Entropy of activation

Lore & Background

The entropy of activation, symbolized as ΔS‡, represents the change in entropy when reactants transform from their initial state into the activated complex, or transition state. It is one of two key parameters—alongside the enthalpy of activation—derived from analyzing how a reaction’s rate constant varies with temperature, using the Eyring equation from transition state theory. This value is obtained by plotting the natural logarithm of the rate constant divided by absolute temperature (ln(k/T)) against the reciprocal of temperature (1/T). The resulting straight line has a slope equal to -ΔH‡/R, from which the enthalpy of activation is found, and an intercept equal to ln(κk_B/h) + ΔS‡/R, allowing calculation of ΔS‡. The entropy of activation directly determines the preexponential factor in the Arrhenius equation, though the precise relationship depends on the reaction’s molecularity: for reactions in solution and unimolecular gas reactions, a specific formula applies, while for bimolecular gas reactions, a different expression is used, incorporating the ideal gas constant to account for pressure dependence. The magnitude and sign of ΔS‡ offer clues about the molecularity of the rate-determining step. Positive values indicate an increase in entropy upon reaching the transition state, often associated with a dissociative mechanism where the activated complex is loosely bound and about to break apart. Negative values suggest a decrease in entropy, typically pointing to an associative mechanism where two reactants combine into a single, more ordered activated complex.

Reader's Guide

The entropy of activation is significant because it determines the preexponential factor A of the Arrhenius equation, which influences the rate of a reaction. The relationship depends on molecularity: for reactions in solution and unimolecular gas reactions, A = (ek_B T/h) exp(ΔS‡/R); for bimolecular gas reactions, A = (e²k_B T/h)(RT/p) exp(ΔS‡/R), where p accounts for pressure dependence. The value of ΔS‡ provides clues about the molecularity of the rate-determining step. Positive ΔS‡ suggests a dissociative mechanism with a loosely bound transition state, while negative ΔS‡ indicates an associative mechanism where two reactants form a single activated complex. This parameter helps chemists infer reaction mechanisms from kinetic data.

Did You Know?

• Entropy of activation is symbolized ΔS‡, where ‡ denotes activation.
• It determines the preexponential factor A of the Arrhenius equation, with different formulas for unimolecular and bimolecular gas reactions.
• Positive ΔS‡ values often indicate a dissociative mechanism; negative values indicate an associative mechanism.
• The Eyring equation is used to derive ΔS‡ from a plot of ln(k/T) versus 1/T.

From Aristotle's Activity to a Measurable Quantity

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The Conservation Law and Its Deep Symmetry Roots

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A Taxonomy of Energy and the Mass-Energy Unity

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Quantization, Wave Functions, and the Statistical Realm

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