Gas EquilibriaGas Equilibria

The Jungle Begins. . . The Jungle Begins. . .

What is Equilibrium?What is Equilibrium?

Reaction is reversibleReaction is reversible Both products and Both products and

reactants are presentreactants are present Forward and reverse Forward and reverse

reactions take place at reactions take place at the same ratethe same rate

BUT the partial BUT the partial pressures must be pressures must be specifiedspecified

For the reaction 2A = BFor the reaction 2A = B

Using the KUsing the Keqeq constant constant

Let's look at the logical consequences of the Let's look at the logical consequences of the assumption that the reaction between assumption that the reaction between ClNO2 and NO eventually reaches ClNO2 and NO eventually reaches equilibriumequilibrium

ClNOClNO22((gg)+NO()+NO(gg) --> NO2() --> NO2(gg)+ClNO()+ClNO(gg))

At equilibrium: rate forward=rate reverse At equilibrium: rate forward=rate reverse

Substituting the rate laws for the forward Substituting the rate laws for the forward and reverse reactions into this equality and reverse reactions into this equality gives the following result. gives the following result.

: : kkf(ClNO2)(NO)=f(ClNO2)(NO)=kkr(NO2)(ClNO)r(NO2)(ClNO) But this equation is only valid when the But this equation is only valid when the

system is at equilibrium, as follows. system is at equilibrium, as follows. At equilibrium: At equilibrium: kkf[ClNO2][NO]=f[ClNO2][NO]=kkr[NO2]r[NO2]

[ClNO][ClNO]

We should replace the (ClNO2), (NO), We should replace the (ClNO2), (NO), (NO2), and (ClNO) terms with symbols (NO2), and (ClNO) terms with symbols that indicate that the reaction is at that indicate that the reaction is at equilibrium. equilibrium.

By convention, we use square brackets By convention, we use square brackets for this purpose. The equation for this purpose. The equation describing the balance between the describing the balance between the forward and reverse reactions when the forward and reverse reactions when the system is at equilibrium should therefore system is at equilibrium should therefore be writtenbe written

kkf[ClNO2][NO]=f[ClNO2][NO]=kkr[NO2][ClNO]r[NO2][ClNO]

Since Since kkf and f and kkr are constants, the ratio r are constants, the ratio of of kkf divided by f divided by kkr must also be a r must also be a constant. This ratio is the constant. This ratio is the equilibrium equilibrium constantconstant for the reaction, for the reaction, KcKc. The ratio . The ratio of the concentrations of the reactants of the concentrations of the reactants and products is known as the and products is known as the equilibrium constant expressionequilibrium constant expression. .

K expressionK expression

Keq = Keq = [ClNO][NO2][ClNO][NO2] [ClNO2][NO][ClNO2][NO]

Or in general termsOr in general terms

Keq = Keq = [C][C]cc[D][D]dd

[A][A]aa[B][B]bb

For aA + bB --> cC + dDFor aA + bB --> cC + dD

Or, the expression could be written for Or, the expression could be written for gases, in which case we will use gases, in which case we will use pressures rather than moles/liter or pressures rather than moles/liter or molarity.molarity.

NN22OO44 --> 2NO --> 2NO22 at 100 C at 100 CColorleless reddish brownColorleless reddish brown

ThenThen2NO2NO22 -->N -->N22OO44 begins to happen until the begins to happen until the

rates become the same and we haverates become the same and we have

NN22OO44 <--> 2NO <--> 2NO22

What is the equilibrium constant expression What is the equilibrium constant expression for this equation?for this equation?

Keq = Keq = (PNO2)(PNO2) (PN2O4)(PN2O4)22

Gaseous Equilibrium ExpressionGaseous Equilibrium Expression

So we can also write So we can also write the general equilibrium the general equilibrium constant as constant as

K = K = (PC)(PC)cc(PD)(PD)dd

(PA)(PA)aa(PB)(PB)bb

Note that the expression will change Note that the expression will change

depending on the form of the equation.depending on the form of the equation.

Rules of KRules of K

1.1. Reciprocal RuleReciprocal RuleNN22OO44 --> 2NO --> 2NO22

KKoriginaloriginal = = [NO[NO22]]22

[N[N22OO44]]

For the reverse reactionFor the reverse reaction2NO2NO2 2 -->--> NN22OO44

KKreversereverse = 1/K = 1/Korigorig

Rules of K continuedRules of K continued

Coefficient RuleCoefficient RuleNN22OO44 --> 2NO --> 2NO22

KKoriginaloriginal = = [NO[NO22]]22

[N[N22OO44]]

If we change the coefficients to 2 and 4 If we change the coefficients to 2 and 4 (doubling the molar ratio)(doubling the molar ratio)

KKnewnew = K = Korigorig22

Rules of K, concludedRules of K, concluded

Multiple EquilibriaMultiple Equilibria

K1 2NOK1 2NO2 2 --> --> NN22OO44

K2 NK2 N22OO4 4 -->--> NN2 2 ++ OO22

KKnewnew 2NO2NO2 2 -->--> NN2 2 ++ OO22

KKnewnew = K = K11KK22

Want to know why? Read the text Want to know why? Read the text for a great explanation!for a great explanation!

ICE (ice, ice baby)ICE (ice, ice baby)

I I initial initial concentrationconcentration

C C change in change in concentrationconcentration

E E final or ending final or ending concentrationconcentration

Remember this--you will use Remember this--you will use it over and over and over it over and over and over and over. . .and over. . .

When? With experimental When? With experimental Data!Data!

Protocol for Gas Equilibrium Protocol for Gas Equilibrium ProblemsProblems

1.1. Write the equationWrite the equation

2.2. ICEICE

3.3. Find KFind K

4.4. Plug and Chug Plug and Chug (check units)(check units)

5.5. Does this answer Does this answer make sense?make sense?