Equilibrium

Reactions are reversible Z A + B C + D ( forward) Z C + D A + B (reverse) Z Initially there is only A and B so only the forward reaction is possible Z As C and D build up, the reverse reaction speeds up while the forward reaction slows down. Z Eventually the rates are equal

Reaction Rate Time Forward Reaction Reverse reaction Equilibrium

What is equal at Equilibrium? Z Rates are equal Z Concentrations are not. Z Rates are determined by concentrations and activation energy. Z The concentrations do not change at equilibrium. Z or if the reaction is verrrry slooooow.

Law of Mass Action Z For any reaction Z jA + kB lC + mD Z K = [C] l [D] m PRODUCTS power [A] j [B] k REACTANTS power Z K is called the equilibrium constant. Z is how we indicate a reversible reaction

Playing with K Z If we write the reaction in reverse. Z lC + mD jA + kB Z Then the new equilibrium constant is Z K ’ = [A] j [B] k = 1/K [C] l [D] m

Playing with K Z If we multiply the equation by a constant Z njA + nkB nlC + nmD Z Then the equilibrium constant is Z K’ = [A] nj [B] nk = ([A] j [B] k ) n = K n [C] nl [D] nm ( [C] l [D] m ) n

The units for K Z Are determined by the various powers and units of concentrations. Z They depend on the reaction.

K is CONSTANT Z At any temperature. Z Temperature affects rate. Z The equilibrium concentrations don’t have to be the same only K. Z Equilibrium position is a set of concentrations at equilibrium. Z There are an unlimited number.

Equilibrium Constant One for each Temperature

Calculate K Z N 2 + 3H 2 2NH 3 Z Initial At Equilibrium Z [N 2 ] 0 =1.000 M [N 2 ] = 0.921M Z [H 2 ] 0 =1.000 M [H 2 ] = 0.763M Z [NH 3 ] 0 =0 M [NH 3 ] = 0.157M

Calculate K Z N 2 + 3H 2 2NH 3 Z Initial At Equilibrium Z [N 2 ] 0 = 0 M [N 2 ] = M Z [H 2 ] 0 = 0 M [H 2 ] = M Z [NH 3 ] 0 = M [NH 3 ] = 0.203M Z K is the same no matter what the amount of starting materials

Equilibrium and Pressure Z Some reactions are gaseous Z PV = nRT Z P = (n/V)RT Z P = CRT Z C is a concentration in moles/Liter Z C = P/RT

Equilibrium and Pressure Z 2SO 2 (g) + O 2 (g) 2SO 3 (g) Z Kp = (P SO3 ) 2 (P SO2 ) 2 (P O2 ) Z K = [SO 3 ] 2 [SO 2 ] 2 [O 2 ]

Equilibrium and Pressure Z K = (P SO3 /RT) 2 (P SO2 /RT) 2 (P O2 /RT) Z K = (P SO3 ) 2 (1/RT) 2 (P SO2 ) 2 (P O2 ) (1/RT) 3 Z K = Kp (1/RT) 2 = Kp RT (1/RT) 3

General Equation Z jA + kB lC + mD Z K p = (P C ) l (P D ) m = (C C xRT ) l (C D xRT ) m (P A ) j (P B ) k (C A xRT ) j (C B xRT ) k Z K p = (C C ) l (C D ) m x(RT) l+m (C A ) j (C B ) k x(RT) j+k  K p = K (RT) (l+m)-(j+k) = K (RT)  n   n= (l+m)-(j+k) = Change in moles of gas

Homogeneous Equilibria Z So far every example dealt with reactants and products where all were in the same phase. Z We can use K in terms of either concentration or pressure. Z Units depend on reaction.

Heterogeneous Equilibria Z If the reaction involves pure solids or pure liquids the concentration of the solid or the liquid doesn’t change. Z As long s they are not used up they are not used up we can leave them out of the equilibrium expression. Z For example

For Example Z H 2 (g) + I 2 (s) 2HI(g) Z K = [HI] 2 [ H 2 ][ I 2 ] Z But the concentration of I 2 does not change. Z K [ I 2 ] = [HI] 2 = K’ [ H 2 ]

Solving Equilibrium Problems Type 1

The Reaction Quotient Z Tells you the directing the reaction will go to reach equilibrium Z Calculated the same as the equilibrium constant, but for a system not at equilibrium Z Q = [Products] coefficient [Reactants] coefficient Z Compare value to equilibrium constant

What Q tells us Z If Q<K : Not enough products : Shift to right Z If Q>K : Too many products : Shift to left Z If Q=K system is at equilibrium

Example Z for the reaction Z 2NOCl(g) 2NO(g) + Cl 2 (g) Z K = 1.55 x M at 35ºC Z In an experiment 0.10 mol NOCl, mol NO(g) and mol Cl 2 are mixed in 2.0 L flask. Z Which direction will the reaction proceed to reach equilibrium?

Solving Equilibrium Problems Z Given the starting concentrations and one equilibrium concentration. Z Use stoichiometry to figure out other concentrations and K. Z Learn to create a table of initial and final conditions.

Z Consider the following reaction at 600ºC Z 2SO 2 (g) + O 2 (g) 2SO 3 (g) Z In a certain experiment 2.00 mol of SO 2, 1.50 mol of O 2 and 3.00 mol of SO 3 were placed in a 1.00 L flask. At equilibrium 3.50 mol SO 3 were found to be present. Calculate Z The equilibrium concentrations of O 2 and SO 2, K and K P

Z Consider the same reaction at 600ºC Z In a different experiment.500 mol SO 2 and.350 mol SO 3 were placed in a L container. When the system reaches equilibrium mol of O 2 are present. Z Calculate the final concentrations of SO 2 and SO 3 and K

What if you’re not given equilibrium concentration? Z The size of K will determine what approach to take. Z First let’s look at the case of a LARGE value of K ( >100). Z Allows us to make simplifying assumptions.

Example Z H 2 (g) + I 2 (g) 2HI(g) Z K = 7.1 x 10 2 at 25ºC Z Calculate the equilibrium concentrations if a 5.00 L container initially contains 15.9 g of H g I 2. Z [ H 2 ] 0 = (15.7g/2.02)/5.00 L = 1.56 M Z [I 2 ] 0 = (294g/253.8)/5.00L = M Z [HI] 0 = 0

Z Q= 0<K so more product will be formed. Z Assumption since K is large reaction will go to completion. Z Stoichiometry tells us I 2 is LR, it will be smallest at equilibrium let it be x Z Set up table of initial, final and change in concentrations.

Z Choose X so it is small. Z For I 2 the change in X must be X-.232 M Z Final must = initial + change H 2 (g) I 2 (g) HI(g) initial1.56 M0.232 M 0 M change final X

Z Using to stoichiometry we can find Z Change in H 2 = X M Z Change in HI = -twice change in H 2 Z Change in HI = X H 2 (g) I 2 (g) HI(g) initial1.56 M0.232 M 0 M changeX final X

Z Now we can determine the final concentrations by adding. H 2 (g) I 2 (g) HI(g) initial 1.56 M0.232 M 0 M change X X X final X

Z Now plug these values into the equilibrium expression Z K = ( X) 2 = 7.1 x 10 2 (1.328+X)(X) Z Now you can see why we made sure X was small. H 2 (g) I 2 (g) HI(g) initial 1.56 M0.232 M 0 M change X X X final X X X

Why we chose X Z K = ( X) 2 = 7.1 x 10 2 (1.328+X)(X) Z Since X is going to be small, we can ignore it in relation to and Z So we can rewrite the equation Z 7.1 x 10 2 = (0.464) 2 (1.328)(X) Z Makes the algebra easy

Z When we solve for X we get 2.8 x Z So we can find the other concentrations Z I 2 = 2.8 x M Z H 2 = M Z HI = M H 2 (g) I 2 (g) HI(g) initial 1.56 M0.232 M 0 M change X X X final X X X

Checking the assumption Z The rule of thumb is that if the value of X is less than 5% of all the other concentrations, our assumption was valid. Z If not we would have had to use the quadratic equation Z More on this later. Z Our assumption was valid.

Practice Z For the reaction Cl 2 + O 2 2ClO(g) K = 156 Z In an experiment mol ClO, 1.00 mol O 2 and mol Cl 2 are mixed in a 4.00 L flask. Z If the reaction is not at equilibrium, which way will it shift? Z Calculate the equilibrium concentrations.

Problems with small K K<.01

Process is the same Z Set up table of initial, change, and final concentrations. Z Choose X to be small. Z For this case it will be a product. Z For a small K the product concentration is small.

For example Z For the reaction 2NOCl 2NO +Cl 2 Z K= 1.6 x Z If 1.20 mol NOCl, 0.45 mol of NO and 0.87 mol Cl 2 are mixed in a 1 L container Z What are the equilibrium concentrations Z Q = [NO] 2 [Cl 2 ] = (0.45) 2 (0.87) = 0.15 M [NOCl] 2 (1.20) 2

Z Choose X to be small Z NO will be LR Z Choose NO to be X 2NOCl 2NOCl 2 Initial Change Final

Z Figure out change in NO Z Change = final - initial Z change = X NOCl 2NOCl 2 Initial Change Final X

Z Now figure out the other changes Z Use stoichiometry Z Change in Cl 2 is 1/2 change in NO Z Change in NOCl is - change in NO 2NOCl 2NOCl 2 Initial Change X-.45 Final X

l Now we can determine final concentrations l Add 2NOCl 2NOCl 2 Initial Change0.45-X X X Final X

l Now we can write equilibrium constant l K = (X) 2 (0.5X+0.645) (1.65-X) 2 l Now we can test our assumption X is small ignore it in + and - 2NOCl 2NOCl 2 Initial Change0.45-X X X Final1.65-X X 0.5X

l K = (X) 2 (0.645) = 1.6 x (1.65) 2 l X= 8.2 x l Figure out final concentrations 2NOCl 2NOCl 2 Initial Change0.45-X X X Final1.65-X X 0.5X

l [NOCl] = 1.64 l [Cl 2 ] = l Check assumptions l.0082/.649 = 1.2 % OKAY!!! 2NOCl 2NOCl 2 Initial Change0.45-X X X Final1.65-X X 0.5X

Practice Problem Z For the reaction 2ClO(g) Cl 2 (g) + O 2 (g) Z K = 6.4 x Z In an experiment mol ClO(g), 1.00 mol O 2 and 1.00 x mol Cl 2 are mixed in a 4.00 L container. Z What are the equilibrium concentrations.

Mid-range K’s.01<K<10

No Simplification Z Choose X to be small. Z Can’t simplify so we will have to solve the quadratic (we hope) Z H 2 (g) + I 2 (g) HI(g) K=38.6 Z What is the equilibrium concentrations if mol H 2, mol I 2 and mol HI are mixed in a L container?

Problems Involving Pressure Z Solved exactly the same, with same rules for choosing X depending on K P Z For the reaction N 2 O 4 (g) 2NO 2 (g) K P =.131 atm. What are the equilibrium pressures if a flask initially contains atm N 2 O 4 ?

Le Chatelier’s Principle Z If a stress is applied to a system at equilibrium, the position of the equilibrium will shift to reduce the stress. Z 3 Types of stress

Change amounts of reactants and/or products Z Adding product makes Q>K Z Removing reactant makes Q>K Z Adding reactant makes Q<K Z Removing product makes Q<K Z Determine the effect on Q, will tell you the direction of shift

Change Pressure Z By changing volume Z System will move in the direction that has the least moles of gas. Z Because partial pressures (and concentrations) change a new equilibrium must be reached. Z System tries to minimize the moles of gas.

Change in Pressure Z By adding an inert gas Z Partial pressures of reactants and product are not changed Z No effect on equilibrium position

Change in Temperature Z Affects the rates of both the forward and reverse reactions. Z Doesn’t just change the equilibrium position, changes the equilibrium constant. Z The direction of the shift depends on whether it is exo- or endothermic

Exothermic  DH<0 Z Releases heat Z Think of heat as a product Z Raising temperature push toward reactants. Z Shifts to left.

Endothermic  DH>0 Z Produces heat Z Think of heat as a reactant Z Raising temperature push toward products. Z Shifts to right.