Question

Calculate the free energy change for translocating a proton out of the mitochondrial matrix =(1, where H⁺ in the matrix =

8.8×10⁻⁸ M, and H⁺ out in the intermembrane space = 7.9×10⁻⁷ M,∆ψ=191 Mv, and T=37°C

A. 12 Kj/mol
B. 31 Kj/mol
C. 24 Kj/mol
D. 18 Kj/mol

Answer 1

The free energy change for translocating a proton out of the mitochondrial matrix is calculated using the chemiosmotic hypothesis formula, which includes the membrane potential, the temperature in Kelvin, and the concentrations of protons inside and outside the matrix. The calculation yields a free energy change of approximately 18 kJ/mol.

Step-by-step explanation:

To calculate the free energy change for translocating a proton out of the mitochondrial matrix, the following formula based on the chemiosmotic hypothesis is used:

ΔG = ΔG'0 + RT ln([H+] out/[H+] in) + zFΔΨ

Where:

• ΔG'0 is the standard free energy change
• R is the gas constant (8.314 J·mol−1·K−1)
• T is the temperature in Kelvin
• [H+] out is the concentration of protons outside the matrix
• [H+] in is the concentration of protons inside the matrix
• z is the charge of the ion (for H+, z = 1)
• F is the Faraday constant (96485 C·mol−1)
• ΔΨ is the membrane potential in volts

Converting the temperature to Kelvin: T = 37°C + 273 = 310 K

Plugging values into the formula:

ΔG = 0 + (8.314 J·mol−1·K−1)(310 K)ln(7.9×10−7 M / 8.8×10−8 M) + (1)(96485 C·mol−1)(0.191 V)

This yields a free energy change of approximately 18 kJ/mol, which corresponds to answer D.