Lecture 4. Phase Equilibrium PhD Falfushynska H.

Sulfur phase diagram triple point

Gibb’s Phase Rule: a tool to define the number of phases and/or degrees of phase changes that can be found in a system at equilibrium For any system under study the rule determines if the system is at equilibrium For a given system, we can use it to predict how many phases can be expected Using this rule, for a given phase field, we can predict how many independent parameters (degrees of freedom) we can specify Typically, N = 1 in most condensed systems – pressure is fixed!

A system involving one pure chemical is an example of a one-component system.

A typical phase diagram. The solid green line applies to most substances; the dotted green line gives the anomalous behavior of water. The green lines mark the freezing point and the blue line the boiling point, showing how they vary with pressure.

Clausius–Clapeyron relation is a way of characterizing a discontinuous phase transition between two phases of matter of a single constituent. dP/dT is the slope of tangent to the coexistence curve at any point

Gibbs–Duhem relation For a liquid-gas transition, L is the specific latent heat (or specific enthalpy) of vaporization, whereas for a solid-gas transition, L is the specific latent heat of sublimation Application of Clausius–Clapeyron relation

Dependence of melting on solid solution composition Dependence of crystallization temperature on fusion

The iron–iron carbide (Fe– Fe 3 C) phase diagram. The percentage of carbon present and the temperature define the phase of the iron carbon alloy and therefore its physical characteristics and mechanical properties. The percentage of carbon determines the type of the ferrous alloy: iron, steel or cast iron

Eutectic system A eutectic system is a mixture of chemical compounds or elements that has a single chemical composition that solidifies at a lower temperature than any other composition made up of the same ingredients. Lidocaine and prilocaine, both solids at room temperature, form a eutectic that is an oil with a 16 °C (61 °F) melting point, used in eutectic mixture of local anesthetic (EMLA) preparations.

the intersection of the eutectic temperature and the eutectic composition gives the eutectic point

Ternary igneous phase diagrams are triangular diagrams that show melting relationships involving three chemical components. The diagrams may involve eutectic, peritectic and cotectic relationships.

Metamorphic T-X Phase Diagrams For some rock compositions, metamorphic assemblages vary greatly depending on the composition of the fluid present. Metamorphic fluids are generally dominated by H 2 O and CO 2, and the ratio H 2 O:CO 2 can control mineral stability. So, phase equilibria are plotted on T-X diagrams instead of P-T diagrams. (X refers to the mole fraction of 2 or H 2 O in the metamorphic fluid that is present.)

wt% Ni T(°C) L (liquid)  (FCC solid solution) L +  liquidus solidus Cu-Ni phase diagram Phase Diagrams: Rule 1: If we know T and C o then we know the # and types of all phases present. Examples: A(1100°C, 60): 1 phase:  B(1250°C, 35): 2 phases: L +  B (1250°C,35) A(1100°C,60)

wt% Ni T(°C) L (liquid)  (solid) L +  liquidus solidus L +  Cu-Ni system Phase Diagrams: Rule 2: If we know T and C o we know the composition of each phase Examples: T A A 35 C o 32 C L At T A = 1320°C: Only Liquid (L) C L = C o ( = 35 wt% Ni) At T B = 1250°C: Both  and L C L = C liquidus ( = 32 wt% Ni here) C  = C solidus ( = 43 wt% Ni here) At T D = 1190°C: Only Solid (  ) C  = C o ( = 35 wt% Ni) C o = 35 wt% Ni adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, B T B D T D tie line 4 C  3

Rule 3: If we know T and C o then we know the amount of each phase (given in wt%) Examples: At T A : Only Liquid (L) W L = 100 wt%, W  = 0 At T D : Only Solid (  ) W L = 0, W  = 100 wt% C o = 35 wt% Ni Therefore we define wt% Ni T(°C) L (liquid)  (solid) L +  liquidus solidus L +  Cu-Ni system T A A 35 C o 32 C L B T B D T D tie line 4 C  3 R S At T B : Both  and L = 27 wt% WLWL  S R+S WW  R R+S Notice: as in a lever “the opposite leg” controls with a balance (fulcrum) at the ‘base composition’ and R+S = tie line length = difference in composition limiting phase boundary, at the temp of interest

wt% Ni L (liquid)  (solid) L +  L +  T(°C) A 35 C o L: 35wt%Ni Cu-Ni system Phase diagram: Cu-Ni system. System is: --binary i.e., 2 components: Cu and Ni. --isomorphous i.e., complete solubility of one component in another;  phase field extends from 0 to 100 wt% Ni. Adapted from Fig. 9.4, Callister 7e. Consider C o = 35 wt%Ni. Ex: Cooling in a Cu-Ni Binary  :43 wt% Ni L: 32 wt% Ni L: 24 wt% Ni  :36 wt% Ni B  : 46 wt% Ni L: 35 wt% Ni C D E 24 36

Partition Coefficient Kp (Distribution Coefficient Kd) When a compound is shaken in a separatory funnel with two immiscible solvents, the compound will distribute itself between the two solvents. Normally one solvent is water and the other solvent is a water-immiscible organic solvent. Most organic compounds are more soluble in organic solvents, while some organic compounds are more soluble in water.

Here is the universal rule: At a certain temperature, the ratio of concentrations of a solute in each solvent is always constant. ﾊ And this ratio is called the distribution coefficient, K. (when solvent 1 and solvent 2 are immiscible liquids For example,Suppose the compound has a distribution coefficient K = 2 between solvent 1 and solvent 2 By convention the organic solvent is (1) and waater is (2)

(1)If there are 30 particles of compound, these are distributed between equal volumes of solvent 1 and solvent 2.. (2) If there are 300 particles of compound, the same distribution ratio is observed in solvents 1 and 2 (3) When you double the volume of solvent 2 (i.e., 200 mL of solvent 2 and 100 mL of solvent 1 ), the 300 particles of compound distribute as shown If you use a larger amount of extraction solvent, more solute is extracted

Separatory Funnel Extraction Procedure 1. Support the separatory funnel in a ring on a ringstand. Make sure stopcock is closed 2. Pour in liquid to be extracted 3. Add extraction solvent 4. Add ground glass Stopper (well greased)

Separatory Funnel Extraction Procedure Pick up the separatory funnel with the stopper in palce and the stopcock closed, and rock it once gently. Then, point the stem up and slowly open the stopcock to release excess pressure. Close the stopcock. Repeat this procedure until only a small amount of pressure is released when it is vented Shake the separatory funnel.

Separatory Funnel Extraction Procedure Shake the separatory funnel vigorously. Now, shake the funnel vigorously for a few seconds. Release the pressure, then again shake vigorously. About 30 sec total vigorous shaking is usually sufficient to allow solutes to come to equilibrium between the two solvents. Vent frequently to prevent pressure buildup, which can cause the stopcock and perhaps hazardous chemicals from blowing out. Take special care when washing acidic solutions with bicarbonate or carbonate since this produces a large volume of CO 2 gas

Separatory Funnel Extraction Procedure Separate the layers. Let the funnel rest undisturbed until the layers are clearly separated While waiting, remove the stopper and place a beaker or flask under the sep funnel. Carefully open the stopcock and allow the lower layer to drain into the flask. Drain just to the point that the upper liquid barely reaches the stopcock

Chlorophyll extraction