Energetics of Solute Diffusion

Diffusion is the process of transferring matter from an area of high concentration to an area of low concentration under the influence of thermal energy. For biological applications, it is important to evaluate diffusion of solute molecules, particularly across cell membranes. Diffusion always proceeds toward an equilibrium where the concentrations are equal, but life is always a non-equilibrium process and there are many situations where non-equilibrium concentrations of solute are maintained.

扩散是在热能作用下，物质从高浓度区域向低浓度区域转移的过程。在生物应用中，评估溶质分子的扩散，特别是穿过细胞膜的扩散是重要的。扩散总是朝着浓度相等的平衡状态进行，但生命始终是一个非平衡过程，有许多情况下需要维持非平衡状态的溶质浓度。

It is useful to know the energy required to maintain non-equilibrium concentrations, and in biological contexts this energy is usually expressed in terms of the Gibbs free energy. The change in free energy associated with the movement of an uncharged solute (a non-electrolyte) across a cell membrane can be expressed as

了解维持非平衡浓度所需的能量是有用的，在生物背景下，这种能量通常以吉布斯自由能的形式表达。带电溶质（非电解质）跨细胞膜运动所伴随的自由能变化可以表示为

If the solute is charged (an electrolyte), then the voltage difference between the inside and outside must be taken into account. The expression for free energy difference then becomes

如果溶质带电（即为电解质），则必须考虑细胞内外的电压差。此时自由能差的表达式则变为

where z is the charge of the solute and F is the Faraday constant 23.06 kcal/V equivalent where an equivalent is the amount of the electrolyte having one mole of charge.

其中 z 是溶质的电荷，F 是法拉第常数 23.06 kcal/V 等效量，其中等效量是指具有一摩尔电荷的电解质的量。

其中 C_i 和 C_o 是细胞内外的浓度，R = 8.3145 J/mol = 1.987 cal/mole 是气体常数。通常使用 25°C = 298.15K 作为生物参考计算温度，在此温度下该关系式变为