The experimental results presented earlier demonstrate that a maximum in the rate constant for electron transfer (∼2.0×10^9 s-¹) occurs when -ΔG°=1.20 eV. Given this observation, estimate the rate constant for electron transfer when 2-naphthoquinoyl is employed as the acceptor for which -ΔG°=1.93

Question

The experimental results presented earlier demonstrate that a maximum in the rate constant for electron transfer [latex]\left( \sim 2.0 ×10^{9} s^{-1}\right)[/latex] occurs when [latex]-\Delta G°=1.20 eV[/latex]. Given this observation, estimate the rate constant for electron transfer when 2-naphthoquinoyl is employed as the acceptor for which [latex]-\Delta G°=1.93 eV[/latex].

Accepted Answer

The rate constant for electron transfer is predicted to be at a maximum when [latex]-\Delta G°=\lambda[/latex]; therefore, [latex]\lambda=1.20 eV[/latex]. Using this information, the barrier to electron transfer is determined as follows:

[latex]\Delta G°^{\ddagger}=\frac{\left( \Delta G+\lambda \right)^{2}}{4\lambda}=\frac{\left( -1.93 eV+1.20 eV \right)^{2}}{4\left( 1.20 eV \right)}=0.111 eV[/latex]

With the barrier to electron transfer, the rate constant is estimated as follows:

[latex]\frac{k_{1.93 eV}}{k_{\max}}=e^{-\Delta G^{\ddagger}/kt}=\exp\left( -0.111 eV×\frac{1.60×10^{-19}J}{eV}/\left( 1.38×10^{-23} J K^{-1}\right) \left( 296 K \right)\right)[/latex]

[latex]=0.0129[/latex]

[latex]k_{1.93 eV}=k_{\max}\left( 0.0129 \right)=\left( 2.0×10^{9}s^{-1} \right)\left( 0.0129 \right)=2.6 ×10^{7} s^{-1}[/latex]

Question 19.7: The experimental results presented earlier demonstrate that ...

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