## Property Estimation Joback Method

The Joback method is a group contribution method which calculates thermophysical and transport properties as a function of the sum of group parameters. It uses a very simple and easy to assign group scheme.

This article shows how to calculate properties using Joback Method in an excel spreadsheet.

**Example**

*Estimate properties for 1-Butanol based on Joback Method*

Structure of 1-Butanol consists of following groups

`-CH`

_{3}Group : 1`-CH`

_{2}Group : 3`-OH (alcohol) Group : 1`

*Normal Boiling Point*

`T`_{NBP} (K) = 198 + ΣT_{b,i}

where T_{b,i} is contribution due to each group. These values for individual group are available in literature and Wikipedia reference below. On combining values for each group normal boiling point comes out to be –

`T`_{NBP} (K) = 383.10

*Critical Temperature*

`Tc (K) = T`

_{NBP}/(0.584 + 0.965*ΣT_{c,i}- (ΣT_{c,i})²)`Tc (K) = 545.08`

*Critical Pressure*

`Pc (bar) = (0.113 + 0.0032*N`

_{A}- ΣP_{c,i})^{-2}`Pc (bar) = 43.86`

where N_{A} is number of atoms in the molecular structure.

*Critical Volume*

`Vc (cm³/mol) = 17.5 + ΣV`

_{c,i}`Vc (cm³/mol) = 278.50`

*Critical Compressibility*

`Zc = (Pc.Vc)/(R.Tc)`

`Zc = 0.2695`

*Acentric Factor*

Lee-Kesler method can be used to estimate the acentric factor.

`ω = α/β`

`θ = T`

_{NBP}/ Tc`α = -ln(Pc) - 5.92714 + 6.09648/θ + 1.28862.ln(θ) - 0.169347.θ`

^{6}`β = 15.2518 - 15.6875/θ - 13.4721.ln(θ) + 0.43577.θ`

^{6}`ω = 0.6602`

*Freezing Point*

`Tm (K) = 122.5 + ΣT`

_{m,i}`Tm (K) = 195.66`

*Heat of Formation (Ideal Gas, 298 K)*

`H`

_{formation}(kJ/mol) = 68.29 + ΣH_{form,i}`H`

_{formation}(kJ/mol) = -278.12

*Gibbs Energy of Formation (Ideal Gas, 298 K)*

`G`

_{formation}(kJ/mol) = 53.88 + ΣG_{form,i}`G`

_{formation}(kJ/mol) = -154.02

*Heat of Vaporization (at Normal Boiling Point)*

Reidel’s equation can be used to estimate a liquid’s heat of vaporization at its normal boiling point.

`ΔHv (kJ/mol) = 1.092.R.T`

_{NBP}.(ln(Pc) -1.013)/(0.930 - (T_{NBP}/ Tc))`ΔHv (kJ/mol) = 42.38`

*Heat of Fusion*

`ΔH`

_{fus}(kJ/mol) = -0.88 + ΣH_{fus,i}`ΔH`

_{fus}(kJ/mol) = 10.2

*Heat Capacity (Ideal Gas)*

`C`

_{P}(J/mol.K) = A + B.T + C.T² + D.T³`A = Σai - 37.93`

`B = Σbi + 0.210`

`C = Σci - 3.91*10`

^{-4}`D = Σdi + 2.06*10`

^{-7}`C`

_{P}(J/mol.K) = 110.96 (at 300 K)

*Heat of Vaporization (@ Temperature T)*

Watson equation can be used to estimate heat of vaporization at different temperature as following.

`ΔHv,2 (kJ/mol) = Hv,1*((Tc - T`

_{2})/(Tc - T_{1}))^{0.38}`ΔHv,2 (kJ/mol) = 49.60 (at 300 K)`

*Liquid Viscosity*

`η`

_{L}(Pa.s) = Mw.exp(A/T + B)`A = Σηa - 597.82`

`B = Σηb - 11.202`

`η`

_{L}(Pa.s) = 1.936*10^{-3}(at 300 K)

where Mw is the molecular weight.

*Liquid Density*

Rackett equation can be used to estimate liquid density from critical properties as following –

`ρ`

_{L}(gm/cm³) = Mw/( (R.Tc/Pc)*Zc^(1 + (1- T/Tc)^{2/7}))`ρ`

_{L}(gm/cm³) = 0.756 (at 300 K)

*Liquid Vapor Pressure*

Lee-Kesler equation can be used to estimate liquid vapor pressure as following –

`Pvp (bar) = Pc.exp(f`

_{0}+ ω.f_{1})`f`

_{0}= 5.92714 - 6.09648/Tr - 1.28862*ln(Tr) + 0.169347.Tr^{6}`f`

_{1}= 15.2518 - 15.6875/Tr - 13.4721*ln(Tr) + 0.43577.Tr^{6}`Tr = T / Tc`

`Pvp (bar) = 0.018`

Web based calculation available at CheCalc.com

### Spreadsheet

Spreadsheet for property estimation based on Joback Method