In the study of thermodynamics related to membrane diffusion, it is essential to differentiate between uncharged molecules and charged ions. When focusing on charged ions, particularly cations, the transmembrane potential, denoted as Δψ, plays a crucial role. This potential represents the difference in electrical charge across the membrane and must be considered when analyzing the diffusion of charged particles.
The transport free energy change for ions, ΔGtransport, can be expressed by the equation:
ΔGtransport = Z × F × Δψ
In this equation, Z represents the net charge of the diffusing ion, while F is Faraday's constant, which quantifies the charge of one mole of electrons. Faraday's constant is approximately 96,485 C/mol (coulombs per mole), and it is always expressed as a positive value, despite the negative charge of electrons. Understanding the units of Faraday's constant is important; it can be represented as J/V·mol (joules per volt per mole) or C/mol.
However, the diffusion of ions is not solely influenced by the electrical gradient. It is essential to consider the electrochemical gradient, which combines both the chemical gradient and the electrical gradient. The chemical gradient portion of the equation remains the same as that for uncharged molecules, while the electrical gradient is added for charged ions. Thus, the complete equation for the thermodynamics of membrane diffusion for charged ions incorporates both gradients:
ΔGtransport = ΔGchemical + Z × F × Δψ
This comprehensive approach allows for a more accurate understanding of how charged ions diffuse across membranes, taking into account both the concentration differences and the electrical forces at play. In future applications, this equation will be utilized to calculate specific scenarios involving the thermodynamics of membrane diffusion for charged ions.