Quick Equilibrium review

The Concept of Equilibrium• As the substance warms it begins to

decompose: N2O4(g) 2NO2(g)

• When enough NO2 is formed, it can react to form N2O4:

2NO2(g) N2O4(g).• At equilibrium, as much N2O4 reacts to

form NO2 as NO2 reacts to re-form N2O4

• The double arrow implies the process is dynamic.

N2O4(g) 2NO2(g)

The Concept of EquilibriumAs a system

approaches equilibrium, both the forward and reverse reactions are occurring.

At equilibrium, the forward and reverse reactions are proceeding at the same rate.

A System at Equilibrium

Once equilibrium is achieved, the amount of each reactant and product remains constant.

The Equilibrium Constant

To generalize this expression, consider the reaction

• The equilibrium expression for this reaction would be

Kc = [C]c[D]d

[A]a[B]b

aA + bB cC + dD

The Equilibrium Constant

Because pressure is proportional to concentration for gases in a closed system, the equilibrium expression can also be written

Kp =(PC)c (PD)d

(PA)a (PB)b

Relationship between Kc and Kp

Plugging this into the expression for Kp for each substance, the relationship between Kc and Kp becomes

Where

Kp = Kc (RT)n

n = (moles of gaseous product) − (moles of gaseous reactant)

What Does the Value of K Mean?If K >> 1, the

reaction is product-favored; product predominates at equilibrium.

• If K << 1, the reaction is reactant-favored; reactant predominates at equilibrium.

Manipulating Equilibrium ConstantsThe equilibrium constant of a reaction that has been multiplied by a number is the equilibrium constant raised to a power that is equal to that number.

Kc = = 0.212 at 100C[NO2]2

[N2O4]N2O4 (g) 2 NO2 (g)

Kc = = (0.212)2 at 100C[NO2]4

[N2O4]22 N2O4 (g) 4 NO2 (g)

Manipulating Equilibrium Constants

The equilibrium constant of a reaction in the reverse reaction is the reciprocal of the equilibrium constant of the forward reaction.

10.212=

Kc = = 0.212 at 100C[NO2]2

[N2O4]N2O4 (g) 2 NO2 (g)

Kc = = 4.72 at 100C

[N2O4][NO2]2N2O4 (g)2 NO2 (g)

Applications of Equilibrium ConstantsPredicting the Direction of Reaction• We define Q, the reaction quotient, for a

reaction at conditions NOT at equilibrium

as

where [A], [B], [P], and [Q] are molarities at any time.

• Q = K only at equilibrium.

aA + bB(g) pP + qQ

ba

qpQ

BA

QP

The Reaction Quotient (Q)

To calculate Q, one substitutes the initial concentrations on reactants and products into the equilibrium expression.

Q gives the same ratio the equilibrium expression gives, but for a system that is not at equilibrium.

Applications of Equilibrium ConstantsPredicting the Direction of Reaction• If Q > K then the reverse reaction

must occur to reach equilibrium (go left)

• If Q < K then the forward reaction must occur to reach equilibrium (go right)

Applications of Equilibrium ConstantsPredicting the Direction of Reaction• If Q > K then the reverse reaction

must occur to reach equilibrium (go left)

• If Q < K then the forward reaction must occur to reach equilibrium (go right)

Le Châtelier’s PrincipleChange in Reactant or Product

Concentrations• Adding a reactant or product shifts the

equilibrium away from the increase.• Removing a reactant or product shifts the

equilibrium towards the decrease.• To optimize the amount of product at

equilibrium, we need to flood the reaction vessel with reactant and continuously remove product (Le Châtelier).

• We illustrate the concept with the industrial preparation of ammoniaN2(g) + 3H2(g) 2NH3(g)

Le Châtelier’s PrincipleEffects of Volume and Pressure• The system shifts to remove gases and

decrease pressure.• An increase in pressure favors the

direction that has fewer moles of gas.• In a reaction with the same number of

product and reactant moles of gas, pressure has no effect.

• Consider N2O4(g) 2NO2(g)

Le Châtelier’s PrincipleEffect of Temperature Changes• Removing heat (i.e. cooling the vessel),

favors towards the decrease:– if H > 0, cooling favors the reverse

reaction,– if H < 0, cooling favors the forward

reaction.• Consider

for which H > 0.– Co(H2O)6

2+ is pale pink and CoCl42- is blue.

Cr(H2O)6(aq) + 4Cl-(aq) CoCl42-(aq) + 6H2O(l)

CATALYST—EQUILIBRIUM is achieved faster, but the equilibrium composition remains unaltered.

Manipulating Equilibrium Constants

The equilibrium constant for a net reaction made up of two or more steps is the product of the equilibrium constants for the individual steps.

EQUILIBRIUM INVOLVING THE SOLUBILITY AND PRECIPITATION OF

COMPOUNDSEquilibrium and Solubility

Saturated solutions

A saturated solution is a solution that is in equilibrium with undissolved solute

Example: BaSO4 (s)

D Ba+2 (aq)+ SO4-2 (aq)

Solubility Products

The equilibrium constant expression for this equilibrium is

Ksp = [Ba2+] [SO42-]

where the equilibrium constant, Ksp, is called the solubility product.

Solubility Products

The equilibrium constant expression for this equilibrium is

Ksp = [Ba2+] [SO42-]

where the equilibrium constant, Ksp, is called the solubility product.

Solubility ProductsKsp is not the same as solubility.Solubility is generally expressed as the

mass of solute dissolved in 1 L (g/L) or 100 mL (g/mL) of solution, or in mol/L (M).

Will a Precipitate Form?

In a solution, If Q = Ksp, the system is at equilibrium and

the solution is saturated. If Q < Ksp, more solid will dissolve until Q

= Ksp. If Q > Ksp, the salt will precipitate until Q

= Ksp.

Selective Precipitation of Ions

One can use differences in solubilities of salts to separate ions in a mixture.

Common Ion Effect

If a solution containing two dissolved substances share a common ion, then the solubility of the salt is more difficult to determine

Adding “common ion” will cause the solubility to be less in the presence of the common ion

Causes less of the substance with the smaller Ksp

will dissolve.