Chapter 16: Chemical Equilibrium What is meant by an equilibrium system? What is an equilibrium expression? N 2 +3 H 2 2 NH 3 1) Only gases and dissolved species appear in an equilibrium expression. 4 NH 3 + 7 O 2 4 NO 2 + 6 H 2 O K c = 2.) HCl(aq) + H 2 O(l) H 3 O + (aq) + Cl(aq) K c = 3) Pure solids and liquids have a value of 1, so are not explicitly written in the equilibrium expression. 4.) What do we do for heterogeneous systems? a) Si 3 N 4 (s) + 4 O 2 3 SiO 2 (s) + 2N 2 O K c = b) O 2 + 2 H 2 O(l) 2 H 2 O 2 (aq) K c = 1. What does an equilibrium constant mean? 2. Is it truly a constant value??? Example. Is the formation of HI favored more at a high or a low temperature? H 2 + I 2 2 HI K c = 794 at 298K; K c = 54 at 700 K For gases, we can also write an equilibrium expression in terms of partial pressures, P. K p = K c [RT] n Evaluate n for the following equations: CH 4 + H 2 O CO + 3 H 2 PCl 5 PCl 3 + Cl 2 N 2 + 3 H 2 2 NH 3
Equilibrium can be reached from either direction---but look at what happens to the value of K c! 1 N 2 O 4 2 NO 2 K c = 0.212 (100 C) 2 NO 2 N 2 O 4 K c = (100 C) 0. 212 How Do We Calculate An Equilibrium Constant? It depends on what is given. An equilibrium constant must be calculated using equilibrium values of pressure or concentration. If you are given the equilibrium concentrations, it is a plug and chug. If not, it becomes an algebraic problem. 1. Given: all equilibrium concentrations. Equilibrium expressions must use equilibrium concentrations (or pressures, if you are using a K p value). Ex. In the reaction, 3 NO 2 Cl 2 NO 2 + Cl 2, calculate K c if the equilibrium concentrations are as follows: P NO2 Cl = 0.0.00106 M, P NO2 = 0.0.0108 M, and P Cl2 = 0.0.00538 M. b) What is K p for this reaction? 2. Given: not equilibrium concentrations. You must use stoichiometry relationships to find equilibrium concentrations for all reactants and products. Formulate an ICE table Ex 1. Suppose you have initial concentrations of 0.95 M PCl 3 and 1.20 M Cl 2 and the final equilibrium concentration of PCl 5 = 0.30 M. Calculate the equilibrium constant for the reaction, PCl 3 + Cl 2 PCl 5 Ex2. Calculate the equilibrium constant for the following reaction, given initial concentration of 6.09 10 3 M SO 3 and a final equilibrium concentration of 3.69 10 3 M SO 3. 2 SO 3 2 SO 2 + O 2
Magnitude of K tells whether products or reactants are favored: K >>1; equilibrium lies to the right and products are favored. K << 1; equilibrium lies to the left and reactants are favored. Predicting the direction of a reaction: the reaction quotient Q. Equilibrium constants are calculated from equilibrium partial pressures. When the system is NOT at equilibrium, calculate the reaction quotient, Q, to find in which direction the reaction has to go to reach an equilibrium state. Ex.1) The equilibrium constant (K c )for the reaction P 4 2 P 2 is 1.39 at 400 o C. Suppose that 1.40 mol of P 4 and 1.25 mol of P 2 are mixed in a closed 25.0 L container at 400 o C. Compute Q at the moment of mixing and state the direction in which the reaction will proceed. Ex 2). Some Al 2 Cl 6 (partial pressure of 0.473 atm) is placed in a closed container at 454K with some Al 3 Cl 9 (partial pressure of 1.02 x 10-2 atm). Enough Argon is added to raise the initial pressure to 1 atm. Calculate Q for the reaction. K p = 1.04 10 4. 3Al 2 Cl 6 2 Al 3 Cl 9 How To Calculate Equilibrium Partial Pressures A. Simple case; missing one of the variables but everything is at equilibrium conditions). At 900 K, the equilibrium constant for the following reaction is 0.64. CO + H 2 O CO 2 + H 2 K p = 0.64 Suppose the partial pressures of three of the gases at equilibrium are measured to be P CO = 2.00 atm, P CO2 = 0.80 atm, P H2 = 0.48 atm. Calculate the equilibrium partial pressure of H 2 O.
B. More usual case: Calculate equilibrium partial pressures when given initial partial pressures 1) The reaction, I 2 + H 2 2HI K p = 92.6 is performed at 200 C. The initial partial pressure of H 2 is 1.140 atm; the initial partial pressure of I 2 is 1.320 atm. Calculate the equilibrium partial pressures of I 2 and H 2. LeChatelier's Principle; If a system at equilibrium is disturbed by a change in temperature, pressure, or concentration of one of the components, the system will shift its equilibrium position so as to counteract the effect of the disturbance. Change in system Increasing concentration of a reactant; Increasing concentration of product direction reaction will go to reach equilibrium state again Decreasing concentration of reactant; Decreasing concentration of product Increasing pressure Decreasing pressure Increasing temperature Exothermic reaction Endothermic reaction Decreasing temperature Exothermic reaction Endothermic reaction Example. What will happen to the number of moles of SO 3 in equilibrium with SO 2 and O 2 in the reaction, 2 SO 3 2 SO 2 + O 2 + heat in each of the following cases? a. More oxygen is added. b. The pressure is increased on the system. c. the total gas pressure is increased by adding argon gas. d. The temperature is decreased. e. A catalyst is added. f. Gaseous sulfur dioxide is removed.
Relationships Among equilibrium expressions. Equations are often manipulated (added, reversed, multiplied by some scalar) in order to obtain some equation in which we are interested. For equilibrium problems, we do this manipulation so that we might obtain the equilibrium constant for some reaction difficult or impossible to measure in the lab. We can obtain the equilibrium constant for any reaction provided we have the equilibrium constants for other reactions whose equations can be algebraically manipulated to give us the equation we desire. Manipulating equations Equations can be added together. Effect on equilibrium constant, K Equations can be reversed. Equations can be multiplied through by some scalar number, n. 1. Suppose I want the equilibrium constant for the reaction, 2 CH 4 + 2 O 2 CH 2 CO + 3 H 2 0 K =??????? and I have found the following information in handbooks (or measured them myself). (1) CH 2 CO + 2 O 2 2 CO 2 + H 2 O K 1 = 9.81 (2) CH 4 + 2 O 2 CO 2 + 2 H 2 O K 2 = 8.02 2. Find the equilibrium constant for the reaction, 5 CO 2 + Si 3 N 4 3 SiO + 2 N 2 O + 5 CO by using the following information. (1) CO + SiO 2 SiO + CO 2 K 1 = 5.20 (2) 8 CO 2 + Si 3 N 4 3 SiO 2 + 2 N 2 O + 8 CO K 2 = 4.61
2) At 100 o C, the K p = 89.6 for the reaction H 2 + Si 2 H 6 2 SiH 4 The two reactant gases are mixed in a sealed flask at 100 o C and before any reaction takes place, the partial pressure each reactant is 0.560 atm. a) Calculate the partial pressure of SiH 4 when the reaction comes to equilibrium. b) What percentage of the Si 2 H 6 remains unreacted at equilibrium?