ΔG‡ from a rate constant

Worked example

A unimolecular reaction has k = 6.8 s⁻¹ at 347 K. Use the Eyring equation to find ΔG‡.

1. 1. Eyring equation (ΔG‡): solve for ΔG‡

   $\Delta G^\ddagger = RT\ln\dfrac{k_\mathrm{B}T}{hk}$

   = 79.90 kJ mol⁻¹

Answer: ΔG‡ = 79.9 kJ mol⁻¹

Method

ΔG‡ = RT ln(k_BT / hk). At 298 K, k_BT/h ≈ 6.2 × 10¹² s⁻¹.

Formulas used

• Eyring equation (ΔG‡)

  $k = \dfrac{k_\mathrm{B}T}{h}\,e^{-\Delta G^\ddagger/RT}$

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