Chapter 18, Problem 2SEPP

Physical and Biological Sciences

In chemistry, the standard state for a solution is $1M.$ This means that each solute concentration expressed in molarity is divided by $1M.$ In biological systems, however, we define the standard state for the ${\text{H}}^{\text{+}}$ ions to be $\text{1 }\times {\text{ 10}}^{\text{-7}}M.$ Consequently, the change in the standard Gibbs free energy according to these two conventions will be different for reactions involving the uptake or release of ${\text{H}}^{\text{+}}$ ions, depending on which convention is used. We trill therefore replace $\Delta G°$ with $\Delta G°\text{'}$, where the prime denotes that it is the standard Gibbs free-energy change for a biological process.

Consider the reaction:

$\text{A + B C + }x{\text{H}}^{\text{+}}$

where x is a stoichiometric coefficient. Using the equation:

$\Delta G\text{ = }\Delta G°\text{ + RTln Q}$

determine the relationship between $\Delta G°\text{'}$ and $\Delta G°$, keeping in mind that $\Delta G$ is the same for a process regardless of which convention is used.

$\begin{array}{l}\text{a)}\\ \Delta G°\text{'}\text{ = }\Delta G°\text{ + RTln (1}\times {\text{ 10}}^7\text{)}\\ \text{b)}\\ \Delta G°\text{' = }\Delta G°\text{ + RTln (1 }\times {\text{ 10}}^{\text{-7}})x\\ \text{C)}\\ \Delta G°\text{' = }\Delta G°\text{ + }{e}^{\text{-7/RT}}\\ \text{d)}\\ \Delta G°\text{' = }\Delta G°\text{ + RT }\times e^{\text{-7}}\end{array}$