$$\newcommand{\arrows}{\,\rightleftharpoons\,} % double arrows with extra spaces$$ A melting process with this behavior is called a dystectic reaction. Figure 11.22 "A Typical Phase Diagram for a Substance That Exhibits Three Phases—Solid, Liquid, and Gas—and a Supercritical Region", Figure 11.23 "Two Versions of the Phase Diagram of Water", Figure 11.24 "The Phase Diagram of Carbon Dioxide", Section 11.6 "Critical Temperature and Pressure".  $$\newcommand{\dq}{\dBar q} % heat differential$$ 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.  $$\newcommand{\R}{8.3145\units{J\,K\per\,mol\per}} % gas constant value$$ The possible solid phases are pure A, pure B, and the solid compound AB. Points on the vaporus curve are calculated from $$p=p\A/y\A$$. The total pressure (equal to the sum of the partial pressures) has a maximum value greater than the vapor pressure of either pure component. At every point along this line, the liquid boils to Figure 13.2 shows two temperature–composition phase diagrams with single eutectic points. The ease with which ice skaters glide across a frozen pond can be That line represents solid-vapour equilibrium. The cooling curve for liquid of this composition would display a halt at the melting point. The dashed curve is the azeotrope vapor-pressure curve. Phase diagrams are useful for predicting the boiling point of a compound as a function of pressure. 13.13 and the pressure is then increased by isothermal compression along line a–b. Various types of behavior have been observed in this region. Since carbon disulfide is the more dense of the two pure liquids, the bottom layer is phase $$\phb$$, the layer that is richer in carbon disulfide. It resembles two simple phase diagrams like Fig. A Identify the region of the phase diagram corresponding to the initial conditions and identify the phase that exists in this region. 12.5.4). The BD line is almost vertical because the melting point of a solid is not You can apply Le Chatelier's Principle to this equilibrium just as if it was a chemical equilibrium. (Data from Roger Cohen-Adad and John W. Lorimer, Alkali Metal and Ammonium Chlorides in Water and Heavy Water (Binary Systems), Solubility Data Series, Vol. The normal melting and boiling points are those when the pressure is 1 atmosphere.  $$\newcommand{\units}[1]{\mbox{\thinspace#1}}$$ 12.8.1), so that it is a good approximation to apply the equations to a binary liquid–gas system and treat $$p\A^*$$ and $$p\B^*$$ as functions only of $$T$$. Some mixtures, however, have specific A–B interactions, such as solvation or molecular association, that prevent random mixing of the molecules of A and B, and the result is then negative deviations from Raoult’s law. This suggests that ethanol molecules have fewer attractive forces among themselves than propanol molecules do. Now suppose the system point is back at point a and we raise the temperature while keeping the overall composition constant at $$z\B=0.40$$. the ice that lies beneath the blades. Moving from liquid to gas is called boiling, and the temperature at which boiling occurs is called the boiling point. The two-phase areas are hatched in the direction of the tie lines. Triple point is the temperature and pressure at which all the three phases i.e solid, liquid and gas coexist. equilibrium. It resembles two simple phase diagrams like Fig. The line  $$\newcommand{\fric}{\subs{fric}} % friction$$ There is only one difference between this and the phase diagram that we've looked at up to now. Can a phase diagram have more than one point where three lines intersect? the temperature of the system at constant pressure. If you repeated this at a higher fixed pressure, the melting temperature would be higher because the line between the solid and liquid areas slopes slightly forward. When the binary system contains a liquid phase and a gas phase in equilibrium, the pressure is the sum of $$p\A$$ and $$p\B$$, which from Eq. If you increase the pressure on a gas (vapour) at a temperature lower than the critical temperature, you will eventually cross the liquid-vapour equilibrium line and the vapour will condense to give a liquid. solid.  $$\newcommand{\G}{\varGamma} % activity coefficient of a reference state (pressure factor)$$ In the case of water, the melting point gets lower at higher pressures. At this point, both solid A and solid B can coexist in equilibrium with a binary liquid mixture. The phase can be spotted at the top left corner in the graph. This is the reason that solid carbon dioxide is often known as "dry ice". The lines in a phase diagram represent boundaries between different phases; at any combination of temperature and pressure that lies on a line, two phases are in equilibrium. The state exhibited by a given sample of matter depends on the identity, temperature, and pressure of the sample. Figure 13.1 is a temperature–composition phase diagram at a fixed pressure. The solid phase is favored at low temperature and high pressure; the gas phase is favored at high temperature and low pressure. If the liquidus and vaporus curves exhibit a maximum on a pressure–composition phase diagram, then they exhibit a minimum on a temperature–composition phase diagram. Figure 13.8 Binary system of methanol (A) and benzene at $$45\units{\(\degC$$}\) (Hossein Toghiani, Rebecca K. Toghiani, and Dabir S. Viswanath, J. Chem. The diagram shows the effect of increasing the temperature of a solid at a (probably very low) constant pressure. 13.1 placed side by side.  $$\newcommand{\xbC}{_{x,\text{C}}} % x basis, C$$ For instance, the dissociation pressure of $$\ce{CuSO4*5H2O}$$ is $$1.05\timesten{-2}\units{\(\br$$}\). Note that both segments of the right-hand boundary of the one-phase solution area have positive slopes, meaning that the solubilities of the solid hydrate and the anhydrous salt both increase with increasing temperature.