Phase Diagram and Phase Rule Lecture Notes PDF

Phase diagram and phase rule Lec.5 BY: Dr. Haithem N. Abed  Phase diagram A graph of pressure versus temperature (liquid and gas ) or temperature versus concentration (two liquids or solid liquid ) state phases in which these substance present at any given te...

Phase diagram and phase rule Lec.5 BY: Dr. Haithem N. Abed  Phase diagram A graph of pressure versus temperature (liquid and gas ) or temperature versus concentration (two liquids or solid liquid ) state phases in which these substance present at any given temperature , pressure and concentration. Ternary phase diagrams represent the phase behavior of mixtures containing three components in a triangular diagram P= 0.06 atm  For example Phase diagram of water on phase diagram of that is in which all of water present (Water , Ice , Vapor) under I. Pressure = 0.06 atm II. Temperature = zero °C All phase transitions occur, melting , freezing , sublimation, deposition, evaporation and condensation  Phase diagram: critical point of water Point B : critical point of water , all water evaporate and supercritical phase of water result (one phase) Critical Pressure = 218 atm Critical Temperature=374°C  normal freezing point at zero °C and 1 atm water exist as ice (one phase)  Normal boiling point At 100 °C and 1 atm , water and vapor exist (two phases)  terminology Independent Variables : conditions that affect the system , temp. , pressure , concentration not related to the number of particles. Component of the system Number of different chemical compounds Ex. water : just H2O so just one chemical comp. NaCl solution : two chemical components 1. NaCl 2. H2O  terminology Phase : a region within the phase diagram with distinct structure and physical properties , can be isolated , Can be solid, liquid or gas Two types: A single-phase system is called homogeneous system , example NaCl solution systems with two or more phases heterogeneous systems example ice cubes in water.  The Phase Rule J. Willard Gibbs formulated the phase rule, which is a relationship for determining the least number of intensive variables (independent variables that do not depend on the volume or size of the phase, e.g., temperature, pressure, density, and concentration) that can be changed without changing the equilibrium state of the system, or, alternately, the least number required to define the state of the system. The phase rule  C = number of components, is the smallest number of constituents by which the composition of each phase in the system at equilibrium can be expressed in the form of a chemical formula or equation.  P = number of phases  F = The number of degrees of freedom is the least number of intensive variables that must be fixed/known to describe the system completely. Phase diagram  One component system For example water Water – vapor phases (2 phase) F= C – P + 2 C = 1, P = 2 , so F = 1-2+2 = 1 (one variable can be fixed so no change in the number of phases in the system) OA curve in the following diagram called vapor pressure curve.  One component system Water (1 phase) F= C – P + 2 C = 1 , P = 1 , so F = 1-1+2 = 2 two variable can be fixed so no change in the number of phases in the system  One component system Water-ice –vapor F= C – P+ 2 C = 1, P = 3 so F = 1- 3 + 2 = zero zero mean no degree of freedom so neither P or T can be changed because in this system if pressure or temperature is altered , three phases will not remain in equilibrium and one of the phases disappears (F=0).  Two-Component Systems Containing Liquid Phases Two liquid systems Water / phenol system F=C–P+1 C = 2, P = 2 , F = 1. either conc. or temp. can be fixed so no change in the number of phases in the system.  Two-Component Systems Containing Liquid Phases Starting at the point a, a system containing 100% water (i.e., pure water) at 50°C, adding known increments of phenol with temp. fixed at 50°C, will result in the formation of a single liquid phase At point b ,temp. 50°C but concentration increased to 11%by weight of phenol in water, a minute amount of a second phase appears From point b to c , the two phase continue at fixed temp. of 50°C , Once the total concentration of phenol exceeds 63% at 50°C, a single phenol-rich liquid phase is formed.  Two-Component Systems Containing Liquid Phases Critical solution temperature (CST) or upper consolute temperature (plait point). Is the maximum temperature at which the two-phases region exists. In the case of the phenol–water system, this is 66.8°C (point h in Fig. 2–23). All combinations of phenol and water above this temperature are completely miscible and yield one-phase liquid systems.  Two-Component Systems Containing Liquid Phases The line bc drawn across the region containing two phases is termed a tie line; it is always parallel to the base line in two component systems. An important feature of phase diagrams is that all systems prepared on a tie line, at equilibrium, will separate into phases of constant composition. These phases are termed conjugate phases. The relative amounts of the two layers or phases vary. Tie-Line calculations and mass ratio Example: a system of phenol/water weight (100 g) at 50°C, if the concentration of phenol is 24% w/w, calculate: a) Tie line at 50°C? b) mass ratio? c) Amount of phenol and water in each phase? Answer: a) The tie-line at 50°C is 63% ---11% (upper value – lower value) 𝑃ℎ𝑎𝑠𝑒 (𝐴) 𝑈𝑝𝑝𝑒𝑟 𝑣𝑎𝑙𝑢𝑒 −𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 b) mass ratio law = = 𝑃ℎ𝑎𝑠𝑒 (𝐵) 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 −𝑙𝑜𝑤𝑒𝑟 𝑣𝑎𝑙𝑢𝑒 63−24 39 3 = = = 24−11 13 1 ∴ total no. of parts = 3+1 = 4 Tie-Line calculations and mass ratio 3 c) : × 100 = 75 g weight of water 4 1 × 100 = 25g weight of phenol 4 11 × 75 = 8.25 g weight of phenolin phase A 100 - we calculate the weight of phenol in Phase B 63  × 25 = 15.75 g of phenol in phase B (phenol 100 rich phase).  This gives a sum total of 24 g of phenol in the whole system. This equals the amount of phenol originally added.  phase A contains 66.75 g of water and phase B 9.25 g of water.  Two-Component Systems Containing Liquid Phases Lower consolute temperature : a temp. bellow which the components are miscible in all proportions (water- triethylamine system). Sometimes the binary liquid systems show both upper consolute temperature and lower consolute temperature such as water-nicotine system. Two component systems containing solid and liquid phases  solid/liquid state pressure is constant thus either concentration affect the system phases number or temperature. Eutectic mixtures as an approach to enhance solubility, dissolution rate and oral bioavailability of poorly water-soluble drugs. Two component systems containing solid and liquid phases melting point as a function of composition of two or three component in systems. A eutectic system is a homogeneous mixture of two or more components, which together have a lower melting point than each of them separately. The eutectic mixture melts as a whole only at a specific ratio of those two components in the mixture. Two component systems containing solid and liquid phases The eutectic point is the lowest temperature at which a liquid phase exist in equilibrium with a solid phase. The eutectic composition is the composition of a system at its eutectic point. The eutectic point therefore denotes an invariant system because, in a condensed system, F = 2 − 3 + 1 = 0. Two component systems containing solid and liquid phases The phase diagram for the salol–thymol system is shown in Figure 2–26. Notice that there are four regions: (i) a single liquid phase, (ii) a region containing solid salol and a conjugate liquid phase, (iii) a region in which solid thymol is in equilibrium with a conjugate liquid phase, and (iv) a region in which both components are present as pure solid phases.  Three component systems phase diagram Three component system present in one phase , F = 3 - 1 + 2 = 4,. The four degrees of freedom are temperature, pressure, and the concentrations of two of the three components.  Three component systems phase diagram The mutual solubility of two partially miscible solvents influenced by o Temperature o addition of a third liquid. 100 C  Three component systems phase diagram The addition of a third liquid to a binary liquid system to produce a ternary or three component system can results in a several possible combinations: 1- If a third liquid is soluble in only one of the two liquids, mutual solubility of the original liquids is decreased. Example addition of water to ethanol – toluene solution 2- If a third liquid is soluble in the two liquids, the mutual solubility of the original liquids is increased. Benzene and water are immiscible, addition of ethanol to this binary liquid cause increase in the solubility. Third liquid addition  Ternary phase diagram Ternary phase diagram concept used to determine the volume of the third liquid that must be added: to maintaining the system homogenous or to convert the two-immiscible liquids (two phase system) to a homogenous or one phase system.  Ternary phase diagram 1. Each of the three corners or apexes of the triangle represent 100% by weight of one component (A, B, or C). As a result, that same apex will represent 0% of the other two components. 2. The three lines joining the corner points represent two-component mixtures of the three possible combinations of A, B, and C. 3. The area within the triangle represents all the possible combinations of A, B, and C to give three-component systems.  Ternary phase diagram 4. If a line is drawn through any apex to a point on the opposite side (e.g., line DC in Fig. 2–27), then all systems represented by points on such a line have a constant ratio of two components, in this case A and B (see table 2-8). 5. Any line drawn parallel to one side of the triangle, for example, line HI in Figure 2–27, represents ternary system in which the proportion (or percent by weight) of one component is constant.