Wagner equation

The Wagner equation describes the relationship of the saturation vapor pressure P with the temperature T . It is a purely empirical equation.

the equation

In the original publication the following equation is defined:

${\displaystyle \ln P_{\mathrm {r} }={\frac {n_{1}\cdot \tau +n_{2}\cdot \tau ^{1,5}+n_{3}\cdot \tau ^{3}+n_{4}\cdot \tau ^{6}}{T_{\mathrm {r} }}}}$

with , the reduced pressure and , the reduced temperature, and . ${\displaystyle P_{\mathrm {r} }={\frac {P}{P_{\mathrm {c} }}}}$ ${\displaystyle T_{\mathrm {r} }={\frac {T}{T_{\mathrm {c} }}}}$ ${\displaystyle \tau =1-T_{\mathrm {r} }=1-{\frac {T}{T_{\mathrm {c} }}}}$

Ambrose changed the exponents as follows:

${\displaystyle \ln P_{\mathrm {r} }={\frac {n_{1}\cdot \tau +n_{2}\cdot \tau ^{1,5}+n_{3}\cdot \tau ^{2,5}+n_{4}\cdot \tau ^{5}}{T_{\mathrm {r} }}}}$

and used this form in the Ambrose-Walton method , a correspondence principle method for estimating the saturation vapor pressure.

The parameters n ₁ , n ₂ , n ₃ and n ₄ are substance-specific and are adapted to experimental saturation vapor pressures. The Wagner equation is able to describe the entire saturation vapor pressure curve from the triple point to the critical point with high accuracy.

Example parameters

The parameters apply to the 2.5 / 5 variant:

	n 1	n 2	n 3	n 4	P c / kPa	T c / K
water	−7.18274	−0.00412	0.00825	−4.46463	22048	647.3
Ethanol	−9.28741	3.15687	−7.72514	6.07037	6383	516.2
benzene	−6.84783	1.01932	−1.02347	−5.1528	4894	562.1
acetone	−7.66267	1.95961	−2.54259	−2.23283	4701	508.1

Further examples:

	n 1	n 2	n 3	n 4	P c / bar	T c / K
water	−7.8687	1.9014	−2.3004	−2.0845	220.64	647.096
ammonia	−7.4648	2.1046	−2.6357	−0.9621	113.5	405.5
2,2-dimethylpropane	−6.9511	1.5422	−1.7735	−3.3642	31.99	433.8

literature

1. ^ Wagner W., "New vapor pressure measurements for argon and nitrogen and an new method for establishing rational vapor pressure equations.", Cryogenics, 13 (8), 470-482, 1973
2. ↑ Ambrose D., "The correlation and estimation of vapor pressures", J. Chem. Thermodyn., 18, p45-51, 1986
3. ↑ Dortmund database