Equation 13.2.4 shows that in the two-phase system, \(p\) has a value between \(p\A^*\) and \(p\B^*\), and that if \(T\) is constant, \(p\) is a linear function of \(x\A\). At the left end of each tie line (at low \(z\A\)) is a vaporus curve, and at the right end is a liquidus curve. Instead of using these variables as the coordinates of a three-dimensional phase diagram, we usually draw a two-dimensional phase diagram that is either a temperature–composition diagram at a fixed pressure or a pressure–composition diagram at a fixed temperature. The partial pressures of both components exhibit positive deviations from Raoult’s law, consistent with the statement in Sec. However, when a liquid phase is equilibrated with a gas phase, the partial pressure of a constituent of the liquid is practically independent of the total pressure (Sec. If we now place the system in thermal contact with a cold reservoir, heat is transferred out of the system and the system point moves down along the At point c on the isopleth, the system point reaches the boundary of the one-phase area and is about to enter the two-phase area labeled A(s) + liquid. Adopted or used LibreTexts for your course? The solid hydrate \(\ce{NaCl*2H2O}\) is \(61.9\%\) NaCl by mass. This point is in the one-phase liquid area, so the equilibrium system at this temperature has a single liquid phase. The phase diagram shows that the ratio \((z\B-x\B\aph)/(x\B\bph-z\B)\) decreases during this change. The prior statements regarding dissociation and hydration now depend on the value of \(p\subs{H\(_2\)O}\).

Find more information onIn this article we derive equations for a binary liquid temperature–composition phase diagram. 13.3 has two eutectic points. 13.5. This pressure is called the The dissociation pressures of the three hydrates are indicated by horizontal lines in Fig. Conversely, the salt formed by the dissociation of a hydrate cannot exist in equilibrium with water vapor at a pressure above the dissociation pressure because hydration would be spontaneous.If the system contains dry air as an additional gaseous component and one of the dissociation equilibria is established, the partial pressure \(p\subs{H\(_2\)O}\) of H\(_2\)O is equal (approximately) to the dissociation pressure \(p\subs{d}\) of the higher hydrate. On the pressure–composition phase diagram, the liquidus and vaporus curves both have maxima at this pressure, and the two curves coincide at an A binary system containing an azeotropic mixture in equilibrium with its vapor has two species, two phases, and one relation among intensive variables: \(x\A =y\A\). These three phases can coexist at equilibrium at \(0\units{\(\degC\)}\). These curves comprise the liquidus. In the phase diagram these formulas are abbreviated A, AB, AB\(_3\), and AB\(_5\). Consider an example of a liquid mixture containing 2 components (A and B) – a binary mixture. The composition variable z B is the mole fraction of component B in the system as a whole. 13.8(a) were calculated from the experimental gas-phase compositions with the relations \(p\A=y\A p\) and \(p\B=p-p\A\). When one of these equilibria is established in the system, there are two components and three phases; the phase rule then tells us the system is univariant and the pressure has only one possible value at a given temperature. 13.1. 13.6(b) shows the relation between \(T\) and \(x\A\), and the vaporus curve shows the relation between \(T\) and \(y\A\), for equilibrated liquid and gas phases at constant \(p\). For example, in the next diagram, if you boil a liquid mixture C1, it will boil at a temperature T1and the vapour over the top of the boiling liquid will have the composition C2. Thus, a hydrate cannot exist in equilibrium with water vapor at a pressure below the dissociation pressure of the hydrate because dissociation would be spontaneous under these conditions. Figure 13.1 is a temperature–composition phase diagram at a fixed pressure. 13.2.3 is given by \begin{gather} \s {\begin{split} p & = x\A p\A^* + (1-x\A)p\B^* \cr & = p\B^* + (p\A^*-p\B^*)x\A \end{split} } \tag{13.2.4} \cond{(\(C{=}2\), ideal liquid mixture)} \end{gather} where \(x\A\) is the mole fraction of A in the liquid phase. The composition variable \(z\A\) is the overall mole fraction of component A (toluene).The equations needed to generate the curves can be derived as follows. A phase transition like this, in which a solid compound changes into a liquid and a different solid, is called Figure 13.4 shows there are two other temperatures at which three phases can be present simultaneously: \(-21\units{\(\degC\)}\), where the phases are ice, the solution at its eutectic point, and the solid hydrate; and \(109\units{\(\degC\)}\), where the phases are gaseous H\(_2\)O, a solution of composition \(28.3\%\) NaCl by mass, and solid NaCl.

The system point moves up the isopleth a–d.

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