Final answer:
The correct formula to calculate the chemical-potential change for transferring H+ from the inter-membrane space into the mitochondria matrix is Δμ = RT ln([H+] inter-membrane / [H+] matrix), which reflects the proton gradient used to drive ATP synthesis.
Step-by-step explanation:
To calculate the chemical-potential change when transferring 1 mole of H+ ion from the inter-membrane space into the mitochondria matrix, we use the formula for the change in chemical potential (Δμ) due to the concentration gradient across the membrane:
Δμ = RT ln([H+] matrix / [H+] inter-membrane)
Here, R is the gas constant, T is the temperature in Kelvin, [H+] matrix is the concentration of hydrogen ions in the mitochondria matrix, and [H+] inter-membrane is the concentration of hydrogen ions in the inter-membrane space. Considering the proton gradient established during the electron transport chain, option (b) Δμ = RT ln([H+] inter-membrane / [H+] matrix) accurately describes the change in potential as the concentration of H+ is higher in the inter-membrane space compared to the matrix, leading to a positive Δμ and driving the synthesis of ATP by ATP synthase.