Taft Equation: Polar and Steric Substituent Effects
The Taft equation is an essential linear free energy relationship in physical organic chemistry. In competitive exams, questions test how substituents alter reaction rates and equilibria in aliphatic systems. While the Hammett equation works for aromatic rings with constant steric factors, it fails for aliphatic reactions. In aliphatic chains, substituents sit near the reaction centre, exerting steric hindrance alongside inductive effects. Robert W. Taft resolved this by separating polar and steric parameters. This model allows accurate rate predictions and mechanism deduction.
Why the Hammett Equation Fails in Aliphatic Systems
The Hammett equation assumes that steric interactions stay unchanged across a reaction series. In rigid aromatic rings, substituents are held far from the reaction site, keeping steric interference minimal. In aliphatic esters R-COOR', substituent R is bonded directly to the carbonyl group. Single-bond rotation brings bulky groups into the reagent path, retarding attack via steric crowding. Because Hammett constants account only for electronic effects, plotting aliphatic rates against them causes severe scatter. A dual-parameter model is required.
Separating Polar and Steric Parameters
Taft separated steric and polar effects by comparing ester hydrolysis (R-COOR') under acidic and basic conditions.
In acid-catalysed hydrolysis (AAC2 mechanism), protonation precedes water attack. Because transition state charge distribution resembles the protonated intermediate, little net charge develops and polar sensitivity is near zero (ρ* ≈ 0). Rates depend almost entirely on the steric bulk of R. Taft defined Es as:
Steric Parameter: Es = log10(kA / k0,A)
Where kA is the acid hydrolysis rate constant of R-COOR', and k0,A is that for reference methyl ester (R = -CH3). By definition, Es = 0.00 for -CH3. Bulky groups give negative Es values.
In base-catalysed hydrolysis (BAC2 mechanism), hydroxide attacks the neutral ester, forming a negatively charged tetrahedral transition state stabilised by electron-withdrawing groups. Because steric demand matches that of acid hydrolysis, subtracting the acid logarithm cancels steric effects, isolating the polar parameter σ*:
Polar Parameter: σ* = [log10(kB / k0,B) - log10(kA / k0,A)] / 2.48
Where kB and k0,B are base hydrolysis rate constants for R-COOR' and reference methyl ester. The constant 2.48 matches σ* to the Hammett scale. For methyl (-CH3), σ* = 0.00.
The Dual-Parameter Taft Equation
Combining polar and steric terms gives the Taft equation for reaction rates and equilibria:
Taft Equation: log10(k / k0) = ρ* σ* + δ Es
For equilibria: log10(K / K0) = ρ* σ* + δ Es
Where k and k0 are rate constants for substituent R and methyl reference; σ* is the polar substituent constant; ρ* is the polar reaction constant; Es is the steric substituent constant; δ is the steric susceptibility factor.
Worked Numerical Examples
Question: The alkaline hydrolysis of aliphatic ethyl esters R-COOEt at 25 °C has ρ* = +1.80 and δ = 0.85. The reference methyl ester has k0 = 1.60 × 10-3 dm3 mol-1 s-1. Calculate the rate constant k for the ester with substituent R = -CH2Cl, given σ* = +1.05 and Es = -0.24.
Step 1: Apply the Taft equation: log10(k / k0) = ρ* σ* + δ Es.
Step 2: Polar term: ρ* σ* = 1.80 × 1.05 = 1.890.
Step 3: Steric term: δ Es = 0.85 × (-0.24) = -0.204.
Step 4: Total log ratio: log10(k / k0) = 1.890 - 0.204 = 1.686.
Step 5: Antilogarithm: k / k0 = 101.686 = 48.529.
Step 6: Compute rate constant: k = (1.60 × 10-3 dm3 mol-1 s-1) × 48.529 = 7.765 × 10-2 dm3 mol-1 s-1.
Double-check via natural logarithm: ln(k / k0) = 1.686 × 2.3026 = 3.8822; exp(3.8822) × (1.60 × 10-3) = 7.76 × 10-2 dm3 mol-1 s-1.
Answer: 7.76 × 10-2 dm3 mol-1 s-1
Question: Hydrolysis rate constants for an aliphatic methyl ester R-COOCH3 and reference methyl ester CH3COOCH3 at 25 °C are: basic hydrolysis kB = 8.92 × 10-2 dm3 mol-1 s-1, k0,B = 2.45 × 10-3 dm3 mol-1 s-1; acidic hydrolysis kA = 3.12 × 10-4 dm3 mol-1 s-1, k0,A = 6.24 × 10-4 dm3 mol-1 s-1. Calculate Es and σ* for substituent R.
Step 1: Steric parameter: Es = log10(kA / k0,A) = log10(3.12 × 10-4 / 6.24 × 10-4) = log10(0.500) = -0.301.
Step 2: Base hydrolysis ratio: log10(kB / k0,B) = log10(8.92 × 10-2 / 2.45 × 10-3) = log10(36.4082) = 1.5612.
Step 3: Difference of logarithms: 1.5612 - (-0.3010) = 1.8622.
Step 4: Polar parameter: σ* = 1.8622 / 2.48 = 0.7509 ≈ +0.751.
Double-check via combined ratio: log10[(kB × k0,A) / (k0,B × kA)] / 2.48 = log10(72.8163) / 2.48 = 0.751.
Answer: Es = -0.301, σ* = +0.751
Exam details
- Source: practice problem written for this article (not a past-paper question)
- Relevant exams: CSIR NET, GATE, IIT JAM, CUET PG
- Topic: Taft Equation and Linear Free Energy Relationships
- Difficulty: Advanced
Common Mistakes Students Make
1. Confusing reference standards: In Hammett's equation, hydrogen on benzene is the standard (σ = 0). In Taft's equation, the standard is methyl (-CH3), where σ* = 0.00 and Es = 0.00. For hydrogen (-H), σ* is +0.49, not zero.
2. Omitting the negative sign on Es: Bulky groups hinder reactions, making kA smaller than k0,A. Because log10 of a value below 1 is negative, Es is negative for bulky groups.
3. Forgetting the 2.48 divisor: When calculating σ* from rate data, students often omit dividing [log(kB/k0,B) - log(kA/k0,A)] by 2.48, overestimating σ*.
4. Misinterpreting the sign of ρ*: A positive ρ* means electron-withdrawing groups accelerate the reaction due to developing negative charge in the transition state. A negative ρ* means electron-donating groups accelerate the reaction.
Exam Relevance and Problem Types
| Examination | Question Format | Key Skills Tested |
|---|---|---|
| CSIR NET | Conceptual MCQs and matching questions | Interpreting signs of ρ* and δ, identifying reference standards, and evaluating steric hindrance trends. |
| GATE | Numerical answer type and MCQs | Calculating rate constants from σ* and Es, determining σ* using the 2.48 factor, and separating effects. |
| IIT JAM | Multiple-choice and numerical questions | Comparing Hammett vs Taft applicability, calculating rate ratios, and understanding steric vs polar contributions. |
| CUET PG | Objective concept questions | Definitions of Es and σ*, identifying ester hydrolysis conditions, and reference substituent values. |
Previous-year CSIR-NET questions and timed quizzes to check what you just read.
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