chemical equilibrium

reversible reactions

reversible reactions are reactions that proceed in both forward and backward reactions

• denoted using a double arrow (⇌)

• in a closed system:

  • when A and B are reacted, they are not completely converted to C and D

  • reversible reactions are never complete, and a mixture of reactants and products is obtained

graph of concentration vs time for reversible reactions

• at t = 0, there is no C and D ⇒ rate of backward reaction is zero

• as the reaction proceeds, [C] and [D] increases ⇒ rate of backward reaction increases + [A] and [B] decreases ⇒ rate of forward reaction decreases

• after some time, a state will be reached when C and D is used up as soon as they are formed:

  • rate of forward reaction = rate of backward reaction

  • no further changes in [A], [B], [C], and [D]

  • the reaction has reached a state of dynamic equilibrium ⇒ substances, A & B and C & D, are still reacting together although the concentrations of reactants and products
    remain constant (reaction is still proceeding)

graph of rate against time for reversible reactions

dynamic chemical equilibrium

when a reversible reaction in a closed system reaches dynamic chemical equilibrium,

• reaction continues to occur

• rates of the forward and backward reactions are equal hence there is no net change in the concentrations of the reactants and products

• equilibrium can only be achieved in a closed system → no loss/gain of matter to or from the surroundings but does allow the free transfer of energy

K_c → equilibrium constant (definition)

the ratio of the product of the concentrations of products raised to the appropriate powers to the product of the concentrations of reactants raised to the appropriate powers at equilibrium at a given temperature

units for K_c

• may or may not have units, depending on the form of expression

  • units may/may not cancel out

expressions for K_c

• expressions do not include term for solids

• in an aqueous system where water is used as a solvent, the expression does not include the concentration of water, [H2O(l)]

  • only included in the expression if it is specified for use in the question

• in a non-aqueous system, the expression includes the concentration of water, [H2O(l)]

  • concentration of water is included as concentration of water in this reaction is not constant ⇒ water is not used as a solvent in this reaction but produced as a product

K_p → equilibrium constant

• for reactions involving gases, the equilibrium constant can be expressed in:

  1. K_c ⇒ if concentrations of the reactants and products are used

  2. K_p ⇒ if partial pressures of the reactants and products are used

• K_p can be only applied if the equilibrium has at least 1 gaseous species

units for K_p

• for pressure: Pa (Pascal), atm (atmosphere), bar

• may or may not have units, depending on the form of expression

  • units may/may not cancel out

partial pressure

the pressure which the gas would exert if it alone occupies the same volume as the mixture in the container

• formula for partial pressure:

  • P_a = (n_a/n_T) x P_T

relationship between K_c and K_p

• K_p = K_c(RT)^Δn

  • Δn: sum of the coefficients of the gaseous products in the chemical equation minus the sum of the coefficients of the gaseous reactants

• K_c ∝ K_p at constant temperature

• K_c = K_p only when the number of moles of gaseous reactants is equal to the number of moles of gaseous products in the equation ⇒ Δn = 0

significance of K_c and K_p

K_c measures the extent to which a reversible reaction takes place, which is the proportion of products to reactants in the equilibrium mixture, and it is independent of the initial composition of the reaction mixture

K_c > 1

• reaction proceeds from left to right to a greater extent and formation of products are favoured ⇒ position of equilibrium lies to the right

• when K_c > 1000 / >>> 1 ⇒ reaction “is effectively complete”

K_c < 1

• reaction proceeds from right to left to a greater extent and formation of reactants are favoured ⇒ position of equilibrium lies to the left

• when K_c < 0.001 / <<<1 ⇒ reaction “is negligible”

factors affecting K_c and K_p

• are temperature dependent only

• not affected by:

  1. changes in concentrations of reactants and products

  2. changes in pressure of gaseous reactions

  3. addition of catalysts

procedure for solving equilibrium problems

• use ICE table → initial amount, change in amount and equilibrium amount

  • if question specifies the initial and equilibrium amount (mol) OR percentage dissociation

    • percentage dissociation = amount dissociated/initial amount x 100%

    • degree of dissociation/fraction dissociated = amount dissociated/initial amount

• if question only gives values for equilibrium number of moles ⇒ no need to draw table

  • find equilibrium concentration by dividing by volume of vessel, substitute in values into K_c and K_p expression and solve

factors affecting equilibrium

1. change in concentration

2. change in pressure

3. change in temperature

4. addition of catalyst

limitations: not useful in predicting or explaining the changes where the disturbance impacts the system in more than one way ⇒ no conclusion can be reached

Le Chatelier’s Principle

when a system at dynamic equilibrium is subjected to a change which disturbs the equilibrium, the system will react in a way so as to counteract the effect of the change to re-establish equilibrium

change in concentration

1. if more of 1 reactant (A) is added:

   • by Le Chatelier’s Principle, the equilibrium position will shift right to decrease the concentration of A

   • the concentration of products increases until a new equilibrium is attained

   • the new equilibrium will contain more products, more A, and less of the other reactant (B)

2. if A is removed:

   • by Le Chatelier’s Principle, the equilibrium position will shift left to increase the concentration of A

   • concentration of products decreases until a new equilibrium is attained

   • the new equilibrium mixture will contain less products and less A, and more of the other reactant (B)

why K_c is not affected by changes in concentration

• the concentrations of reactants and products will increase/decrease to the extent that K_c is kept constant

change in pressure

• pressure changes only affect gaseous reactions ⇒ negligible
  effect on the volumes of solids and liquids

• pressure of a gas is the force exerted by the gas particles on the walls of its container → P ∝ n

• for pressure changes, use number of moles instead of concentration due to a change in volume in the system

  • ↑ n = ↑ P; ↓ n = ↓ P

1. if pressure is increased:

   • the system will try to reduce the pressure

   • by Le Chatelier’s Principle, the equilibrium position shifts left/right decrease the number of moles of gas, hence decreasing pressure

   • the new equilibrium mixture contains more/less reactant, and more/less product

2. if pressure is decreased:

   • the system will try to increase the pressure

   • by Le Chatelier’s Principle, the equilibrium position shifts left/right to increase the number of moles of gas, hence increasing pressure

   • the new equilibrium mixture contains more/less product, and more/less reactant

pressure has no effect on the equilibrium position of the composition of the equilibrium mixture when:

• total number of moles of gaseous reactants = total number of moles of gaseous products

change in temperature

• K_c and K_p are temperature dependent ⇒ values change with temperature

main concept for effect of temperature on equilibrium position

• increases temperature → equilibrium position shifts towards the endothermic reaction to absorb heat

• decrease temperature → equilibrium position shifts towards the exothermic reaction to release heat

forward reaction is endothermic → absorb heat

1. surrounding temperature increases:

   • the system will try to remove the heat added

   • by Le Chatelier’s Principle, the equilibrium position shifts right towards the endothermic reaction to absorb heat

   • the new equilibrium mixture contains more products, and less reactants

2. surrounding temperature decreases

   • the system will try to produce heat

   • by Le Chatelier’s Principle, the equilibrium position shifts left towards the exothermic reaction to release heat

   • the new equilibrium mixture contains less products, and more reactants

forward reaction is exothermic → release heat

1. surrounding temperature increases

   • the system will try to remove the heat added

   • by Le Chatelier’s Principle, the equilibrium position shifts left towards the endothermic reaction to absorb heat

   • the new equilibrium mixture contains less product, and more reactants

2. surrounding temperature decreases

   • the system will try to produce heat

   • by Le Chatelier’s Principle, the equilibrium position shifts right towards the exothermic reaction to release heat

   • the new equilibrium mixture contains more product, and less reactants

how does K_c vary with temperature

1. endothermic reaction

   • increase in temperature: [C] increases, [A] and [B] decreases ⇒ K_c increases

   • decrease in temperature: [C] decreases, [A] and [B] increases ⇒ K_c decreases

2. exothermic reaction

   • increase in temperature: [C] decreases, [A] and [B] increases ⇒ K_c decreases

   • decrease in temperature: [C] increases, [A] and [B] decreases ⇒ K_c increases

addition of catalyst

• catalysts have no effect on K_c or K_p, the yield of the product and the equilibrium of the position (does not change the concentration of reactants)

1. increase the rate of forward and backward reaction to the same extent hence position of equilibrium remains unchanged

2. catalysts increase the rate of reaction so that dynamic equilibrium is established more quickly

• with a catalyst, the rate of reaction is faster and equilibrium is reached faster, however, the yield of product remains the same

Haber process

• manufacture of ammonia: N₂ (g) + 3H₂ (g) ⇌ 2NH₃ (g), ΔH = -92 kJ mol^-1

• common operating conditions

  1. high pressure of 250 atm

  2. moderate temperature of 450°C

  3. iron catalyst

  4. molar ratio of N₂ : H₂ is 1 : 3

• Le Chatelier’s Principle indicates that to increase the yield of NH₃, high pressure and low temperature should be used

• there is a compromise between the conflicting demands of high yield and high rate of reaction in the conditions

explain choice of pressure of 250 atm → Haber process

• by Le Chatelier’s Principle, a high pressure will cause the equilibrium position to shift right to decrease the number of moles of gas to decrease pressure ⇒ yield of ammonia increases

• however, too high a pressure (i.e. > 250 atm) would be too expensive to maintain as thicker pipes would need to be built to withstand the higher pressure ⇒ pressure of 250 atm is used

explain choice of moderate temperature of 450°C → haber process

• by Le Chatelier’s Principle, a low temperature will cause the equilibrium position to shift right towards the exothermic reaction to release heat ⇒ yield of ammonia increases

• however, too low a temperature would decrease the rate of reaction, making it not feasible industrially ⇒ moderate temperature of 450ºC is used

explain why iron catalyst is required → haber process

iron catalyst (heterogeneous catalyst) is used to increase reaction rate ⇒ does not affect the yield of ammonia

significance of Q, the reaction quotient

when a reversible reaction has not yet reached equilibrium: the reaction quotient (Q) is the ratio of the product of the concentrations of products raised to the appropriate powers to the product of the concentrations of reactants raised to the appropriate powers at a given temperature

• unlike K_c, Q is not a constant value as the concentration of products and reactants are always changing, until the reaction reaches equilibrium

  • K_c: special Q that defines the proportion of each species in a reaction mixture at dynamic equilibrium

• Q has the same expression as the equilibrium constant, K but
  represents the quantity of reactants and products at any composition

1. if Q < K_c → not at dynamic equilibrium yet

   • proportion of products to reactant is less than at equilibrium

   • to attain dynamic equilibrium, increases the proportion of products to reactants ⇒ increase conversion of reactants to products until Q = K_c

2. if Q > K_c → not at dynamic equilibrium yet

   • proportion of products to reactant is more than at equilibrium

   • to attain dynamic equilibrium, decrease the proportion of products to reactants ⇒ increase conversion of products to reactants until Q = K_c

3. Q = K_c → system is at equilibrium

relationship between K_c and rate constants, k_f and k_b

K_c = k_f / k_b