Chemical Equilibrium Lesson 16 by Owen Borville 1o.30.2025
Most chemical reactions do not react completely from reactants to products and do not fully complete. Most chemical reactions end when there is both reactants and products remaining.
Decomposition is a reversible process, where in addition to the reactants forming products, the products can also in turn create reactants. A + B ⇌ C + D
A chemical reaction system is in equilibrium when the rates of the forward reaction and the reverse reaction are the same. A reversible can have one, two, or more reactants and one, two or more products, depending on the reaction.
Equilibrium is a dynamic state where both the forward and reverse reactions continue to occur but there is no net change in reactant or product concentration. Equilibrium can begin with only reactants, only products, or with any mixture of reactants and products.
The Equilibrium Constant: the reaction quotient (Qc) is a fraction with product concentrations in the numerator and reactant concentrations in the denominator. Each concentration is raised to a power equal to the corresponding stoichiometric coefficient in the balanced chemical equation: aA + bB⇌ cC + dD
Qc = ([C]^c[D]^d)/([A]^a[B]^b) =Kc (at equilibrium) This law of mass action applies to elementary and complex reactions.
The value of the reaction quotient, Q, changes as the reaction progresses.
The equilibrium constant reveals the extent a reaction will proceed at a particular temperature. Three outcomes are possible: (1) The reaction will occur until completion and the equilibrium mixture will consist mostly of products. (2) The reaction will not occur significantly, and the equilibrium mixture will contain mostly reactants. (3) The reaction will occur to a significant extent, but will not complete, and the equilibrium mixture will contain large amounts of both reactants and products.
When the species in a reversible chemical reaction are not all in the same phase, the equilibrium is heterogeneous. Only gaseous species (g) and aqueous species (aq) appear in equilibrium expressions, pure solids (s) and pure liquids (l) do not because their concentrations remain constant. Aqueous species are dissolved in water, so their concentrations can change, whereas a pure liquid's and solid's concentration does not change.
If a reversible chemical reaction is changed, appropriate changes to the equilibrium expression and equilibrium constant must be made. If the original reaction equation is reversed, the new equilibrium constant is the reciprocal. If the original equation is multiplied by a number, the new constant is the original raised to the same number. If the original equation is divided by 2, the new constant is the square root of the original. If the original equations are added, the new constant is the product of the two original constants.
Gas Equilibria: When equilibrium expressions contain only gases, an alternate form of the expression can be written in which the concentration of gases are expressed as partial pressures (atm)
Kc = ([C]^c[D]^d)/([A]^a[B]^b)
Kp = (Pc)(Pd)/(Pa)(Pb)
or Kp = (Pc)^2/(Pa)(Pb)
Pa = partial pressure of A reactant
Pb = partial pressure of B reactant
Pc = partial pressure of C product
Pd = partial pressure of D product
Using PV = nRT,
Kp = Kc(RT)^Δn
Δn = (moles of gaseous products-moles of gaseous reactants)
R = 0.08206 (L*atm)(mol*K)
Chemical Equilibrium and Free Energy:
The magnitude of K gives us the same information as the sign of ΔG°.
A reaction with K>1 (K greater than 1) has a negative ΔG°.
A reaction with K<1 (K less than 1) has a positive ΔG°.
The magnitude of K and sign of ΔG° allow us to solve more problems.
Using Q and K to Predict the Direction of the Reaction: The equilibrium expression may be used to predict the direction of a reaction and to calculate equilibrium concentrations. Predictions are made based on comparisons between Qc and Kc. There are three possibilities: (1) Q<K The ratio of initial concentrations of products to reactants is too small. To reach equilibrium, reactants must be converted to products. The system proceeds in the forward direction until equilibrium is reached. (2) Q=K The initial concentrations are equilibrium concentrations and the system is at equilibrium. (3) Q>K The ratio of initial concentrations of products to reactants is too large. To reach equilibrium products must be converted to reactants. The system proceeds in the reverse direction.
𝛥𝐺 and 𝛥𝐺° the sign of 𝛥𝐺 (not 𝛥𝐺°) determines spontaneity. The relationship between 𝛥𝐺 and 𝛥𝐺° is 𝛥𝐺 = 𝛥𝐺° + RT lnQ
R is the gas constant (8.314 J/K*mol)
T is the Kelvin temperature
Q is the reaction quotient
For the reaction H2(g) + I2(g) ⇌ 2HI(g), 𝛥𝐺 at 25°C = 2.60 kJ/mol
Qp = p(HI)^2/p(H2)p(I2)
Then solve 𝛥𝐺 = 𝛥𝐺° + RT lnQ
The spontaneity can be manipulated by changing the partial pressures of the reaction components. H2(g) + I2(g) ⇌ 2HI(g), 𝛥𝐺 at 25°C = 2.60 kJ/mol
If P(H2) = 2.0 atm; P12 = 2.0 atm; and P(HI) = 1.0 atm:
Qp = p(HI)^2/p(H2)p(I2) = 0.25
The solve 𝛥𝐺 = 𝛥𝐺° + RT lnQ = -0.8 kJ/mol
At equilibrium, 𝛥𝐺 = 0 and Q=K
𝛥𝐺° =-RT ln K
0 = 𝛥𝐺° + RT lnK
K>1, In K is positive, 𝛥𝐺° is negative, result at equilibrium is products are favored.
K=1, In K is 0, 𝛥𝐺° = 0 result at Equilibrium is neither products or reactants are favored.
K<1 In K is negative, 𝛥𝐺° is positive, result at equilibrium is reactants are favored.
Calculating Equilibrium Concentrations: Equilibrium concentrations can be calculated from initial concentrations if the equilibrium constant is known.
For example, cis-Stilbene and its reaction to trans-Stilbene, Kc = 24.0 (200°C)
If the initial concentration (M) of cis-Stilbene is 0.850, the change in concentration of (M) is x, and the equilibrium concentration (M) is (0.850-x) and x.
Kc = [trans-stilbene]/[cis-stilbene]
24.0 = [x]/[0.850-x]
x = 0.816 M (represents the change in initial concentrations)
If the initial concentration (M) of cis-Stilbene is (0.850), the change in concentration (M) is (0.816)
The equilibrium concentration (M) on each side of the equation is (0.850-0.816) and (0.816)
To calculate the equilibrium concentrations of cis- and trans-stilbene:
Concentration of [cic-stilbene] = (0.850-x) M = (0.850-0.816) M = 0.034 M
Concentration of [trans-stilbene] = x M = 0.816 M
Le Chatelier's Principle of Chemical Equilibrium: Le Chatelier's principle states that when a stress is applied to a system at equilibrium, the system will respond by shifting in the direction that minimizes the effect of the stress. Stress refers to: (1) the addition of a reactant or product (2) the removal of a reactant or product (3) a change in volume of the system, resulting in a change in concentration or partial pressure of the reactants and products (4) a change in temperature.
For the Addition or Removal of a Substance, consider the Haber process at 700 K: N2(g) + 3H2(g) ⇌ 2NH3(g)
At equilibrium: [N2] = 2.05 M, [H2] = 1.56 M, [NH3] = 1.52 M
Kc = [NH3]^2/[N2][H2]^3 = (1.52)^2/(2.05)(1.56)^3 = 0.297
Applying stress by the addition to N2 to give the following concentrations:
[N2] = 3.51 M, [H2] = 1.56 M, [NH3] = 1.52 M
Qc = [NH3]^2/[N2][H2]^3 = (1.52)^2/(3.51)(1.56)^3 = 0.173, which is not equal to Kc. The reaction will shift to the right.
Addition of a reactant or removal of a product will cause an equilibrium to shift to the right. Addition of a product or removal of a reactant will cause an equilibrium to shift to the left.
Changes in Volume: When volume is decreased, the equilibrium is driven toward the side with the smallest number of moles of gas. As the system remains at equilibrium, Q will remain equal to K.
Changes in Temperature: While changes in volume and concentration do not change the value of the equilibrium constant, however a change in temperature can alter the value of the equilibrium constant. Adding heat to an endothermic process shifts the equilibrium toward the products.
For any endothermic reaction, heat is a reactant: heat + reactants ⇌ products (𝛥H > 0 kJ/mol)
Adding heat shifts the reaction towards the products and Kc increases. Removing heat shifts the reaction towards the reactants and Kc decreases.
For any exothermic reaction, heat is a product: reactants ⇌ products + heat (𝛥H < 0 kJ/mol)
Adding heat shifts the reaction toward the reactants and Kc decreases. Removing heat shifts the reaction towards the products and Kc increases.
Most chemical reactions do not react completely from reactants to products and do not fully complete. Most chemical reactions end when there is both reactants and products remaining.
Decomposition is a reversible process, where in addition to the reactants forming products, the products can also in turn create reactants. A + B ⇌ C + D
A chemical reaction system is in equilibrium when the rates of the forward reaction and the reverse reaction are the same. A reversible can have one, two, or more reactants and one, two or more products, depending on the reaction.
Equilibrium is a dynamic state where both the forward and reverse reactions continue to occur but there is no net change in reactant or product concentration. Equilibrium can begin with only reactants, only products, or with any mixture of reactants and products.
The Equilibrium Constant: the reaction quotient (Qc) is a fraction with product concentrations in the numerator and reactant concentrations in the denominator. Each concentration is raised to a power equal to the corresponding stoichiometric coefficient in the balanced chemical equation: aA + bB⇌ cC + dD
Qc = ([C]^c[D]^d)/([A]^a[B]^b) =Kc (at equilibrium) This law of mass action applies to elementary and complex reactions.
The value of the reaction quotient, Q, changes as the reaction progresses.
The equilibrium constant reveals the extent a reaction will proceed at a particular temperature. Three outcomes are possible: (1) The reaction will occur until completion and the equilibrium mixture will consist mostly of products. (2) The reaction will not occur significantly, and the equilibrium mixture will contain mostly reactants. (3) The reaction will occur to a significant extent, but will not complete, and the equilibrium mixture will contain large amounts of both reactants and products.
When the species in a reversible chemical reaction are not all in the same phase, the equilibrium is heterogeneous. Only gaseous species (g) and aqueous species (aq) appear in equilibrium expressions, pure solids (s) and pure liquids (l) do not because their concentrations remain constant. Aqueous species are dissolved in water, so their concentrations can change, whereas a pure liquid's and solid's concentration does not change.
If a reversible chemical reaction is changed, appropriate changes to the equilibrium expression and equilibrium constant must be made. If the original reaction equation is reversed, the new equilibrium constant is the reciprocal. If the original equation is multiplied by a number, the new constant is the original raised to the same number. If the original equation is divided by 2, the new constant is the square root of the original. If the original equations are added, the new constant is the product of the two original constants.
Gas Equilibria: When equilibrium expressions contain only gases, an alternate form of the expression can be written in which the concentration of gases are expressed as partial pressures (atm)
Kc = ([C]^c[D]^d)/([A]^a[B]^b)
Kp = (Pc)(Pd)/(Pa)(Pb)
or Kp = (Pc)^2/(Pa)(Pb)
Pa = partial pressure of A reactant
Pb = partial pressure of B reactant
Pc = partial pressure of C product
Pd = partial pressure of D product
Using PV = nRT,
Kp = Kc(RT)^Δn
Δn = (moles of gaseous products-moles of gaseous reactants)
R = 0.08206 (L*atm)(mol*K)
Chemical Equilibrium and Free Energy:
The magnitude of K gives us the same information as the sign of ΔG°.
A reaction with K>1 (K greater than 1) has a negative ΔG°.
A reaction with K<1 (K less than 1) has a positive ΔG°.
The magnitude of K and sign of ΔG° allow us to solve more problems.
Using Q and K to Predict the Direction of the Reaction: The equilibrium expression may be used to predict the direction of a reaction and to calculate equilibrium concentrations. Predictions are made based on comparisons between Qc and Kc. There are three possibilities: (1) Q<K The ratio of initial concentrations of products to reactants is too small. To reach equilibrium, reactants must be converted to products. The system proceeds in the forward direction until equilibrium is reached. (2) Q=K The initial concentrations are equilibrium concentrations and the system is at equilibrium. (3) Q>K The ratio of initial concentrations of products to reactants is too large. To reach equilibrium products must be converted to reactants. The system proceeds in the reverse direction.
𝛥𝐺 and 𝛥𝐺° the sign of 𝛥𝐺 (not 𝛥𝐺°) determines spontaneity. The relationship between 𝛥𝐺 and 𝛥𝐺° is 𝛥𝐺 = 𝛥𝐺° + RT lnQ
R is the gas constant (8.314 J/K*mol)
T is the Kelvin temperature
Q is the reaction quotient
For the reaction H2(g) + I2(g) ⇌ 2HI(g), 𝛥𝐺 at 25°C = 2.60 kJ/mol
Qp = p(HI)^2/p(H2)p(I2)
Then solve 𝛥𝐺 = 𝛥𝐺° + RT lnQ
The spontaneity can be manipulated by changing the partial pressures of the reaction components. H2(g) + I2(g) ⇌ 2HI(g), 𝛥𝐺 at 25°C = 2.60 kJ/mol
If P(H2) = 2.0 atm; P12 = 2.0 atm; and P(HI) = 1.0 atm:
Qp = p(HI)^2/p(H2)p(I2) = 0.25
The solve 𝛥𝐺 = 𝛥𝐺° + RT lnQ = -0.8 kJ/mol
At equilibrium, 𝛥𝐺 = 0 and Q=K
𝛥𝐺° =-RT ln K
0 = 𝛥𝐺° + RT lnK
K>1, In K is positive, 𝛥𝐺° is negative, result at equilibrium is products are favored.
K=1, In K is 0, 𝛥𝐺° = 0 result at Equilibrium is neither products or reactants are favored.
K<1 In K is negative, 𝛥𝐺° is positive, result at equilibrium is reactants are favored.
Calculating Equilibrium Concentrations: Equilibrium concentrations can be calculated from initial concentrations if the equilibrium constant is known.
For example, cis-Stilbene and its reaction to trans-Stilbene, Kc = 24.0 (200°C)
If the initial concentration (M) of cis-Stilbene is 0.850, the change in concentration of (M) is x, and the equilibrium concentration (M) is (0.850-x) and x.
Kc = [trans-stilbene]/[cis-stilbene]
24.0 = [x]/[0.850-x]
x = 0.816 M (represents the change in initial concentrations)
If the initial concentration (M) of cis-Stilbene is (0.850), the change in concentration (M) is (0.816)
The equilibrium concentration (M) on each side of the equation is (0.850-0.816) and (0.816)
To calculate the equilibrium concentrations of cis- and trans-stilbene:
Concentration of [cic-stilbene] = (0.850-x) M = (0.850-0.816) M = 0.034 M
Concentration of [trans-stilbene] = x M = 0.816 M
Le Chatelier's Principle of Chemical Equilibrium: Le Chatelier's principle states that when a stress is applied to a system at equilibrium, the system will respond by shifting in the direction that minimizes the effect of the stress. Stress refers to: (1) the addition of a reactant or product (2) the removal of a reactant or product (3) a change in volume of the system, resulting in a change in concentration or partial pressure of the reactants and products (4) a change in temperature.
For the Addition or Removal of a Substance, consider the Haber process at 700 K: N2(g) + 3H2(g) ⇌ 2NH3(g)
At equilibrium: [N2] = 2.05 M, [H2] = 1.56 M, [NH3] = 1.52 M
Kc = [NH3]^2/[N2][H2]^3 = (1.52)^2/(2.05)(1.56)^3 = 0.297
Applying stress by the addition to N2 to give the following concentrations:
[N2] = 3.51 M, [H2] = 1.56 M, [NH3] = 1.52 M
Qc = [NH3]^2/[N2][H2]^3 = (1.52)^2/(3.51)(1.56)^3 = 0.173, which is not equal to Kc. The reaction will shift to the right.
Addition of a reactant or removal of a product will cause an equilibrium to shift to the right. Addition of a product or removal of a reactant will cause an equilibrium to shift to the left.
Changes in Volume: When volume is decreased, the equilibrium is driven toward the side with the smallest number of moles of gas. As the system remains at equilibrium, Q will remain equal to K.
Changes in Temperature: While changes in volume and concentration do not change the value of the equilibrium constant, however a change in temperature can alter the value of the equilibrium constant. Adding heat to an endothermic process shifts the equilibrium toward the products.
For any endothermic reaction, heat is a reactant: heat + reactants ⇌ products (𝛥H > 0 kJ/mol)
Adding heat shifts the reaction towards the products and Kc increases. Removing heat shifts the reaction towards the reactants and Kc decreases.
For any exothermic reaction, heat is a product: reactants ⇌ products + heat (𝛥H < 0 kJ/mol)
Adding heat shifts the reaction toward the reactants and Kc decreases. Removing heat shifts the reaction towards the products and Kc increases.
