Joback Method

Category: scientific calculator (group-contribution method, not an ML model) · Discipline: chemical engineering

1. Overview

The Joback method estimates a pure compound’s critical and thermophysical properties directly from its molecular structure, by summing tabulated contributions from the functional groups the molecule is built from.

• Input — a SMILES string, e.g. CCO (ethanol) or c1ccccc1 (benzene).

• Output — a JSON object of estimated properties:

  {
    "tb": 337.5,   // normal boiling point (K)
    "tc": 499.4,   // critical temperature (K)
    "pc": 57.6,    // critical pressure (bar)
    "omega": 0.635 // acentric factor (derived, see §6)
  }

2. Approach

The molecule is decomposed into a multiset of first-order functional groups. Each group $i$ contributes a tabulated increment to each property; the property is then a simple sum (for $T_b$) or a closed-form function of the group sums (for $T_c$, $P_c$). Let $n_i$ be the number of times group $i$ appears and $n_A$ the total number of atoms in the molecule.

SMILES → first-order group decomposition → summed contributions → estimated properties.

3. Equations

Normal boiling point:

$$T_b = 198.2 + \sum_i n_i\, \Delta T_{b,i}$$

Critical temperature (uses $T_b$, predicted or experimental):

$$T_c = T_b \left[\, 0.584 + 0.965 \sum_i n_i \Delta T_{c,i} - \left(\sum_i n_i \Delta T_{c,i}\right)^{2} \right]^{-1}$$

Critical pressure ($n_A$ = number of atoms in the molecule):

$$P_c = \left( 0.113 + 0.0032\, n_A - \sum_i n_i \Delta P_{c,i} \right)^{-2}$$

Note

Coefficients and the additive form are from Joback & Reid (1987). $T_c$ and $P_c$ are returned in kelvin and bar respectively; $P_c$‘s constant $0.113$ carries units that yield bar.

4. Representative group contributions

Group	$\Delta T_{b,i}$ (K)	$\Delta T_{c,i}$	$\Delta P_{c,i}$
-CH3	23.58	0.0141	−0.0012
-CH2-	22.88	0.0189	0.0000
>CH-	21.74	0.0164	0.0020
-OH (alcohol)	92.88	0.0741	0.0112
ring =CH- (aromatic)	26.73	0.0082	0.0011

Tip

Full coefficient tables cover ~40 first-order groups; the rows above are those needed for the worked example plus a couple of common ring/branch groups for orientation.

5. Worked example — ethanol (CCO)

Ethanol decomposes into one -CH3, one -CH2-, and one -OH, with $n_A = 9$ atoms (C₂H₆O).

$$\sum_i n_i \Delta T_{b,i} = 23.58 + 22.88 + 92.88 = 139.34 \;\Longrightarrow\; T_b = 198.2 + 139.34 = 337.5\ \text{K}$$ $$\sum_i n_i \Delta T_{c,i} = 0.1071 \;\Longrightarrow\; T_c = \frac{337.5}{0.584 + 0.965(0.1071) - (0.1071)^2} = 499.4\ \text{K}$$ $$\sum_i n_i \Delta P_{c,i} = 0.0100 \;\Longrightarrow\; P_c = \left( 0.113 + 0.0032(9) - 0.0100 \right)^{-2} = 57.6\ \text{bar}$$

Property	Joback (predicted)	Literature	Rel. error
$T_b$ (K)	337.5	351.4	4.0 %
$T_c$ (K)	499.4	513.9	2.8 %
$P_c$ (bar)	57.6	61.4	6.2 %

The errors are typical of first-order group contribution: a few percent on $T_c$, somewhat larger on $P_c$. The example above uses the predicted $T_b$ in the $T_c$ correlation so the result is fully structure-derived; substituting the experimental $T_b = 351.4\ \text{K}$ gives $T_c \approx 520\ \text{K}$.

6. Acentric factor (omega)

Joback does not provide a group contribution for the acentric factor $\omega$. The calculator derives it from the estimated $T_b$, $T_c$, and $P_c$ via the Lee–Kesler vapor-pressure correlation (the Pitzer definition $\omega = -\log_{10}(P^{\mathrm{sat}}_r)\big|_{T_r=0.7} - 1$). For ethanol this yields $\omega \approx 0.635$, consistent with the literature value.

7. References

• K. G. Joback and R. C. Reid, “Estimation of pure-component properties from group-contributions,” Chemical Engineering Communications, 57(1–6):233–243, 1987.
• B. E. Poling, J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, 2001 — Joback method and coefficient tables.
• Model implementation: carnotai/models/chemical_engineering/joback (CarnotAI repository).