Tony Withers: Fugacity Calculator

## The Pitzer and Sterner Equation of State for Water

The fugacity calculator uses JavaScript to determine the molar volume and fugacity of pure water from the Pitzer and Sterner (1994) equation of state. The Dekker method is employed to solve numerically for volume as a function of pressure and temperature. Fugacity is calculated using the analytical solution presented in Sterner and Pitzer (1994):

ln f = [lnρ + Ares/RT + P/ρRT]P,T + ln(RT) - 1,

where f is fugacity, Ares is residual Helmholtz energy, ρ is 'molar' density (n/V) and P, T, R are pressure, temperature and the universal gas constant, respectively.

# Fugacity Calculator

Enter pressure (GPa), Temperature (°C) and click the "Calculate" button:

Pressure:
GPa
Volume =
cc/mol
Temperature:
°C
Fugacity =
GPa

You can adjust the initial guesses for the bracketing interval:
Low bracket:
cc/mol
High bracket:
cc/mol

##### Notes
The code is based on a JavaScript root finding algorithm adapted from a Fortran routine written by Shapine and Watts ( fzero.f , part of the SLATEC library of programs). Any errors that have been introduced are due to my bastardisation of the code. I don't guarantee that it works! I'm at least reassured that my independently coded numerical integration of the Pitzer and Sterner EOS gives the same results as this JavaScript implementation of the analytical solution. You can always check by calculating the fugacity for yourself, using the equations in Pitzer and Sterner (1994).

#### References

```	Dekker, T.J. Finding a Zero by Means of Successive Linear Interpolation.
In: Constructive Aspects of the Fundamental Theorem of Algebra.
Ed. B. Dejon and P. Henrici. Wiley-Interscience, 1969.

Pitzer, K.S. and Sterner, S.M. (1994). Equations of state valid continuously
from zero to extreme pressures for H2O and CO2. Journal of Chemical Physics.
101: 3111-3116.

Shampine, L.F. and Watts, H.A.(1970). FZERO, A Root-solving Code.
Report SC-TM-70-631, Sandia Laboratories.
Sterner, S.M. and Pitzer, K.S. (1994). An equation of state for carbon dioxide
valid from zero to extreme pressures. Contributions to Mineralogy and Petrology.
117: 362-374.

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We gratefully acknowledge the National Science Foundation and the
University of Minnesota for support of the research and information
described on these pages.

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The views and opinions expressed in this page are strictly those of the page author.
The contents of this page have been neither reviewed nor approved by the University of Minnesota.