Expression for Boiling Point Prediction 1

[niallmacdubhghaill]

Hi all,

I have a question regarding the prediction of a boiling point of an oil at varying pressures.

I have a natural/essential oil whose thermodynamic properties I know at 1atm. The properties I have are density, viscosity, specific heat capacity, latent heat of vapourisation and its vapour pressure.

What I want to do is to predict the boiling point at 1.5atm. I would imagine that there should be some expression to predict this, but Im having difficulty in finding it.

Note: I do not know the critical temperature or critical pressure of this substance (it is D-Limonene, is that helps anyone)

If anyone knows a good method of predicting the boiling point at a different temperature, that is suitable for use by hand, please let me know.

All help/input appreciated.

Niall

 

[mbeychok]

Niall:

If your oil is a single-component oil (as differentiated from multi-component petroleum oils), then you may be able to find the Antoine equation coefficients for your oil. To learn more about the Antoine equation coefficients and where to find lists of them, read [URL unfurl="true"]http://antoine.frostburg.edu/chem/senese/101[/url] and search for "Antoine equation".

You might also find the Antoine coefficients for your oil in the NIST web site at [URL unfurl="true"]http://webbook.nist.gov/chemistry/[/url]

The Antoine equation is usually in this form:

Log P = A - B/(T - C)

where P is the vapor pressure; A, B and C are coefficients; and T is the absolute temperature.

Hope this helps.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[25362]

The Clausius-Clapeyron equation may be of help:

dlnP/dT = [λ][sub]vap[/sub]/RT[sup]2[/sup]​

which, after integration, becomes:

ln P[sub]2[/sub]/P[sub]1[/sub]= -[λ][sub]vap[/sub]/R(1/T[sub]2[/sub]-1/T[sub]1[/sub])​

[λ][sub]vap[/sub], latent heat of evaporation, in cal/mol
R =1.987 cal/(mol.K)
T is in K

 

[niallmacdubhghaill]

Thanks 25362,

I had considered using that expression, but I was under the impression that it was just for phase change operations, or does the question of boiling point presuppose a phase change and as such this expression is valid to use here?

Im sorry, my thermo is a little rusty!!

Niall

 

[25362]

Yes, the boiling point pressuposes a phase change.
Yes, the given formula is used to predict the boiling point at other pressures, as you requested.

The C-C equation started from dP/dT = [Δ]S/[Δ]V. For a (reversible) equilibrium change of phases [Δ]S ~ [λ]/T.
Since [Δ]V ~ RT/P, we obtain the C-C equation

dlnP/dT ~ [λ]/RT[sup]2[/sup]​

which, we repeat, contains the following approximations:

[•] [λ][sub]vap[/sub] ~ constant,
[•] the specific volume of the vapor phase is larger
than that of the liquid (or solid) [Δ]V = V[sub]gas[/sub]-V[sub]liq[/sub] = V[sub]gas[/sub],
[•] V[sub]gas[/sub] = RT/P as for an ideal gas,

all of which have a minor effect on the precision of the result when dealing with low and close pressures, as in the case in hand.

Of course, the accuracy of the C-C equation depends on the accuracy of [λ][sub]vap[/sub] and T[sub]1[/sub].
BTW, if [λ] is in J/mol, R = 8.314 J/(mol.K).

 

[insult2injury]

I believe at low temperatures, the C-C equation produces a large amount of error. The error is also somewhat dependent on the material as well.

 

[25362]

More exact correlations involve knowing the critical properties. However, it has been shown for many compounds that lnP = [ƒ] (1/T) is nearly a straight line (see, for example, the Cox chart).

The C-C formula, apparently preferred by chemists, sometimes called the approximate Clapeyron equation, is better applied in a narrow interval of temperatures or pressures (to justify the reasonable constancy of [λ]) and well-distanced from the critical point.

 

[niallmacdubhghaill]

All,
thanks for the help. I have used the C-C eqn, and have gotten an answer which seems to have met with some general agreement.
Your help is greatly appreciated.
Cheers
Niall

 

[DickRussell]

For D-limonene, NBP= 450.6 K, Tc= 653 K, and vp= 1.5 atm at T=468.6 K.

 

[niallmacdubhghaill]

Dick
Thanks for that, the Tc value is really useful to have.
Niall

 

[niallmacdubhghaill]

Dick,
I dont suppose you know what the critical pressure is as well?
Thanks again
Niall

 

[joerd]

I found slightly different values in HYSYS:
Mol weight 136.21
NBP 176.5 C
Tc 376.85 C
Pc 27.5 bara
Vc 0.524 m3/kgmole
Acentricity 0.3123

Cheers,
Joerd

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[niallmacdubhghaill]

Joerd,
thanks,thats really useful.
Niall

 

[niallmacdubhghaill]

Guys,

I wonder if any of you would have access to the archives of the journal "Industrial & Engineering Chemistry Research".
I would be very interested in seeing a copy of an article from 1943, the reference is as follows:

Watson, K.M. Ind. Eng. Chem., 35, 398 (1943)

Thanks

Niall