(Solved): Calculate the free energy change of hydrogen ions across the mitochondrial membrane if the concentr ...

Calculate the free energy change of hydrogen ions across the mitochondrial membrane if the concentration of hydrogen is \( 10^{-8} \) in the mitochondrial matrix and \( 10^{-7} \) in the intermembrane space. Assume the gas constant to be \( 8.314 \mathrm{~J} / \mathrm{molK} \), temperature to be \( 310 \mathrm{~K} \), Faraday's constant is \( 9.65 \times 10^{4} \mathrm{C} / \mathrm{mol} \), and the membrane potential is \( -160 \mathrm{mV} \). Recall the electrochemical potential equation: \[ \mu=\mu^{0}+R T \ln \left(\frac{C_{i}}{C_{0}}\right)+F\left(\Psi_{i}-\Psi_{0}\right) \] Express your answer as \( \mathrm{k} / / \mathrm{mol} \) and report answers using either \( 0.0 \) or \( 0.00 \).