Dependence of pressure on the potential

If the mole numbers in Equation (14.18) referred to species rather than components, then the condition of constant mass of components would lead to the condition for chemical equilibrium 

However, v,Mt = 0 because of the conservation of mass and, therefore, we have for chemical equilibrium the condition 

We thus determine that the condition for chemical equilibrium is independent of the field and is the same throughout the entire system. 

We were not able to obtain a condition of equilibrium with regard to the pressure in the previous section, because a change of volume of a region was not considered to be a possible variation. We consider the problem of the dependence of pressure on the potential in this section. 

Let us consider a closed, single-phase system containing C components in a gravitational field. The state of the system is fixed and the system is in equilibrium. The condition of equilibrium is that for each component the quantity (pt + Af ) must have the same value in each homogenous region of the phase. In general, (pt + Af, ) is a function of the temperature, pressure, (C — 1) mole fractions, and the potential, so the differential of (pt + M,0) may be written as 

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