Chapter 12 Solutions

1. Chapter 12Solutions

2. Solution Concentration • There are a number of ways to express concentration. You have seen: • molarity; • mole fraction; • mass percentage: • for expressing the composition of a compound; • and can be used for solutions, as well. • normality

3. Solution Concentration • All concentration units are fractions. • The numerator contains the quantity of solute. • The denominator is the quantity of either solution or solvent. • They differ in the units used to express these two quantities.

4. Units of Concentration Used Earlier

5. Mass Percent Composition

6. Example: Percent Composition • A solution is prepared by dissolving 3.00 g of NaCl (molar mass = 58.44 g/mol) in 150 g of water. Express its concentration as mass percent.

7. Molality • Molality (m or molal) is defined as

8. Example: Calculate Molality • What is the molality of a solution prepared by dissolving 3.00 g NaCl (molar mass = 58.44 g/mol) in 150 g of water?

9. Example: Concentration Conversion • Express the concentration of a 3.00% H2O2 solution as (a) molality; (b) mole fraction.

10. Test Your Skill • Calculate (a) the molality, and (b) the mole fraction of alcohol (C2H5OH; molar mass = 46.07 g/mol) in a wine that has an alcohol concentration of 7.50 mass percent.

11. Example: Conversion to Molarity • Conversion of most concentration units to molarity usually involve using the density of the solution to convert units of mass to units of volume. • The density of a 12.0% sulfuric acid (H2SO4; molar mass = 98.08 g/mol) is 1.080 g/mL. What is the molarity of this solution?

12. Principles of Solubility • For most substances, there is a limit to the quantity of solute that dissolves in a specific quantity of solvent. • A dynamic equilibrium exists between the solute particles in solution and the undissolved solute.

13. Normality • Normality, (N) is defined as the number of equivalents per liter of solution. • Problem – what are equivalents – depends on reaction • Not used very often • One place that normality is sometimes encountered is with acid-base chemistry. • How many protons are release by an acid defines the equivalents • EX: • HCl – releases 1 H+ so… 1M = 1N • H2SO4 – releases 2H+ so… 1M = 2N • We will not be using normality, but you might encounter it in other chemistry classes!!

14. Definitions • Solubility is the concentration of solute that exists in equilibrium with an excess of that substance. • A saturated solution has a concentration of solute equal to its solubility.

15. Definitions (continued) • An unsaturated solution is one that has a solute concentration less than the solubility. • A supersaturated solution is one with a solute concentration that is greater than the solubility. • Supersaturation is an unstable condition.

16. Solute-Solvent Interactions • Many spontaneous processes are exothermic. • Enthalpy of solution: the DH that accompanies the dissolution of one mole of solute. • When a solid and a liquid form a solution, the enthalpy change arises mainly from changes in the intermolecular attractions.

17. The Solution Process • Steps 1 and 2 are endothermic; step 3 is exothermic.

18. Spontaneity • A decrease in enthalpy is an important factor in causing spontaneous change. • However, many endothermic processes are spontaneous, suggesting another contribution to spontaneity. • In increase in disorder also favors spontaneous change.

19. Spontaneous Mixing of Gases • An example of increasing disorder as a driving force is illustrated by the mixing of gases. (a) separated gases (b) spontaneously mixed

20. Disorder and Spontaneity • An increase in disorder generally accompanies the mixing of molecules in the formation of a solution. • Ammonium nitrate is very soluble in water because of the increase in disorder upon mixing, even though the process is quite exothermic (DHsoln = +26.4 kJ/mol).

21. Solubility of Molecular Compounds • Relative solubilities can often be predicted by comparing the relative strengths of the intermolecular attractions of solute-solute, solvent-solvent, and solute-solvent interactions.

22. Like Dissolves Like • In general, substances that have similar intermolecular forces have strong solute-solvent interactions and tend to form solution.

23. Example: Relative Solubility • (a) Is iodine (I2) more soluble in water or in hexane (C6H14)? • (b) Is methanol (CH3OH) more soluble in water or in octane (C8H18)?

24. Interaction of Ions with Water • Hydrationis the interaction of water molecules with ions, and is very exothermic.

25. Ionic Compounds in Water • When an ionic compound dissolves in water, disorder changes because: • separating the ions increases disorder; • separating the water molecules increases disorder; • hydrating the ions, which restricts some water molecules, decreases disorder. • A few examples are known where disorder decreases on dissolving ionic compounds.

26. Pressure and Solubility • Pressure has very little effect on the solubilities of liquids and solids. • The solubility of gases in a liquid depends on the pressure of the gas. • Henry’s Law: The solubility of a gas is directly proportional to its partial pressure at any given temperature: C = kP

27. Henry’s Law Constants in Water for Various Gases (molal/atm)

28. Henry’s Law Calculation • Water at 20C is saturated with air that contains CO2 at a partial pressure of 8.0 torr. What is the molal concentration of CO2 in the solution?

29. Solubility and Temperature • Experiments show that the way solubility changes with temperature depends on the sign of the enthalpy of solution. • Solubility increases with increasing temperature if DHsoln is positive (endothermic). • Solubility decreases with increasing temperature if DHsoln is negative (exothermic).

30. Solubility and DHsoln K2Cr2O7(s) → K2Cr2O7(aq) DH = +66.5 kJ/mol The solubility increases with increasing temperature when DHsoln is positive.

31. Temperature Dependence on Solubility

32. Colligative Properties of Solutions • Colligative property: Any property of a solution that changes in proportion to the concentration of solute particles. • Many colligative properties are directly related to the lowering of solvent vapor pressure by the presence of solute particles.

33. Effect of Solute on Evaporation • The rate of evaporation of solvent in a solution is lower than that of the pure solvent. Solute particles block opportunities for solvent particles to enter the vapor phase.

34. Raoult’s Law • Raoult’s law: The vapor pressure of solvent above a dilute solution equals the mole fraction of the solvent times the vapor pressure of the pure solvent. Psolv = csolvPsolv • Another form of this equation gives the lowering of the vapor pressure. DPsolv = csolutePsolv

35. Example: Raoult’s Law • At 27C, the vapor pressure of benzene is 104 torr. What is the vapor pressure of a solution that has 0.100 mol of naphthalene in 9.90 mol of benzene?

36. Boiling Point Elevation • Because a solute lowers the vapor pressure of the solvent, it raises the boiling point of the solution. Below, the concentration of the solution is increasing from (a) to (e).

37. Boiling Point Elevation • The boiling point elevation is DTb = mkb where m is the molal concentration and kb is the boiling point constant for the solvent.

38. Freezing Point Depression • Solute particles interfere with the ability of solvent particles to form a crystal and freeze. Thus, it takes a lower temperature to freeze solvent from a solution than from the pure solvent. This is freezing point depression.

39. Freezing Point Depression • The freezing point depression is DTf = mkf where m is the molal concentration and kf is the freezing point constant for the solvent.

40. Example: Calculate kf • Benzophenone freezes at 48.1C. A solution of 1.05 g urea ((NH2)2CO, molar mass = 60.06 g/mol) in 30.0 g of benzophenone freezes at 42.4C. What is kf for benzophenone?

41. Test Your Skill • Benzophenone freezes at 48.1C and has a kf of 9.8C/molal. A 2.50-g sample of solute whose molar mass is 130.0 g/mol is dissolved in 32.0 g of benzophenone. What is the freezing point of the solution?

42. Osmosis • Semipermeable membranes allow water and small molecules to pass through them. • Osmosis is the diffusion of a fluid through a semipermeable membrane.

43. Osmosis (continued) • When a semipermeable membrane separates a solution from the pure solvent, the net effect is for pure solvent to move through the membrane into the solution. • The higher level of liquid produces an additional pressure, called osmotic pressure.

44. Osmotic Pressure • Osmotic pressure is a colligative property, and can be calculated by the equation P = MRT where: P = osmotic pressure M = molar concentration of solute R = ideal gas law constant T = temperature in Kelvin

45. Example: Molar Mass by Osmotic Pressure • A 5.70 mg sample of protein is dissolved in water to give 1.00 mL of solution. Calculate the molar mass of the protein if the solution has an osmotic pressure of 6.52 torr at 20C.

46. Colligative Properties - Summary

47. Electrolyte Solutions • The colligative properties of electrolyte solutions are more pronounced because electrolytes separate into ions in solution. • The van’t Hoff factor, i, is defined by the equation

48. The van’t Hoff Factor • In dilute solution, the van’t Hoff factor for salts approaches the number of ions produced by one formula unit of the substance. NaCl → Na+(aq) + Cl-(aq) i = 2 MgBr2 → Mg2+(aq) + 2Br-(aq) i = 3 • The van’t Hoff factor generally decreases as the concentration increases.

49. Example: the van’t Hoff Factor • Arrange the following aqueous solutions in order of increasing boiling points: 0.03 m urea (a nonelectrolyte), 0.01 m NaOH, 0.02 m BaCl2, 0.01 m Fe(NO3)3.

50. Mixtures of Volatile Substances • In a solution of two or more volatile compounds, all components of the mixture are in equilibrium with their vapors. • An ideal solution is one in which all volatile components obey Raoult’s law for all compositions. PA = cAPA, PB = cBPB,PC = cCPC, etc.