The Law of Partial Pressures in Liquid Mixtures and Osmotic Pressures

When an osmotic system is composed of 1- and 0-species particles, which are confined to the volumes, $V\equiv V_{\rm a}+V_{\rm b}$ and $V_{\rm b}$, by the wall pressures, $P_1^{{\rm w}_{\rm a}}$ and $P_0^{{\rm w}_{\rm b}}$, respectively, we obtain a law of partial pressures as described in the forms: $P_1^{\rm w_{\rm a}}=P_{\rm 1b}^{\rm vir}+\Gamma$, $P_0^{\rm w_{\rm b}}=P_{\rm 0b}^{\rm vir}-\Gamma$ and $P=P_0^{\rm w_{\rm b}} + P_1^{\rm w_{\rm a}}= P_{\rm 0b}^{\rm vir}+P_{\rm 1b}^{\rm vir}$. Here, the partial pressures, $P_{\rm \alpha b}^{\rm vir}$, are given by the virial equation in the solution of 0- and 1-species in $V_{\rm b}$, and the pressure difference $\Gamma$ on a semipermeable membrane appears owing to the presence of density discontinuity at the membrane. On the basis of this result, we show that the partial pressures defined by the wall pressures are measurable in liquid mixtures, and satisfy the law of partial pressures, which gives the total pressure by the sum of partial pressures. Also, the partial pressures are shown to play an important role in treating the gas-liquid equilibrium as well as osmotic systems. In fluid physiology, the partial pressure of water in solutions is important to determine water balance in body fluids.