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Equilibrium Calculations Chapter 15

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Equilibrium Constant Review consider the reaction, The equilibrium expression for this reaction would be K c = [C] c [D] d [A] a [B] b aA + bBcC + dD c=concentration

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Calculating K when all equilibrium concentrations are known A mixture of hydrogen and nitrogen in a reaction vessel is allowed to attain equilibrium at 472°C. The equilibrium mixture of gases was 7.38 atm H 2, 2.46 atm N 2, and 0.166 atm NH 3. Calculate the equilibrium constant K p for the reaction. N 2 (g) + 3H 2 (g) 2NH 3

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Equilibrium Calculations when equilibrium concentrations are not all known… A closed system initially containing 1.000 x 10 −3 M H 2 and 2.000 x 10 −3 M I 2 At 448 C is allowed to reach equilibrium. Analysis of the equilibrium mixture shows that the concentration of HI is 1.87 x 10 −3 M. Calculate K c at 448 C for the reaction taking place, which is H 2 (g) + I 2 (g) 2 HI (g)

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What Do We Know? H 2 (g) + I 2 (g) 2 HI (g) K c = [HI] 2 /[H 2 ][I 2 ]

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ICE Table [H 2 ], M[I 2 ], M[HI], M Initially1.000 x 10 -3 2.000 x 10 -3 0 Change At equilibrium 1.87 x 10 -3

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[HI] Increases by 1.87 x 10 -3 M [H 2 ], M[I 2 ], M[HI], M Initially1.000 x 10 -3 2.000 x 10 -3 0 Change+1.87 x 10 -3 At equilibrium 1.87 x 10 -3

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Stoichiometry tells us [H 2 ] and [I 2 ] decrease by half as much [H 2 ], M[I 2 ], M[HI], M Initially1.000 x 10 -3 2.000 x 10 -3 0 Change-9.35 x 10 -4 +1.87 x 10 -3 At equilibrium 1.87 x 10 -3

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We can now calculate the equilibrium concentrations of all three compounds… [H 2 ], M[I 2 ], M[HI], M Initially1.000 x 10 -3 2.000 x 10 -3 0 Change-9.35 x 10 -4 +1.87 x 10 -3 At equilibrium 6.5 x 10 -5 1.065 x 10 -3 1.87 x 10 -3

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…and, therefore, the equilibrium constant Kc =Kc = [HI] 2 [H 2 ] [I 2 ] = 51 = (1.87 x 10 -3 ) 2 (6.5 x 10 -5 )(1.065 x 10 -3 )

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Practice Question: SO 3 decomposes at high temperature in a sealed container: 2SO 3 (g) ↔ 2SO 2 (g) + O 2 (g). Initially, the vessel is charged at 1000K with SO 3 (g) at a partial pressure of 0.500 atm. At equilibrium the SO 3 partial pressure is 0.200 atm. Calculate the value of K p at 1000K.

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The Reaction Quotient (Q) Provides convenient measure of the progress of the reaction To calculate Q, one substitutes the initial concentrations on reactants and products into the equilibrium expression. Q gives the same ratio the equilibrium expression gives, but for a system that is not at equilibrium.

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If Q = K, the system is at equilibrium.

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If Q > K, there is too much product and the equilibrium shifts to the left.

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If Q < K, there is too much reactant, and the equilibrium shifts to the right.

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The value of K and Q changes when the reaction is reversed (inverses) When reactions are added together through a common intermediate, the Q or K of the resulting reaction is a product of the values of the K/Q for the original reactions

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Predicting the Direction of Approach to Equilibrium At 448°C the equilibrium constant Kc for the reaction H 2 (g) + I 2 (g) ↔2HI(g) is 50.5. Predict in which direction the reaction will proceed to reach equilibrium at 448°C if we start with 2.0 x 10 -2 mol of HI, 1.0 x 10 -2 mol of H 2, and 3.0 x 10 -2 mol of I 2 in a 2.00 L container. Step 1: determine [HI], [H 2 ], and [I 2 ] Step 2: determine Q Step 3: compare Q to K, if Q>K moves R to L, if Q<K moves L to R

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