At dynamic equilibrium, Ratef = Rater, the forward rate equals the reverse rate. Both sides are always reacting at a microscopic level at the same rate.
Chemical Equilibrium: the state reached by a reaction mixture when the rates of forward and reverse reactions have become equal.
In a Moles vs Time graph, notice the amounts of substances become constant at equilibrium:
In a Rate vs Time graph, notice that the forward rate is large at first but steadily decreases, while the reverse rate starts at zero and steadily increases, until both rates are equal at equilibrium:
Molar Composition:
Example:
For the reaction
CO (g) + 3H2 (g) ⇌ CH4 (g) + H2O (g)
When 1.000 mol CO and 3.000 mol H2 are placed in a 10.00 L vessel at constant temperature and allowed to come to equilibrium, the mixture is found to contain 0.387 mol H2O. How many moles of each substance are present in the equilibrium mixture?
Think about the starting amounts in moles, which are known. The change in the amount of moles as the reaction proceeds is an unknown, so we can label it "x". Each reactant will decrease by a factor of x (the factor is indicated by the coefficient of that particular reactant) and each product will increase by a factor of x (also found by the coefficient). The resulting amounts can be found by combining our known information into equations and solving for x.
It is easiest to do this by making a table. I, C, and E indicate Initial, Change, and Equilibrium.
If the initial amounts of products isn't stated, it is assumed to be 0. Also, if we know each product (with a coefficient of 1) increases by x, and we know the resulting amount of that product, then we know x. So here, x = 0.387 mol.
If the problem were to ask for concentrations, divide the results by the volume given, in this case 10.00L.
The Equilibrium Constant:
General Form of an Equation:
aA + bB ⇌ cC + dD
Where capital letters are reactants and products and lowercase letters are coefficients of the balanced chemical equation.
-The equilibrium constant can be obtained by multiplying the concentrations of products, dividing by the product of the concentrations of reactants, and raising each concentration term to a power equal to the coefficient in the chemical equation. This is much easier to see when it's written out:
-Kc can also be denoted as Keq
-Kc has no units
-Concentrations must be entered in mols/Liter (M), otherwise convert to these units
-Must have an equilibrium to find Kc
-Ignore concentrations of pure liquids and solids, they are constant. Another way of writing concentrations is density (same dimensions of mass over volume) which will remain the same no matter how much of a solid or liquid you have.
-Just use the concentrations of gaseous and aqueous reactants and products.
Example:
CO (g) + 3H2 (g) ⇌ CH4 (g) + H2O (g)
Kc = [CH4][H2O] / [CO][H2]3
Example:
N2 (g) + 3H2 (g) ⇌ 2NH3 (g)
Kc = [NH3]2 / [NH2][H2]3
Example:
2A (g) + B(s) + 7C (aq) ⇌ 14D (l) + 3/2E (g)
Kc = [E]3/2 / [A]2[C]7
-Manipulating the balanced chemical equation will change Kc:
-If you multiply the coefficients of a reaction through by a number, A, then Kc = KcA
-Suppose you multiply a reaction through by 2, then you must square Kc
-If you flip a reaction around so the reactants are now the products and the products are now the reactants, then you get the reciprocal, Kc = 1 / Kc
The Pressure Equilibrium Constant, Kp:
-Won't use this until later when we study Thermodynamics, but it is relevant now.
-Kp is another version of Kc
-The values plugged into Kp are partial pressures converted to atm instead of concentrations.
-Related to Kc via the ideal gas law (PV = nRT → n/V = P/RT)
-In other words, the molar concentration of a gas equals its partial pressure divided by RT, which is constant at a given temperature.
Example:
For the reaction
CH4 (g) + 2O2 (g) ⇌ CO2 (g) + 2H2O (g)
Kc = [CO2][H2O]2 / [CH4][O2]2
Kp = PCO2 · PH2O2 / PCH4 · PO22
-Sometimes Kc = Kp, but not always, it depends on the coefficients of the chemical equation.
Kc = Kp when the sum of reactant coefficients equals the sum of the product coefficients.
Example:
For the same reaction
CH4 (g) + 2O2 (g) ⇌ CO2 (g) + 2H2O (g)
1 + 2 = 1 + 2
Kc = Kp
Equation to relate Kp to Kc:
Kp = Kc (RT)Δn
R = the ideal gas constant (0.0821 atm.L/mol.K)
T = Temperature in degrees Kelvin
Δn = sum of the coefficients of the products – the sum of the coefficients of the reactants.
Note: when the sum of the reactant coefficients equals the sum of product coefficients, Δn will be zero. Anything raised to the zero power is 1, so RTΔn will equal 1, and Kp will equal Kc times 1, or just Kc.
Equilibrium Constant for the Sum of Reactions:
-If a given chemical equation can be obtained by taking the sum of other equations, the equilibrium constant for the given equation equals the product of the equilibrium constants of the other equations.
-Note: use Hess's Law
Example:
Equation 1:
CO (g) + 3H2 (g) ⇌ CH4 (g) + H2O (g)
Equation 2:
CH4 (g) + 2H2S (g) ⇌ CS2 (g) + 4H2 (g)
Hess's Law:
CO + 3H2 + CH4 + 2H2S ⇌ CH4 + H2O + CS2 + 4H2
Equation 3:
CO (g) + 2H2S (g) ⇌ H2O (g) + CS2 (g) + H2 (g)
Kc for Equation 1 = K1
K1 = [CH4][H2O] / [CO][H2]3
Kc for Equation 2 = K2
K2 = [CS2][H2]4 / [CH4][H2S]2
Kc for Equation 3 = K1 · K2
K3 = [CS2][H2O][H2] / [CO][H2S]2
(K3 can be verified by looking at Equation 3 and writing Kc directly from it)
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