= Liquid immiscibility
\b[Liquid immiscibility] is the failure of a mixture to form one homogeneous liquid at the specified composition and conditions. In a two-liquid <phase equilibrium>, each <thermodynamic phase> can contain some of both components, but their equilibrium compositions differ. “Immiscible” therefore need not mean that no molecules of either component dissolve in the other.
<Hexane> and <water> provide a concrete example of limited mutual <solubility>. A NIST-compiled experimental record describes overnight shaking, microsyringe sampling of an aqueous solution, and <gas chromatography> with flame-ionization detection to measure the dissolved hydrocarbon. Detecting a small dissolved amount does not imply that every bulk mixing ratio gives one liquid phase.<Hexane with water in the IUPAC-NIST Solubility Database>[Record37_269, Experimental Data and Method/Apparatus/Procedure]{ref}
An original <lever rule> example shows how phase amounts differ from phase compositions. Suppose a binary system at fixed temperature and pressure has coexisting liquid compositions $x_\alpha=0.1$ and $x_\beta=0.8$, where $x$ is the <mole fraction> of componentB. These stipulated values are not measurements of hexane/water. If the overall mole fraction is $z=0.4$, material balance gives
$$
z=(1-\lambda)x_\alpha+\lambda x_\beta,\qquad
\lambda=\frac{z-x_\alpha}{x_\beta-x_\alpha}=\frac37.
$$
Here $\lambda$ is the fraction of the total <amount of substance> in phaseβ. A100-mole sample therefore contains $300/7\simeq42.86$ moles in phaseβ and $400/7\simeq57.14$ moles in phaseα. The phase compositions stay0.8 and0.1; neither is the overall composition0.4.
Shaking the sample can create dispersed droplets without making a single molecularly homogeneous phase. Equilibration, temperature, pressure and composition must be stated when testing <liquid-liquid equilibrium>. The lever-rule fraction is a mole-amount fraction, not necessarily the fraction of vessel height or volume occupied by one layer.
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