2. Solutions and Chemical Equilibrium Preparation for College Chemistry Columbia University Department of Chemistry

3. Chapter Outline Concentration of Solutions Colligative Properties Chemical Equilibrium Osmosis and Osmotic Pressure Ion Product of Water

4. Types of Solutions PhaseSoluteSolventExample Gas Liquid Solidalloys H 2 in Pt Coke antifreeze Coke airgas liquid solid gas solid liquid gas Liquid Solid

5. Concentration of Solutions UnitsSymbol Definition Mass percent Parts per million Mass/volume percent Volume percent % m/m % v/v % m/v ppm (m solute /m solution ) x100 (v solute /v solution ) x100 (m solute /v solution ) x100 mg solute /L solution Parts per billionppbµg solute /L solution Molarity Molality M m mol solute /L solution mol solute /kg solvent

6. Mass % Solute mass solute Total mass solution Mass % solute = x 100 ppb solute = mass % x 10 9 mass solute total mass solution ppm solute = x 10 6 ppm solute (aqueous solutions) = mg solute / L solution ppbppb solute (aqueous solutions) = µg solute / L solution http://pubs.acs.org:80/hotartcl/est/99/oct/oct-news5.html When concentration is so low that the d ~ d water :

7. Molarity moles solute Liter solution mol L = What volume of a 0.035 M AgNO 3 solution can be made from 5.0 g AgNO 3 ? 5.0 g AgNO 3 x 0.035 mole AgNO 3 L 169.91g 1 mole AgNO 3 x = 840 mL M =[solute] =

8. 250mL Dilution Equation Only solvent is added Preparing a dilute solution of specified concentration = C i V i C f V f C i V i CfCf VfVf =

9. Raoult’s Law Ideal Positive Negative P1P1 0 P1P1 1 0 X1X1 Basis for four properties of DILUTE SOLUTIONS

10. Colligative Properties m Freezing point depression. K f (°C kg solvent mol -1 solute ) m Boiling point elevation K b (°C kg solvent mol -1 solute ) m Osmotic Pressure (atm) Depend on the concentration of solute species and not on its nature m Vapor-pressure lowering (atm)

11. 0 20 40 6080 100120 Temperature(°C) 200 400 600 800 1000 Vapor pressure (torr) Vapor-pressure of liquids Pressure exerted by a vapor in equilibrium with its liquid Atmospheric pressure boiling point For water:

12. Vapor-pressure lowering For a two component system : solvent 1, solute 2: Raoult Law: The vapor pressure lowering is The change in vapor pressure of the solvent is proportional to the mole fraction of the solute (< 0)

13. Boiling Point Elevation (∆T b ) Vapor Pressure lowering (∆P 1 ) Solvent vapor pressure 1 atm P 0 solvent ∆P 1 ∆T b Temperature P 0 solution TbTb T’ b

14. ∆T b and ∆T f ∆T b =T b ’ - T b = K b m ∆T f = T f ’ - T f = -K f m ∆T b = b.p. elevation ∆T f = f.p. depression K f = f.p. depression constant K b = b.p. elevation constant

15. Solvent Acetic acid Benzene Camphor m.p (°C) KfKf b.p.(°C) KbKb Water 0.00 1.86100.0 0.512 16.6 3.90118.5 3.07 5.5 5.1 80.12.53 178 40 208.1 5.95 K f and K b (°C kg solvent mol -1 solute )

16. Osmosis and Osmotic Pressure,  Jacobus van’t Hoff in 1887 c = M; R = universal gas constant; T absolute temperature Pure water Solution Semipermeable membrane

17. Chemical Equilibrium 2NO 2 N2O4N2O4 N2O4N2O4 N2O4N2O4 forward reverse PRODUCTS REACTANTS REVERSIBLE REACTION: T T

18. Kinetics. Rates of Reaction RATE forward RATE reverse RATE forward = RATE reverse Equilibrium Reaction rate Time A + B C + D A + B

19. Chemical Equilibrium Saturated solution Weak electrolyte dissociation NaCl (s)Na + (aq) + Cl - (aq) HC 2 H 3 O 2 (aq) H 3 O + (aq) + C 2 H 3 O 2 - (aq) Complex ion formation Fe 3+ (aq) + SCN - (aq) Fe(SCN) 2+ ( aq)

20. Le’Chatelier’s Principle “A system in equilibrium that is subjected to a stress will react in ways that counteract the stress” Four ways to stress a chemical system: Concentration Change Volume Change Temperature Change Presence of a Catalyst

21. Equilibrium Constants, K eq aA + bB cC + dD K eq = [A] a [B] b [C] c [D] d aA(g) + bB(g) cC(g) + dD(g) K eq = (P C ) c (P D ) d (P A ) a (P B ) b KcKc KpKp LAW OF MASS ACTION. Guldberg and Waage. 1867

22. RATE forward Q > KQ > K Reaction quotient Time Reaction Quotient, Q RATE reverse Q < KQ < K Q = KQ = K Q = [A] a [B] b [C] c [D] d K eq = [A] a [B] b [C] c [D] d

23. Gases enter equilibrium expressions as partial pressures in atm Dissolved species enter as concentrations in M Pure solids and pure liquids are represented by the number 1 (unity) A solvent in a chemical reaction is represented by 1, provided the solution is diluted Writing Equilibrium Constants

24. Ion Product Constant for Water, K W H 2 O + H 2 OH 3 O + (aq) + OH - (aq) K eq = [H 2 O] 2 [H 3 O + ] [OH - ] =55.5 M 1kg H 2 O 10 3 g H 2 O xx 18 g H 2 O 1 mol H 2 O 1L H 2 O 1kg H 2 O K eq [H 2 O] 2 =[H 3 O + ][OH - ]KwKw ==1x 10 -14 Autoionization of Water [H 3 O + ]=[OH - ]=1x 10 -7 M [H 2 O] =