Phase Equilibrium - Chemical Process Principles - Lecture Slides, Slides of Chemical Processes

Download Phase Equilibrium - Chemical Process Principles - Lecture Slides and more Slides Chemical Processes in PDF only on Docsity! 1 Graphical Methods for Phase Equilibrium Class 21 • Questions about Raoult’s Law – Dew point – Bubble point – Flash • Graphical methods – Vapor-liquid – Lever Rule – Solid-liquid – Liquid-liquid n-pentane and n-heptane at 2 atm 50 60 70 80 90 100 110 120 130 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole Fraction n-pentane yi for vapor xi for liquid T ( C ) Vapor Liquid Dew line Bubble line Generated from Raoult’s law using the DIPPR vapor pressure correlations 40 50 60 70 80 90 100 110 120 130 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 T ( C ) Mole Fraction n-pentane yi for vapor xi for liquid n-pentane and n-heptane at 2 atm Vapor Liquid Dew line Bubble line 40 50 60 70 80 90 100 110 120 130 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 T ( C ) Mole Fraction n-pentane yi for vapor xi for liquid n-pentane and n-heptane at 1.5 atm Vapor Liquid Dew line Bubble line VLE Phase Diagrams (n-pentane/n-heptane) Mole fraction pentane (at 1.5 atm) Mole fraction pentane (at 400 K) (1) 385 K (2) 335 K (3) 358 K 1) What is the boiling point of n-heptane? 2) At what temperature would a liquid mixture of 40% n-heptane and 60% n-pentane begin to boil? 3) At what temperature would a vapor mixture of 40% n-heptane and 60% n-pentane begin to condense? VLE Phase Diagrams (n-pentane/n-heptane) Mole fraction pentane (at 1.5 atm) Mole fraction pentane (at 400 K) (4) 92% pentane (5) 39% pentane (6) 10.2 atm 4) What is the composition of the vapor in equilibrium with a liquid that is 30% n-heptane and 70% n-pentane? 5) What is the composition of the liquid in equilibrium with a vapor that is 75% n-pentane and 25% n-heptane? 6) Using the P-xy diagram, what is the vapor pressure of n- pentane at the temperature for which the diagram was prepared? Lever Rule 2 distinct phases and 2 components • Total mole balance: nF = nL + nV (or nV = nF – nL) • Species mole balance zA nF = xA nL + yA nV • Now substitute for nV zA nF = xA nL + yA (nF – nL) • Group F terms on left and L terms on right (zA - yA) nF = (xA – yA) nL Feed Vapor Liquid nF zA nL xA nV yA AA AA AA AA F L xy zy yx yz n n       2 Lever Rule Graphical Interpretation (very useful) Feed Vapor Liquid nF zA nL xA nV yA AA AA AA AA F L xy zy yx yz n n       T Mole fraction F VL Distance B Distance A xA zA yA • Distance A corresponds to yA – zA. • Distance B corresponds to yV – xA. • Therefore, nL/nF = Distance A / Distance B!! • In practice, you can use the actual mole fractions or use the measured distance using a ruler Intuition: As you get closer to the liquid line, you have more liquid! VLE Phase Diagrams (n-pentane/n-heptane) part (7) Mole fraction pentane (at 1.5 atm) Mole fraction pentane (at 400 K) Use lever rule. L/F = (0.58 – 0.3)/(0.58 – 0.22) or 2.8 boxes/(2.8 + 0.8) = 0.78 7) A feed stream of 30% n-pentane and 70% heptane is brought to a pressure of 1.5 atm and a temperature of 360 K. What is the composition and amount of the liquid and the vapor streams in equilibrium at this condition? xpent = 0.22 ypent = 0.58 Mole fraction of A Solid B + Eutectic Solid A + Eutectic Solid-Liquid Phase Diagrams What is a Eutectic??? • Solid crystals having a composition that is a mixture of pure components • Not in equilibrium with any liquid solution, but may be in equilibrium with a pure solid – i.e., a fraction of the solid is pure component, and the rest is the crystals with mixed composition Mole fraction of A Solid B + Eutectic Solid A + Eutectic Solid-Liquid Phase Diagrams Eutectic composition Eutectic point (no liquid below this temperature) Mole fraction of A Solid B + Eutectic Solid A + Eutectic Solid-Liquid Phase Diagrams (1) (2) (3) (4) 1) What phases are present for a mixture of 30% A at 320 K? 2) What phases are present for a mixture of 60% A at 320 K? 3) What phases are present for mixture of 50% A at 300 K? 4) For a mixture of 80% A, what phases are present at equilibrium at 310 K? How much of each phase is present? 1) Pure Solid B and solution with 52% A 2) Solution with 60% A 3) Solid B and solid eutectic of 65% A 4) Solid A and solution with 68% A 2/3.2 = 62.5% of material is solution, 37.5% solid A