Chemical Equilibrium

Chemical Equilibrium The state of a chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products does not change with time.

aA + bB + cC + ... <=> pP + qQ + rR + ... Law of Mass Action aA + bB + cC + ... <=> pP + qQ + rR + ... Equilibrium Constant [P]p [Q]q [R]r ... K = --------------------- [A]a [B]b [C]c ...

Meaning of Equilibrium Constant K>>1: reaction is product-favored; equilibrium concentrations of products are greater than equilibrium concentrations of reactants. K<<1: reaction is reactant-favored; equilibrium concentrations of reactants are greater than equilibrium concentrations of products.

What is K for the reverse reaction, If K = 100 = [I2 in CCl4] / [I2 in water] for the equilibrium I2 in water = I2 in CCl4 What is K for the reverse reaction, I2 in CCl4 = I2 in H2O? 100, 1, 0.01

Acid-Base Equilibrium in Aqueous Solution Acid Dissociation Constant HC2H3O2 + H2O <=> H3O+ + C2H3O2- [H3O+][C2H3O2-] K = ---------------------- [H2O][HC2H3O2] [H3O+][C2H3O2-] Ka = K*[H2O] = ---------------------- [HC2H3O2]

Acid-Base Equilibrium in Aqueous Solution Base Dissociation Constant NH3 + H2O <=> NH4+ + OH- [NH4+][OH-] K = ----------------- [H2O][NH3] [NH4+][OH-] Kb = K*[H2O] = ---------------- [NH3]

Autoionization of Water H2O + H2O <=> H3O+ + OH- [H3O+][OH-] K = ----------------- [H2O]2 Kw = K [H2O]2 = [H3O+][OH-] = 1.0 x 10-14

Analogy in Semiconductors | | | | -Si:Si- <=> -Si+:Si- + e- | | -Si:Si- <=> h+ + e- K = h+ * e-

e- and h+ in Semiconductors Production electrons (e ) – holes (h ) + Electron energy conduction band valence E g conduction band valence Recombination © 1993 American Chemical Society Si e – + h Localized pictures are on the left, and their delocalized counterparts on the right. In a semiconductor, when an electron is promoted into the conduction band, it leaves a hole in the valence band. Electrons fall from the conduction band back into the valence band, recombining with holes.

Autoionization Equilibria © 1993 American Chemical Society Just as water undergoes autoionization into H+ and OH–, Si-Si bonds in Si can undergo the loss of an electron to produce a mobile hole (a one-electron bond between Si atoms) and a mobile electron. Just as there is an ion product constant for water, Kw, there is an equilibrium constant for the concentration of holes and electrons, p and n, in a semiconductor such as silicon. At the right is a plot of the hole concentration versus 1/T for various semiconductors; and of the proton concentration versus 1/T for water. p-type refers to semiconductors with p > n. n-type refers to semiconductors with n > p. These are endothermic reactions, illustrating Le Chatelier's principle that products are favored by an increase in temperature.

e- and h+ in Semiconductors Si e – (–) (+)

Doping © 1993 American Chemical Society Doping can create additional mobile “electrons” and “holes” in the silicon crystal by substitution of the silicon atoms with Group 15 (VA) atoms or Group 13 (IIIA) atoms, respectively. Doping with P creates a donor level just below the conduction band in silicon and enhances conductivity; a P atom has one more electron than needed to form four bonds. Its extra electron is readily ionized, adding a mobile electron to the conduction band. Doping with Al creates an acceptor level just above the valence band in silicon and enhances conductivity; an Al atom has one less valence electron than needed to form four bonds, adding a mobile hole to the valence band.

Donors and Acceptors in Silicon conduction band donors M ® M + e + – } } © 1993 American Chemical Society Energy levels for dopants in silicon with ionization energies, in electron volts, shown in parentheses. Donors are indicated with a plus charge; acceptors with a negative charge. valence band

Which dopant will act as an acceptor for Si? B, Ge, As As a donor?

Fermi Level Fermi level: the thermodynamic electrochemical potential. © 1993 American Chemical Society Fermi level: the thermodynamic electrochemical potential. Upper left, Fermi level for metal. Upper right, Fermi level in undoped semiconductor is roughly equidistant from the valence and conduction band edges. Lower left, Fermi level in p-type semiconductor is near the valence band. Lower right, Fermi level in n-type semiconductor is near the conduction band.

Le Chatelier's Principle If a stress, such as a change in concentration, pressure, temperature, etc., is applied to a system at equilibrium, the equilibrium will shift in such a way as to lessen the effect of the stress.

Gas Phase Equilibrium catalysis N2(g) + 3 H2(g) <=====> 2 NH3(g) + heat high pressure and temperature

The Principle of Le Chatelier Changes in Concentration or Partial Pressure for N2(g) + 3 H2(g) Û 2 NH3(g) an increase in N2 and/or H2 concentration or pressure, will cause the equilibrium to shift towards the production of NH3

The Principle of Le Chatelier Changes in Concentration or Partial Pressure for N2(g) + 3 H2(g) Û 2 NH3(g) likewise, a decrease in NH3 concentration or pressure will cause more NH3 to be produced

The Principle of Le Chatelier Changes in Temperature for N2(g) + 3 H2(g) Û 2 NH3(g) + heat for an exothermic reaction, an increase in temperature will cause the reaction to shift back towards reactants

The cobalt complexes participating in the equilibrium below comprise a humidity sensor. From Le Châtelier's principle, when the sensor is moist (excess H2O), what color is the cobalt complex? pink, blue

From Le Châtelier's principle, how is CO poisoning reversed? A competition experiment involves O2 and CO vying for hemoglobin (Hb) sites, defined by the equilibrium Hb(O2)4 + 4 CO = Hb(CO)4 + 4O2 From Le Châtelier's principle, how is CO poisoning reversed? decrease O2 pressure, increase O2 pressure, remove Hb

Heterogeneous Equilibrium CaCO3(s) + heat <===> CaO(s) + CO2(g)

Gibbs Free Energy and Equilibrium DG Reaction ------------------------------------- Negative Spontaneous Positive Non-Spontaneous Zero Equilibrium

The Influence of Temperature on Free Energy DG, DH, & DS DG = DH - T DS DH DS DG negative positive negative spontaneous at all temperatures

The Influence of Temperature on Free Energy DG, DH, & DS DG = DH - T DS DH DS DG positive negative positive non-spontaneous at all temperatures

The Influence of Temperature on Free Energy DG, DH, & DS DG = DH - T DS DH DS DG negative negative -------- spontaneous at low temperatures, nonspontaneous at high temperatures

The Influence of Temperature on Free Energy DG, DH, & DS DG = DH - T DS DH DS DG positive positive -------- spontaneous at high temperatures, nonspontaneous at low temperatures

Phase Transitions H2O(s) -----> H2O(l) DH > 0; DS > 0 H2O(l) -----> H2O(g) DH > 0; DS > 0 spontaneous at high temperatures

Phase Transitions H2O(l) -----> H2O(s) DH < 0; DS < 0 H2O(g) -----> H2O(l) DH < 0; DS < 0 spontaneous at low temperatures