creates a lower concentration of positively charged protons inside it, resulting in excess negative charge on the inside of the membrane. The electrical potential gradient is about -170 mV , negative inside (N). These gradients - charge difference and the proton concentration difference both create a combined electrochemical gradient across the membrane, often expressed as the proton-motive force (PMF). In mitochondria, the PMF is almost entirely made up of the electrical component but in chloroplasts the PMF is made up mostly of the pH gradient because the charge of protons H+ is neutralized by the movement of Cl− and other anions. In either case, the PMF needs to be greater than about 460 mV (45 kJ/mol) for the ATP synthase to be able to make ATP. Equations The proton-motive force is derived from the Gibbs free energy. Let N denote the inside of a cell, and let P denote the outside. Then where is the Gibbs free energy change per unit amount of cations transferred from P to N; is the charge number of the cation ; is the electric potential of N relative to P; and are the cation concentrations at P and N, respectively; is the Faraday constant; is the gas constant; and is the temperature. The molar Gibbs free energy change is frequently interpreted as a molar electrochemical ion potential . For an electrochemical proton gradient and as a consequence: where . Mitchell defined the proton-motive force (PMF) as . For example, implies . At this equation takes the form: . Note that for spontaneous proton import from the P side (relatively more positive and acidic) to the N side (relatively more negative and alkaline), is negative (similar to ) whereas PMF is positive (similar to redox cell potential ). It is worth noting that, as with any transmembrane transport process, the PMF is directional. The sign of the transmembrane electric potential difference is chosen to represent the change in potential energy per unit charge flowing into the cell as above. Furthermore, due to redox-driven proton pumping by coupling sites, the proton gradient is always inside-alkaline. For both of these reasons, protons flow in spontaneously, from the P side to the N side; the available free energy is used to synthesize ATP (see below). For this reason, PMF is defined for proton import, which is spontaneous. PMF for proton export, i.e., proton pumping as catalyzed by the