Pailhes method

The Pailhes method is a method for estimating the normal boiling point T _B from a known boiling point at a low temperature, the critical pressure P _c and a ratio T _B / T _c , which can be determined from the Lydersen method .

In the case of high-boiling components, the normal boiling point of which cannot be determined experimentally or only with difficulty, the method is primarily used to nevertheless determine this variable, which is important for many estimation methods, at least with some accuracy.

Determining equations

${\displaystyle T_{\mathrm {B} }=T_{\mathrm {sat} }{\frac {\log _{10}P_{\mathrm {c} }+(1-\theta )x}{\log _{10}P_{\mathrm {c} }}}-3x-1{,}49x^{2}}$

With

${\displaystyle x=\log _{10}\left({\frac {P_{\text{normal}}}{P_{\mathrm {sat} }}}\right)}$

${\displaystyle \theta ={\frac {T_{\mathrm {B} }}{T_{\mathrm {c} }}}}$is calculated in the original publication as well as the critical pressure P _c using the Lydersen method. However, both θ and P _c can be determined using other suitable methods.

${\displaystyle T_{\mathrm {sat} },P_{\mathrm {sat} }}$is a known saturation vapor pressure at a low temperature, often near room temperature .

Sample calculation

The following calculation applies to n -butylacetate (butyl acetate):

Structural formula of n -butylacetate

According to Lydersen, the following group contributions apply to T _c :

-CH3 / -CH2: 0.020 (atoms 1,5,6,7,8)

-COO-: 0.047 (atoms 2,3,4)

and for P _c :

-CH3 / -CH2: 0.227

-COO-: 0.47

This results in

${\displaystyle \sum \Delta T=5\cdot 0{,}020+0{,}047=0{,}147\quad {\text{und}}\quad \theta =0{,}567+0{,}147-0{,}147^{2}=0{,}692391}$

With the molar mass M _W = 116.161 g mol ⁻¹ , the critical pressure is given by

${\displaystyle P_{\mathrm {c} }={\frac {116{,}161}{{0{,}34+5\cdot 0{,}227+0{,}47}^{2}}}=30{,}70585\,\mathrm {atm} \quad {\text{und}}\quad \log P_{\mathrm {c} }=1{,}4872211}$

With P _sat = 1.7732 kPa at T _sat = 293.65 K this results

${\displaystyle x=\log _{10}\left({\frac {101{,}325\,\mathrm {kPa} }{1{,}7732\,\mathrm {kPa} }}\right)=1{,}75696}$

With this, all required values ​​are determined and the determining equation can be occupied:

${\displaystyle T_{\mathrm {B} }=293{,}65\cdot {\frac {1{,}4872211+(1-0{,}692391)\cdot 1{,}75696}{1{,}4872211}}-3\cdot 1{,}75696-1{,}49\cdot 1{,}75696^{2}}$

${\displaystyle T_{\mathrm {B} }=390{,}49\,\mathrm {K} }$

Normal boiling points published in the literature are between T _B = 397.65 K and T _B = 399.85 K.

See also

• Guldberg's rule

literature

1. ↑ Pailhes F., "Estimation of the Boiling Temperature at Normal Pressure for Organic Compounds from Their Chemical Formula and a Known Boiling Temperature at Low Pressure", Fluid Phase Equilib., 41, pp. 97-107, 1988.
2. ↑ Scheller WA, Torres-Soto AR, Daphtary KJ, "Isothermal Vapor-Liquid Equilibrium Data for the Heptane-Butyl Acetate System at 74.7 ° and 100 ° C", J. Chem. Eng. Data, 14 (1), pp. 17-19, 1969.
3. ↑ Dortmund database .