Question

Calculate the change in free energy for the transit of two electrons from the quinone pool to cytochrome c₂ in purple bacterial photosynthetic electron transport. Assume that the reduction potential of cytochromec₂is similar to those of other c-type cytochromes.

Short answer

The change in free energy is $-53.65{\mathrm{Jmol}}^{-1}$.

Step-by-step solution

Cytochrome

Cytochrome is any of a group of haemoprotein cell components that perform a critical function in the transfer of energy inside cells by quickly undergoing reduction and oxidation (gain and loss of electrons) with the help of enzymes.

Step 2: The change in free energy for the transit of two electrons from the quinone pool to cytochrome c2 in purple bacterial photosynthetic electron transport

The difference in reduction potentials causes the free energy required for the passage of two electrons from the Quinone pool to cytochrome$c_2$. The Quinone pool in purple bacterial photosynthetic electron transport is made up of ubiquinone.

Since the reduction potential of cytochrome $c_2$is unknown, utilize the average of the reduction potentials of the other two cytochromes that are known. As cytochrome has $c_1$a $E°$of 0.235V and cytochrome$c_3$ has a$E°$ of 0.22V, the reduction potential of cytochrome$c_2$ is assumed to be 0.233V.

The electrons are transferred from the Quinone pool to the cytochrome, where ubiquinol is oxidized to ubiquinone and cytochrome$c_2$is reduced.

ubiquinol=ubiquinone$+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}{\mathrm{E}}^{\circ }=-0.045\mathrm{V}$

cytochrome${\mathrm{c}}_2\left({\mathrm{Fe}}_3^{+}\right)+{\mathrm{e}}^{-}$= cytochrome${\mathrm{c}}_2\left({\mathrm{Fe}}_2^{+}\right){\mathrm{E}}^{°}=0.233\mathrm{V}$

The reduction potential of cytochrome$c_2$ is not doubled since reduction potential is an intense feature that is independent of the amount of cytochrome.

The difference in reduction potentials is used to determine the free energy change, $△{\mathrm{G}}^{°}$.

Difference in reduction potentials is electromotive force,$\Delta \mathrm{E}°$.

$∆{\mathrm{E}}^{°}={\mathrm{E}}_{electronacceptor}^{°}-{\mathrm{E}}_{\mathrm{electrondonor}}^{°}$

Ubiquinol is an electron giver, whereas cytochrome $c_2$is an electron acceptor.

$\begin{array}{rcl}∆{\mathrm{E}}^{°}& =& 0.233\mathrm{V}-(-0.045)\mathrm{V}\\ & =& 0.278\end{array}$

Free energy change is calculated using the formula:$∆{\mathrm{G}}^{°}=-\mathrm{nF}\Delta {\mathrm{E}}^{°}$

In expression, nis number of electrons transferred and F is Faraday constant,$96.485{\mathrm{JV}}^{-1}{\mathrm{mol}}^{-1}$.

Substituting the values in the equation,

$\begin{array}{c}∆{\mathrm{G}}^{°\text{'}}=-2\times 96.485{\mathrm{JV}}^{-1}{\mathrm{mol}}^{-1}\times 0.278\mathrm{V}\\ =-53.65\mathrm{J}{\mathrm{mol}}^{-1}\end{array}$