SIMPLE MIXTURES thermodynamic description of mixtures

1. SIMPLE MIXTURESthermodynamic description of mixtures ARYO ABYOGA A (080358395) GERALD MAYO L (0806472212) LEONARD AGUSTINUS J (0806472225)

2. Simple Mixtures • Often in chemistry, we encounter mixtures of substances that can react together. • Chapter 7 deals with reactions, but let’s first deal with properties of mixtures that don’t react. • We shall mainly consider binary mixtures – mixtures of two components.

3. Dalton’s Law • The total pressure is the sum of all the partial pressure. • We already used mole fraction to descrice the partial pressure of mixtures of gases which refers to a total pressure

4. partial molar volume The partial molar volume is the contribution that one component in a mixture makes to the total volume of a sample H2OEtOH Add 1.0 mol H2O Add 1.0 mol H2O Volume increases by 18 cm3 mol-1 Volume increases by 14 cm3 mol-1 Molar volume of H2O: 18 cm3 mol-1 Partial molar volume of H2O in EtOH: 14 cm3 mol-1 The different increase in total volume in the H2O/EtOH example depends on the identity of the molecules that surround the H2O. The EtOH molecules pack around the water molecules, increasing the volume by only 14 cm3 mol-1 Partial molar volume of substance A in a mixture is the change in volume per mole of A added to the large volume of the mixture

5. Partial Molar Volumes • Imagine a huge volume of pure water at 25 °C. If we add 1 mol H2O, the volume increases 18 cm3 (or 18 mL). • So, 18 cm3 mol-1 is the molar volume of pure water.

6. Partial Molar Volumes • Now imagine a huge volume of pure ethanol and add 1 mol of pure H2O it. How much does the total volume increase by?

7. Partial Molar Volumes • When 1 mol H2O is added to a large volume of pure ethanol, the total volume only increases by ~ 14 cm3. • The packing of water in pure water ethanol (i.e. the result of H-bonding interactions), results in only an increase of 14 cm3.

8. Partial Molar Volumes • The quantity 14 cm3 mol-1 is the partial molar volume of water in pure ethanol. • The partial molar volumes of the components of a mixture varies with composition as the molecular interactions varies as the composition changes from pure A to pure B.

9. The partial molar volume of components of a mixture vary as the mixture goes from pure A to pure B - that is because the molecular environments of each molecule change (i.e., packing, solvation, etc.) Partial molar volumes of a water-ethanol binary mixture are shown at 25 oC across all possible Compositions. The Partial molar volume, Vj, of a substance j define as :

10. The partial molar volume is the slope of a plot of total volume as the amount of J in the sample is changed (volume vs. composition) Partial molar volumes vary with composition (different slopes at compositions a and b) - partial molar volume at b is negative (i.e., the overall sample volume decreases as A is added)

11. Partial Molar Volumes • When a mixture is changed by dnA of A and dnB of B, then the total volume changes by: If partial molar volumes are known for the two components, then at some temperature T, the total volume V (state function, always positive) of the mixture is

12. Partial Molar Volumes

13. Partial Molar Volumes

14. Partial Molar Volumes

15. Partial Molar Volumes • How to measure partial molar volumes? • Measure dependence of the volume on composition. • Fit a function to data and determine the slope by differentiation.

16. Partial Molar Volumes • Ethanol is added to 1.000 kg of water. • The total volume, as measured by experiment, fits the following equation:

17. Partial Molar Volumes

19. Partial Molar Volumes • Molar volumes are always positive, but partial molar quantities need not be. The limiting partial molar volume of MgSO4 in water is -1.4 cm3mol-1, which means that the addition of 1 mol of MgSO4 to a large volume of water results in a decrease in volume of 1.4 cm3.

20. Partial Molar Gibbs energies • The concept of partial molar quantities can be extended to any extensive state function. • For a substance in a mixture, the chemical potential is defined as the partial molar Gibbs energy.

22. Partial Molar Gibbs energies • For a pure substance:

23. Partial Molar Gibbs energies • Using the same arguments for the derivation of partial molar volumes, • Assumption: Constant pressure and temperature

24. Partial Molar Gibbs energies

25. Chemical Potential

26. Chemical Potential

27. Gibbs-Duhem equation

28. Gibbs-Duhem equation

29. Molarity and Molality • Molarity, c, is the amount of solute divided by the volume of solution. Units of mol dm-3 or mol L-1. • Molality, b, is the amount of solute divided by the mass of solvent. Units of mol kg-1.

30. Using Gibbs-Duhem • The experimental values of partial molar volume of K2SO4(aq) at 298 K are found to fit the expression:

31. Using Gibbs-Duhem

32. Using Gibbs-Duhem

33. Using Gibbs-Duhem

34. Using Gibbs-Duhem

35. Using Gibbs-Duhem

37. Thermodynamics of mixing • So we’ve seen how Gibbs energy of a mixture depends on composition. • We know at constant temperature and pressure systems tend towards lower Gibbs energy. • When we combine two ideal gases they mix spontaneously, so it must correspond to a decrease in G.

38. Thermodynamics of mixing

39. Thermodynamics of mixing

40. Thermodynamics of mixing

41. Thermodynamics of mixing

42. Thermodynamics of mixing

43. Gibbs energy of mixing • A container is divided into two equal compartments. One contains 3.0 mol H2(g) at 25 °C; the other contains 1.0 mol N2(g) at 25 °C. Calculate the Gibbs energy of mixing when the partition is removed.

44. Gibbs energy of mixing • Two processes: 1) Mixing 2) Changing pressures of the gases.

45. Gibbs energy of mixing p p

46. Other mixing functions

48. Other mixing functions