Engineering & Science
Joback Group-Contribution Method: Boiling Point (T_b) & Critical Temp (T_c)
Estimate pure-component normal boiling point T_b = 198.2 + SUMPRODUCT(n, ΔT_b) and Lydersen-Joback critical temperature T_c = T_b / (0.584 + 0.965*ΣΔT_c - (ΣΔT_c)^2) directly from functional group counts.
Estimating T_b and T_c for novel pharma intermediates before a drop is synthesized!
Early-stage process simulation (Aspen/DWSIM) for newly designed pharmaceutical intermediates or green solvents requires normal boiling point T_b and critical temperature T_c before physical samples exist. Kevin G. Joback and Robert C. Reid (Chem. Eng. Commun., 1987) parameterized 41 molecular functional groups so a simple group-count table yields T_b = 198.2 + SUMPRODUCT(n_i, ΔT_b,i) (K) and T_c = T_b / (0.584 + 0.965 * Σ(n_i * ΔT_c,i) - (Σ(n_i * ΔT_c,i))^2) (K)!
Test Joback on acetone (CH_3–CO–CH_3: two -CH_3 groups with ΔT_b = 23.58 K, ΔT_c = 0.0141, plus one non-ring >C=O ketone group with ΔT_b = 76.75 K, ΔT_c = 0.0380): Joback predicts T_b = 322.11 K (vs. experimental 329.2 K) and T_c = 500.56 K (within 1.5% of experimental 508.1 K)! Switching the group counts to ethanol (1 -CH_3, 1 -CH_2-, 1 alcohol -OH) immediately updates T_b = 337.54 K and T_c = 499.41 K!
| Molecule Functional Group Vector | Σ(n_i * ΔT_b,i) | Joback Boiling T_b (K) | Joback Critical T_c (K) |
|---|---|---|---|
| Acetone: 2 (-CH3) + 0 (-CH2-) + 1 (>C=O) + 0 (-OH) | 123.91 K | 322.11 K | 500.56 K (Exp: 508.1 K) |
| Ethanol: 1 (-CH3) + 1 (-CH2-) + 0 (>C=O) + 1 (-OH) | 139.34 K | 337.54 K | 499.41 K (Exp: 513.9 K) |
| Empty Group Vector (SUM(n_i) = 0) | 0 | "Enter At Least One Group" | Input Guard |
Joback Group-Contribution Normal Boiling Point T_b (K)
Sums functional group counts B2:B5 against Joback boiling increments C2:C5 and adds the 198.2 K intercept.
=IF(SUM(B2:B5) <= 0, "Enter At Least One Group", ROUND(198.2 + SUMPRODUCT(B2:B5, C2:C5), 2))Joback-Reid Critical Temperature T_c (K)
Evaluates T_b / (0.584 + 0.965 * S_Tc - S_Tc^2), where S_Tc = SUMPRODUCT(B2:B5, D2:D5).
=IF(SUM(B2:B5) <= 0, "Enter At Least One Group", ROUND((198.2 + SUMPRODUCT(B2:B5, C2:C5)) / (0.584 + 0.965 * SUMPRODUCT(B2:B5, D2:D5) - (SUMPRODUCT(B2:B5, D2:D5) ^ 2)), 2))Try the example
Use the original values or change them to test your understanding.