# Rocket propellants: accuracy of vapor pressure estimation techniques

I would like to determine the vapore pressures of a couple of substances (rocket propellants) over a significant temperature range within a ~10% error margin.

For a first test, I tried to approximate the vapor pressure curve of Dinitrogen Tetroxide (N2O4) via the Clausius-Clapeyron (CC) relation, the Lee-Kesler (LK) method and the Ambrose-Walton (AW) method and compare the results to each other and to literature values that are available for N2O4. Unfortunately my results deviate alot (up to 60%) from the published values.

Attached you find a plot of my attempts and a small table that compares the different methods and their deviation from the literature values. Don't let the first picture mislead you! As the table and the detailview show, even at low pressures/temperatures the deviation is quite significant!

Is this large error margin really within usual boundaries? What are your experiences with vapor pressure approximation? Could you provide some tips on how to improve my results?

Some Details on my approach

Clausius-Clapeyron:

I chose the boiling temperature at atmospheric pressure as input, but I have no idea which value to choose for the enthalpy of vaporisation. Many source state the assumption of a constant enthalpy, but that puzzles me, since for N2O4 it varies by some 16kJ/mol over the temperature range I'm interested in.

Which value is usually taken - the enthalpy corresponding to the values provided as input or the one for the target temperature?

Lee-Kesler / Ambrose-Walton:

As expected both methods produce very similar results and are convenient to use, since they only rely on the critical pressure, critical temperature and the acentric factor. But MY results are really disappointing, especially since Wikipedia promises a maximal deviation of 10%.

As a side note:

For different reasons, I don't want to use interpolation of substance specific vapor pressure tables, but instead I would like to use one of the many vapor pressure equations. It is important that the approximation results in a closed representation of the vapor pressure curve , therefore I would like to avoid methods that have points of discontinuity (e.g. Antoine equation?). Since I don't have access to public databases that cover the substances I'm interested in, approximations that rely on "exotic" empirical parameters (Wagner, DIPPR, etc.) are also out of the question.

• To give a good answer to this question we need to know what compounds you are talking about. Jan 13, 2016 at 14:26
• For a first test, Dinitrogen Tetroxide is my main concern. Later on, I'll have to deal with a range of different substances like: liquid hydrogen and liquid oxygen - all kinds of hydrazines (UDMH, MMH, N2H4) - Nitric Acid (HNO3) - Hydrogen Peroxide (H2O2) Jan 13, 2016 at 14:39
• with N2O4 you should take in account dissociation of N2O4 into NO2 molecules. Which invalidates assumption used by equations present, as the pressure above the liquid is not defined by vaporised compound only, but also by products of its reversable decomposition (which, to lesser extent, happens in liquid state in addition to auto-ionization =)) Jan 13, 2016 at 17:04
• @permeakra How serious is the impact of that effect? Do I have to assume that none of the popular equations will output reasonable results for N2O4 or are the results just less realiable and my calculation are within usual boundaries? (I'm a mechanical engineer and my knowledge about chemistry is very limited) Jan 13, 2016 at 17:45
• Have you tried doing a least squares fit to the ln p vs T data to determine the three parameters in the Antoine equation consistent with your own data? Jan 13, 2016 at 17:46

I would like to determine the vapor pressures of a couple of substances (rocket propellants) over a significant temperature range within a ~10% error margin.

The best way to determine vapor pressures is to measure them. Is that not an option for you?

It is important that the approximation results in a closed representation of the vapor pressure curve , therefore I would like to avoid methods that have points of discontinuity (e.g. Antoine equation?).

The Antoine equation isn't discontinuous by nature, it's only discontinuous if you use two different parameter sets for a single substance in order to widen the temperature range of applicability of the equation.

What are your experiences with vapor pressure approximation? Could you provide some tips on how to improve my results?

I would recommend the Antoine equation as a first step beyond the Clausius Clapeyron equation. Unlike the CC equation, the Antoine equation does not assume that the enthalpy of vaporization is independent of temperature. It also provides a single, closed-form representation of the vapor pressure dependence on temperature.

Unfortunately, the Antoine equation requires compound-specific parameters.

However, many of the other methods you report using, such as the Lee-Kesler and Ambrose-Walton methods, also require compound specific parameters: specifically, the critical temperature and pressure of the compound of interest. Even the Clausius-Clapeyron equation requires an (assumed constant) enthalpy of vaporization, which is also a compound-specific parameter.

Thus, the Antoine equation is probably the best place to start. As Wikipedia shows, it can have accuracy better than 10% deviation for some compounds. Ideally you would measure vapor pressures for your two compounds and then fit the data to the Antoine equation. If measuring the vapor pressure of your compound is not possible, you could start by examining the Antoine equation predictions for a series of compounds that approximate your unknowns in chemical structure and molecular weight. However, with this latter approach, I doubt error under 10% will be possible.

## Antoine equation parameters for your compounds of interest

• Thanks for your great effort on answering my question! I have to play a bit with the Antoine equation before I can make any useful comments on your suggestions. I'll return to you later! PS: I'm don't know much about chemistry, could you maybe comment on cryogenic substances (LH2/LOX) and if vapor pressure approximation for those compounds is any different? Jan 13, 2016 at 15:19
• If you found the answer useful, an upvote would be appreciated :-) [And, if in a few days no one has posted a better answer, an answer acceptance as well] Jan 13, 2016 at 16:06
• Sure, but you need 15 rep to upvote and I only have 6... :) Jan 13, 2016 at 16:28