Topic 17: Equilibrium Law 17.1: The position of equilibrium can be quantified by the equilibrium law. The equilibrium constant for a particular reaction only depends on the temperature.

Important terms for this section Homogeneous equilibria Free energy

Calculating Kc from initial and equilibrium concentrations Homogeneous equilibria: The reactants and products are all in the same state (gas, liquid, solid) Ex: No solid and gas phases in the reaction together Steps for solving I.C.E. problems Write a balanced equation Write three rows: initial, change, equilibrium Initial: original concentration Amount reacts to reach equilibrium Equilibrium: [equilibrium] = [initial] +/- change in concentration Write the expression for Kc from the balanced equation and substitute values for equilibrium concentration and calculate Kc

I.C.E. problem 1 A student placed 0.20mol PCl3(g) and 0.01 mol Cl2(g) into a 1.0 dm3 flask at 350℃. The reaction, which produced PCl5, was allowed to come to equilibrium, at which time it was found that the flask contained 0.12 mol PCl3. What is the value of Kc for this reaction? Step 1: write a balanced reaction PCl3(g) + Cl2(g) ⇌ PCl5(g) Step 2: Step 3:

I.C.E. problem 2 Oxidation of NO to form NO2 occurs during smog formation. When 0.60 mol NO was reacted with 0.60 mol O2 in a 2.0 dm3 container at 500℃, the equilibrium mixture was found to contain 0.20 mol NO2. What is the value of Kc for this reaction? Step 1: write a balanced reaction 2NO(g) + O2(g) ⇌ NO2(g) Step 2: Step 3:

Calc. equilibrium concentrations from Kc We gotta use Algebra, m’kay! Follow the same kinds of steps, but now the change in concentrations are x So this is still an I.C.E. problem, but cooler…  Example: Kc = 6.78 at a certain temp for the reaction SO3(g) + NO(g) ⇌ NO2(g) + SO2(g) Initial [NO] and [SO3] are each 0.0300 mol dm-3 Change in NO = -x change in SO3 = -x Change in NO2 = +x change in SO2 = +x

Calc. equilibrium concentrations from Kc

Calc. equilibrium conc. from itty bitty Kc If Kc is less than 10-3, this is considered pretty small This means the initial reaction concentrations are close to the equilibrium concntrations

Calc. equilibrium conc. from itty bitty Kc

Calc. equilibrium conc. from itty bitty Kc

Free Energy and Equilibrium Remember that if ∆G is negative, then the reaction is spontaneous in that direction Thus, ∆Gθ = Gθproducts – Gθreactants Reaction begins and moves in the forward direction (lots of free energy) As it proceeds, the forward reaction decreases and reverse reaction increases (loss of free energy) At equilibrium, there is not more change in reaction rate, (no more free energy) At equilibrium, since there is a minimum of free energy and entropy is highest

Free Energy and Equilibrium ∆G large and negative ∆G large and positive Equilibrium lies to the right Equilibrium lies to the left

Kc can be calculated from thermodynamic data How are Kc and ∆Gθ related? ∆Gθ = -RT ln K ∆Gθ = standard free energy change of the reaction R = the gas constant 8.31 J K-1 mol-1 T = the absolute temperature in Kelvin ln K = the natural logarithm of the equilibrium constant, Kc This explains why Kc can have different values: ∆Gθ And ∆Gθ depends on ∆H and ∆S

Kinetics and Equilibrium Remember that Kc tells you where equilibrium lies, but says nothing about the rate! But, we can look at an example of forward and backward rate constants to tell us some equilibrium info Example: if we have A + B ⇌ C + D AND If the rate laws were: forward rate = k[A][B] AND backward rate = k’[C][D] Then we also have an equilibrium constant expression that looks like this:

Kinetics and Equilibrium So, this means that: AND for Concentration: Increasing [reactant] increases forward rate so shifts equilibrium to the right Increasing [products] increases backward rate so shifts equilibrium to the left Kc stays the same Catalyst: Increases values of k and k’ by the same factor Temperature: with Arrhenius equation, temp ⇧ = rate ⇧ But if activation energies of forward and backward RXNs are different, then k and k’ are differently affected k/k’ is dependent on temperature: ⇧ temp = ⇧ rate of endothermic reaction (specfifically) Kc will increase if endothermic RXN is the forward RXN