1 EQUILIBRIUM CONSTANT, K eq or K The Law of Chemical Equilibrium: (Guldberg & Waage, 1864) States that: At equilibrium, there is a constant ratio between the concentration of the products and the concentration of reactants in any change. Example: Chemical System: N 2 O 4(g) 2 NO 2(g) Table 1: Different initial and equilibrium concentration values for the above system Initial [ N 2 O 4(g) ] Initial [ NO 2(g) ] Equil. [ N 2 O 4(g) ] Equil. [ NO 2(g) ] 0.1000 0.0000 0.0491 0.1018 0.0000 0.1000 0.0185 0.0627 0.0500 0.0500 0.0332 0.0837 0.0750 0.0250 0.0411 0.0930 Ratio: [ NO 2(g) ] 2 [ N 2 O 4(g) ] The Equilibrium Constant: A mathematical expression that represents the ratio of product concentration to reactant concentration, with each concentration raised to the power of the coefficient. For any reaction: aa + bb cc + dd The equilibrium constant expression: K eq or K = [ C ] c [ D ] d [ A ] a [ B ] b where A, B, C and D represent chemical formulas and a, b, c and d, their respective coefficients. NOTE: 1. Pure liquids and solids are not included in the expression (their concentrations are already constants), thus only gases and solutions are included. 2. Each chemical system has it s own K value. 3. K values change with a change in temperature, therefore K values are usually specified at a particular temperature. (Since forward and reverse reactions have different activation energies).
2 4. K value for a system will depend on how the equation for the reaction is written. Eg: N 2 O 4(g) 2 NO 2(g) vs. 2 NO 2(g) N 2 O 4(g) K = [NO 2(g) ] 2 K = [ N 2 O 4(g) ] [ N 2 O 4(g) ] [NO 2(g) ] 2 5. Only equilibrium concentrations are used to calculate K. 6. Units are not usually associated with K values. 7. The value of K can indicate the position of an equilibrium or whether the formation of reactants or products are favored (in higher concentration): If K > 1, the products are favored If K < 1, reactants are favored If K = 1, neither reactants nor products are favored 8. Percent reaction is also an indicator of whether reactants or products are favored: < 50%, reactants are favored > 50%, products are favored = 50 %, neither reactants nor products are favored Sample Exercises: 1. Write the expression for the equilibrium constant for each of the following chemical systems: a) The decomposition of trinitrogen hexaoxide into nitrogen dioxide. Both compounds are in the gaseous phase. b) The single replacement reaction between zinc metal and hydrochloric acid.
2. Calculate K for the decomposition of trinitrogen hexaoxide into nitrogen dioxide at 25 o C if the equilibrium concentrations of trinitrogen hexaoxide and nitrogen dioxide are 0.0045 mol/l and 0.030 mol/l, respectively. 3 3. PCl 5(g) in the amount of 0.0722 mol and at 25 0 C was added to a 2.00 L container. The temperature was raised to 250 0 C and the PCl 5 decomposed into PCl 3(g) and Cl 2(g). At equilibrium, the concentration of Cl 2 was 0.0257 mol/l. Find K for the system at 250 0 C. 4. The initial concentrations of hydrogen gas and iodine gas in a 2.00 L reaction vessel at 212 0 C were 0.357 mol/l. The equilibrium concentration of the hydrogen iodide produced was measured to be 0.570 mol/l. Calculate the equilibrium concentrations of hydrogen gas and iodine gas.
4 5. A 0.167 mol sample of nitrogen monoxide was placed in a 1.00 L container and decomposed into its elements at 500 0 C. If the percent reaction was 35%, find the equilibrium constant K. 6. A 0.575 mol sample of PCl 5(g) is placed in a 1.00 L reaction vessel and equilibrium is established at 156 0 C. If the percent reaction is 25%, calculate the equilibrium concentration of all species in the vessel. 7. Oxygen and sulfur dioxide combine at 250 o C to produce sulfur trioxide. The K value for the equilibrium is 10.0. Find the equilibrium concentration of sulfur trioxide if the equilibrium concentrations of the reactants are both 0.250 mol/l.
5 EQUILIBRIUM WORKSHEET #3 1. When 0.40 mol/l of PCl 5(g) is heated to 200 o C in a 2.00 L container, the followingequilibrium is established: PCl 5(g) PCl 3(g) + Cl 2(g) If 0.15 mol/l of chlorine gas is present at equilibrium, what is the K eq value for this system? Are reactants or products favored? 2. Initially, the concentrations of nitrogen and oxygen gases are both 1.8 mol/l. If, at equilibrium, the concentration of nitrogen monoxide produced from the combination reaction is 1.8 mol/l, find the value of K eq. 3. In the following reaction system: N 2 O 4(g) 2 NO 2(g) 1.0 L of 0.678 mol/l of N 2 O 4(g) is allowed to establish an equilibrium at 40 0 C. If the percent reaction of N 2 O 4(g) was found to be 26%, find K eq. Are the reactants or products favored? 4. 2.00 L of 1.32 mol/l dinitrogen pentaoxide gas was placed in a sealed vessel. Find the equilibrium concentration of the products, nitrogen dioxide and oxygen, if the percent reaction of dinitrogen pentaoxide was measured to be 65%. 5. When 0.576 mol/l of both H 2(g) and Cl 2(g) were allowed to reach equilibrium at 45 0 C, the equilibrium concentration of HCl (g) was found to be 0.356 mol/l. Find the equilibrium concentrations of the reactants. 6. Find K eq for the system: 2CO (g) + O 2(g) 2CO 2(g) if initially there is 5.0 mol of CO, 10.0 mol of O 2 and 1.0 mol of CO 2 in a 2.0 L container and if at equilibrium there is CO 2 at a concentration of 2.5 mol/l. 7. If K eq is 46 for the equilibrium established when hydrogen and iodine gases react to produce hydrogen iodide gas, and the equilibrium concentrations of both hydrogen and iodine is 0.10 mol/l, what is the equilibrium concentration of the products?