CHEM 1112 Equilibrium

Equilibrium

• rate of the forward reaction is = to the rate of the reverse reaction

• there is no net reaction in both directions

• ∆G = 0

  • no driving force for the forward or reverse process

• the amounts of reactants and products are NOT usually equal to eachother at eqb’m

• system NOT static at equilibrium

  • chemical eq’bm is a dynamic process

Dynamic Equilibrium (example)

N₂O_{4 (g)} → 2NO_{2 (g)}

(colourless) (brown gas)

• when N₂O₄ is placed in a closed container at 100*C, a reddish brown colour develops due to the formation of NO₂

  • the forward reaction occurs

  • rate = k_f[N₂O₄]

• as NO₂ builds up, it can also react to form N₂O₄

  • the reverse reaction occurs

  • rate= k_r[NO₂]²

• at eqb’m, the amounts of reactant and products stop changing

  • reverse and forward reactions are equal

⇋ Eqb’m Arrows

• the symbol ⇋ placed between reactants and products is used to designate reversible reactions

Reaction Quotient (Q)

• allows us to mathematically express the amount of reactants and products present at any point in a reversable reaction

• consider the general reaction: mA + nB ⇋ xC + yD

  • A, B, C, D are gases or aq sol’n

  • m, n, x, y are coefficients in balanced equations

  • Q_c = [C]^x[D]^y /[A]_m[B]_n

WHY no liquids or solids

• Q_c and K_eq are defined in terms of activity of a substance

  • concentration/standard concentration or pressure/standard pressure

• the standard state for liquids/solids is the liquid/solid

  • the concentration of the liquid/solid does not change with the amount of a liquid/solid

Equilbrium Constant (K_eq)

• the value of Q when the reaction is at equilibrium

• K calculated the same as Q…

  • consider the general reaction: mA + nB ⇋ xC + yD

    • A, B, C, D are gases or aq sol’n

    • m, n, x, y are coefficients in balanced equations

    • Q_c = [C]^x[D]^y /[A]_m[B]_n

• independent of the starting amounts of R and P

• dependent on the temp. of the system

• magnitude of K indicates the extent of a reaction

  • small k → mixture contains mostly R at eqb’m

  • large k → mixture contains mostly P at eqb’m

Q vs. K

• K has the same form as Q, however, for K the concentrations MUST be at eqb’m, whereas for Q the concentrations can be those at any point in the reaction

• when eqb’m is reached, Q = K

Equilibrium vs. Rxn Rate

• the net rate of a reaction at equilibrium is 0

Adding k’s together

• if a reaction can be expressed as the sum of two or more reactions, the eqb’m constants for the overall reaction is given by the product of the eqb’m constants of the individual reactions.

Reversing a k

• when the equation for a reversible reaction is written in the opposite direction, the equilibrium constant becomes the reciprocal of the original eq’bm constant

Le Châtelier’s Principle

• when a chemical system at eqb’m is disturbed, it returns to eqb’m by counteracting the disturbance

  • at eqb’m Q = K

  • the distance causes a change in Q

  • the reaction will shift to re-establish Q = K

Adding a R/P

• if a chemical eqb’m is disturbed by adding a R or P, the system will proceed in the direction that consumes part of the added species

Removing a R/P

• if a chemical eqb’m is disturbed by removing a R or P, the system will proceed in the direction that restores part of the removed species

Add/remove a pure liquid or solid

• no effect on the system unless all of the liquid or solid is removed

• because pure liquids and solids no not appear in the equilibrium expression

Changes in Temperature (le chat)

• if you increase the temperature, equilibrium responds in fashion that consumes the added heat

  • the position of equilibrium will change

  • the value of k will change

  • recall that equilibrium constant will change if the temperature changes

• if the forward reaction is EXOthermic, K decreases as T increases

• if the forward reaction is ENDOthermic, K increases as T increases

Catalyst

• a catalyst does not affect the equilibrium position

  • the position of equilibrium depends on ∆G_rxn

  • ∆G = RTlnK

• a catalyst will increase the rate at which a reaction achieves equilibrium

  • k= Ae^-E_a/RT

Effect of changes in volume of a gas

• decreasing the volume of a gas increases the pressure, causing the reaction to shift to the right

  • fewer moles of gas, lower pressure

• increasing the volume reduces the pressure, causing the reaction to shift to the left

  • more moles of gas, higher pressure

Relationship between Q and K_eq

• When we “disturb the equilibrium” by adding more reactant or product, Q does not = K_eq

• the system will react by trying to return to equilibrium, Q does not = K_eq

• the direction of the reaction will depend on if Q > K_eq or Q < K_eq

  • if Q < K_eq the system shifts to the right in favour of the products

  • if Q = K_eq the reaction is at eq’bm and there is no net change

  • if Q > K_eq the system shifts to the left in favour of reactants

Gibbs Free Energy

• ∆G 0

• helps us predict in which direction a reaction is spontaneous

• if ∆G < 0, the reaction is spon in FORWARD direction

• if ∆G = 0, the reaction is not spontaneous as system is at eq’bm

• if ∆G > 0, the reaction is spon in the REVERSE direction

∆G and Q (or K_eq)

• ∆G_rxn = ∆G^o_rxn + RTlnQ

• Q = reaction quotient

• ∆G^o_rxn = change in Gibbs Energy under standard conditions

  • ∆G^o = -RTlnK_eq

• ∆G_rxn = change in Gibbs Energy under actual conditions

• if at eqb’m, ∆G_rxn = 0 and Q= K_eq

Calculating equilibirum constants

• can measure the concentration or pressure of all reactants and products at eq’bm and insert into K_c expression

• can measure the initial concentrations of reactants, and the equilibrium concentrations of ONLY one reactant

  • can deduce the other concentrations using ice tables

Quadratic equation