1. Chemistry 2402 - Thermodynamics Lecture 12 : Kinetic coefficients and Linear response Lecture 13 : Non Ideal Solutions and Activity Lecture 14: Chemical Equilibria

2. Chemical Potential and Semi-Permeable Membranes A membrane that only allow passage of solvent molecules only can result in a cell, when placed in a dilute solution, swelling till it ruptures. Or, when placed in a concentrated solution, shrinking dramatically

3. Osmotic Pressure Consider a solution and the pure solvent, separated by a rigid semi-permeable membranes that permits only the solvent to pass through. Pressure SolutionPure Solvent Rigid semi-permeable membrane =

4. Osmotic Pressure (cont.) the volume per solvent molecule So at equilibrium Or When x 1 < 1, we need to apply an additional pressure ΔP (or Π, the osmotic pressure) to establish equilibrium and stop the flow of solvent into the solution. Note that the chemical nature of the solute is irrelevant (again) in the ideal solution.

5. Example Problem Calculate the osmotic pressure at 300K of an aqueous sucrose solution at a sucrose mole fraction of x sucrose = 0.01. The volume per molecule of water is 3.0 × 10 -29 m 3. Π = 1.39 × 10 3 kPa or 13.7 atm ! k B = 1.381 × 10 -23 JK -1

6. Flash Quiz! Why do your hands go wrinkly after a long time in the water? Is it better or worse in salty water? Source: http://www.katrinahelp.com/hurricane-katrina-pictures-8.html

7. Answer Why do your hands go wrinkly after a long time in the water? –Once any oil washes off the surface of your hands, they become permeable to water. –Skin cells have a higher concentration of solutes (e.g. salt) than the water outside. –Water flows osmotically into these cells, which expand. –The skin wrinkles to accommodate the extra surface area. Is it better or worse in salty water? –Salty water means the osmotic pressure inside and out are more similar. The process occurs more slowly.

8. Non-Ideal Solutions Acetone + Chloroform (dashed lines indicate Raoult’s Law predictions) P acetone P chloroform P = P acetone + P chloroform a negative deviation from Raoult’s Law – the result of additional attraction between the different molecules

9. Introducing the Activity of a Species For many solutions, P i ≠ x i (liq) P i *. To describe these non-ideal solutions while retaining the form of the ideal solution equations, we define a new quantity called the activity a i of species i as a i (liq) = P i /P i * so that P i = a i (liq) P i * is always true (by definition). The activity can be thought of as the “effective mole fraction”. We define the activity coefficient γ i = a i /x i. For an ideal solution, all γ i = 1. In a non-ideal solution γ i maybe greater or less than 1. For the case of acetone + chloroform both γ i ’s are less than 1.

10. The Chemical Potential for a Non-Ideal Solution Replacing the mole fraction by the activity, we have We can take this, rather than a i = P i /P i *, as the definition of the activity a i but we need to understand that this means the definition of activity depends on our choice of reference state. For aqueous solutions we need to choose a new reference state because many of the solutes are not liquids at 1 atm in the temperature range for liquid water Where the reference state is a 1 molar solution of the solute in water.

11. Activity Coefficient depends on the Other Molecules Present The activity coefficient γ i depends on the concentration of species i and what other species are present. In the case of chloroform, γ chloroform = 1 at chloroform mole fractions of 0 and 1 but is less than one in between. Replace acetone by hexane and the activity coefficient becomes closer to 1 over the whole concentration range.

12. Phase Diagrams for Non-Ideal Solutions Acetone + Chloroform A point where gas and liquid have the same composition is called an azeotrope. Distillation cannot work when the system is exactly at the azeotrope.

13. T-x Phase Diagrams Azeotropes can arise from positive and negative deviations from Raoult’s Law. 0 1 xAxA T liquid vapour 0 1 xAxA T liquid vapour negative azeotropepositive azeotrope Toby Hudson

14. Sample exam questions from previous years Consider a gas mixture at equilibrium with a solution of the same species. –What is the relationship between chemical potential and concentration in an non-ideal solution?

15. Summary You should now Understand the connection between the solubility of a solid into an ideal solution, and the free energy of melting that solid Be able to explain the concept of osmosis and osmotic pressure Be able to calculate the osmotic pressure of a solution Understand the concept of activity, and the activity coefficient Qualitatively predict the deviations from ideal behaviour in solutions with non-zero  H mix Be able to explain the concept of an azeotrope, and its role in distillation Next Lecture Chemical Equilibria