300F. 1^3 foot of air at 70F will expand to some new volume when it is heated to 300F. Next, a small amount of gasoline fuel is introduced to the air at 70F with a Stoichiometric Air/Fuel Ratio of about 14:1 AFR. The fuel is mixed, atomized/sprayed, at 70F. As the liquid gasoline goes through the phase change to 300F, it should become much larger. My question is what is the ratio of volumes at 70F and 300F? I have no idea how to arrive at this, not being a chemist, and having long forgotten, if I ever even knew, any of the formulas you have discussed so far. Thanks for any insight you can offer. Keep it simple, in other words, please explain every symbol used so I can follow the logic and calculations. Thanks. Gene

Gene,

Please start this as a separate thread, since it is so different from the original problem.

What is your motivation for asking these questions? Are you trying to understand the gas flow an the intake manifold? I can help you figure out the answers to what you are asking. I will keep a watch out for the new thread that you start. Please use a descriptive title.

Chet