Ch. 14: Chemical Equilibrium I.Introduction II.The Equilibrium Constant (K) III.Values of Equilibrium Constants IV.The Reaction Quotient (Q) V.Equilibrium Problems VI.Le Châtelier’s Principle

I. Introduction Equilibrium will be the focus for the next several chapters. Most reactions are reversible, meaning they can proceed in both forward and reverse directions. This means that as products build up, they will react and reform reactants. At equilibrium, the forward and backward reaction rates are equal.

Equilibrium between two phases of the same substance is called physical equilibrium because the changes that occur are physical processes. Chemical equilibrium is achieved when the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products remain constant

I. Example Equilibrium

II. Equilibrium Concentrations Equilibrium does not mean that concentrations are all equal!! However, we can quantify concentrations at equilibrium. Every equilibrium has its own equilibrium constant.

II. The Equilibrium Constant equilibrium constant: the ratio at equilibrium of the [ ]’s of products raised to their stoichiometric coefficients divided by the [ ]’s of reactants raised to their stoichiometric coefficients. The relationship between a balanced equation and equilibrium constant expression is the law of mass action.

II. The Equilibrium Constant For a general equilibrium aA + bB  cC + dD, the equilibrium expression is:

Homogeneous Equilibria applies to reactions in which all reacting species are in the same phase.

II. Example Write the equilibrium constant expression for the reaction: 2H 2(g) + O 2(g)  2H 2 O (g).

II. Physical Meaning of K Large values of K mean that the equilibrium favors products, i.e. there are high [ ]’s of products and low [ ]’s of reactants at equilibrium. Small values of K mean that the equilibrium favors reactants, i.e. there are low [ ]’s of products and high [ ]’s of reactants at equilibrium.

Value of equilibrium constant (K eq ) shows the extent to which reactants are converted into products. K eq > 1: Products are favored at equilibrium (the equilibrium lie to the right) K eq < 1: Reactants are favored at equilibrium (the equilibrium lie to the left)

II. Rules for Manipulating K 1- If the equation is reversed, the equilibrium constant is inverted.

II. Rules for Manipulating K 2- If the equation is multiplied by a factor, the equilibrium constant is raised to the same factor.

II. Rules for Manipulating K 3- When chemical equations are added, their equilibrium constants are multiplied together to get the overall equilibrium constant.

Home work Predict the equilibrium constant for the first reaction given the equilibrium constants for the second and third reactions. CO 2(g) + 3H 2(g)  CH 3 OH (g) + H 2 O (g) K 1 = ? CO (g) + H 2 O (g)  CO 2(g) + H 2(g) K 2 = 1.0 x 10 5 CO (g) + 2H 2(g)  CH 3 OH (g) K 3 = 1.4 x 10 7

II. K in Terms of Pressure Up to this point, we’ve been using concentration exclusively in the equilibrium expressions. Partial pressures are proportional to concentration via PV = nRT. Thus, for gas reactions, partial pressures can be used in place of concentrations.

II. Two Different K’s For the reaction 2SO 3(g)  2SO 2(g) + O 2(g), we can write two equilibrium expressions.

II. Relationship Between Concentration and Pressure To be able to convert between K c and K p, we need a relationship between concentration and pressure.

II. Converting Between K c and K p

Δn = moles of gaseous products - moles of gaseous reactants the gas constant R is given by L. atm/K. Mol T in kelvin K P = K c (0.0821T) Δn

The Δn is the change in the number of moles of gas when going from reactants to products. When does K p equal K c ?

Example Methanol can be synthesized via the reaction CO (g) + 2H 2(g)  CH 3 OH (g). If K p of this reaction equals 3.8 x at 200 °C, what’s the value of K c ?

II. Heterogeneous Equilibria If an equilibrium contains pure solids or pure liquids, they are not included in the equilibrium constant expression.

III. Values of K Values of K are most easily calculated by allowing a system to come to equilibrium and measuring [ ]’s of the components. For the equilibrium H 2(g) + I 2(g)  2HI (g), let’s say equilibrium [ ]’s at 445 °C were found to be 0.11 M, 0.11 M, and 0.78 M for molecular hydrogen, molecular iodine, and hydrogen iodide, respectively.

III. K c for a H 2 /I 2 Mixture Note that units are not included when calculating K’s. Thus, equilibrium constants are unitless.

III. Equilibrium [ ]’s Vs. K For any reaction, the equilibrium [ ]’s will depend on the initial [ ]’s of reactants or products. However, no matter how you set up the reaction, the value of the equilibrium constant will be the same if the temperature is the same.

III. Equilibrium [ ]’s Vs. K

IV. The Reaction Quotient What happens when we mix reactants together and wait? Can we predict what will happen when we have a mixture of reactants and products? The reaction quotient, Q c or Q p, is used to predict in which direction an equilibrium will move.

IV. Formula for Q c or Q p You already know the formula because it’s the same as for K c or K p !! The difference is, we don’t know if the reaction is at equilibrium, thus, we cannot set the ratio equal to K! For the reaction aA + bB  cC + dD:

Summary of Guidelines for Writing Equilibrium Constant Expressions 1. The concentrations of the reacting species in the condensed phase are expressed in mol/L; in the gaseous phase, the concentrations can be expressed in mol/L or in atm. Kc is related to K P by a simple equation [Equation (14.5)]. 2. The concentrations of pure solids, pure liquids (in heterogeneous equilibria), and solvents (in homogeneous equilibria) do not appear in the equilibrium constant expressions. 3. The equilibrium constant (K c or K P ) is a dimensionless quantity. 4. In quoting a value for the equilibrium constant, we must specify the balanced equation and the temperature. 5. If a reaction can be expressed as the sum of two or more reactions, the equilibrium constant for the overall reaction is given by the product of the equilibrium constants of the individual reactions.

What Does the Equilibrium Constant Tell Us? the equilibrium constant helps us to predict the direction in which a reaction mixture will proceed to achieve equilibrium and to calculate the concentrations of reactants and products once equilibrium has been reached. These uses of the equilibrium constant will be explored in this section.

Predicting the Direction of a Reaction For reactions that have not reached equilibrium The value of Q relative to K tells you whether the reaction will form more products or more reactants to reach equilibrium.  Q < K means reaction forms products. The ratio of initial concentrations of products to reactants is too small. To reach equilibrium, reactants must be converted to products. The system proceeds from left to right (consuming reactants,forming products) to reach equilibrium.

The initial concentrations are equilibrium concentrations. The system is at equilibrium. Q > K means reaction form reactants. The ratio of initial concentrations of products to reactants is too large. To reach equilibrium, products must be converted to reactants. The system proceeds from right to left (consuming products, forming reactants) to reach equilibrium. Q = K means reaction is at equilibrium

Example Consider the reaction N 2 O 4(g)  2NO 2(g) with K c = 5.85 x If a reaction mixture contains [NO 2 ] = M and [N 2 O 4 ] = M, which way will the reaction proceed?