Chemical Kinetics and Equilibrium

Synopsis

Rate of Chemical Reaction

Rate of Chemical Reaction:

• Alternately the rate of reaction can also be expressed as,
  
   

• Consider a hypothetical reaction, assuming that the volume of the system remains constant. R → P One mole of the reactant R produces one mole of the product P.
  
  
• If [R]₁ and [P]₁ are the concentrations of R and P respectively at time t₁ and [R]₂ and [P]₂ are their concentrations at time t₂ then,
  
  The square brackets in the above expressions are used to express molar concentration.
  
  

• Δ[R] is a negative quantity because concentration of reactants is decreasing.
  
  
  

• Equations (1) and (2) given above represent the average rate of a reaction, rav.
  This average rate depends upon the change in concentration of reactants or products and the time taken for that change to occur.
  
  

Units of rate of a reaction:

• From equations (1) and (2), it is clear that units of rate are concentration time^–1.
• For example, if concentration is in mol L^–1 and time is in seconds then the units will be mol L^-1s^–1.
• In gaseous reactions, the concentration of gases is expressed in terms of their partial pressures; hence the units of the rate equation will be atm s^–1.

Instantaneous Rate of Reaction:

• Consider a hydrolysis of butyl chloride (C₄H₉Cl).
  C₄H₉Cl+ H₂O → C₄H₉OH + HCl
  
  
• We have provided the concentrations over different intervals of time below.
  
  

• We can determine the difference in concentration over different intervals of time and thus determine the average rate by dividing Δ[R] by Δt.
• It can be seen from experimental data that the average rate falls from 1.90 × 10^-4 mol L^-1s^-1 to 0.4 × 10^-4 mol L^-1s^-1.
• However, average rate cannot be used to predict the rate of a reaction at a particular instant as it would be constant for the time interval for which it is calculated.
• Hence, to express the rate at a particular moment of time we determine the instantaneous rate.
• It is obtained when we consider the average rate at the smallest time interval say dt, when Δt approaches zero.
  Therefore, for an infinitesimally small dt, instantaneous rate is given by,
  
  

• By drawing the tangent at time t on the either of the curves for concentration of R vs time t or concentration of P vs time t and calculating the slope of the curve, we can determine the instantaneous rate of reaction.
• Hence, here in this example rinst at 600s is calculated by plotting graph of concentration of butyl chloride as against time t.
• A tangent is drawn on the curve at a point t = 600s. 
  
• Now consider a reaction,
  Hg(l) +Cl₂(g) → HgCl₂ (s)
  Here, the stoichiometric coefficients of the reactants and products are same; hence rate of the reaction is given as,
  
  Therefore, we can say that from above equation that the rate of disappearance of any of the reactants is same as the rate of appearance of the products.

• Consider another reaction,
  2HI(g) → H₂(g) +I₂(g)
  In this reaction, two moles of HI decompose to produce one mole each of H₂ and I₂ i.e. the stoichiometric coefficients of reactants or products are not equal to one; hence  we need to divide the rate of disappearance of any of the reactants or the rate of appearance of products by their respective stoichiometric coefficients.
  Since rate of consumption of HI is twice the rate of formation of H₂ or I₂, to make them equal, the term Δ[HI] is divided by 2.
  The rate of this reaction is given by,
  
  

• For a gaseous reaction at constant temperature, concentration is directly proportional to the partial pressure of a species and hence, rate can be expressed as rate of change in partial pressure of the reactant or the product.

Factors affecting the rate of reaction:

EQUILIBRIA IN CHEMICAL PROCESS 

Irreversible Reactions

Irreversible reactions: The chemical reactions which proceed in such a way that reactants are completely converted into products, i.e. the reactions which move in one direction, i.e. forward direction only are called irreversible reactions. 

(a) (i) Thermal decomposition of ammonium nitrite, 

          NH₄NO₂ → N₂+2H₂O

(b) Precipitation reaction,

(ii) AgNO₃+ NaCl  → AgCl +NaNO₃

(iii) Pb(NO₃)₂ +2KI → PbI₂ + 2KNO₃

(c) Neutralisation reactions: 

     H₂SO₄ + 2NaOH  →  Na₂SO₄ + 2H₂O
     Strong Acid   Strong Base         

Reversible Reactions:

Reactions which thus proceed in both the directions and do not reach to completion are known as reversible reactions. The reaction proceeding from left to right is conventionally called the forward reaction and the opposite one proceeding from right to left is called the reverse or backward reaction. In such reactions the arrow (→ ) or sign of equality (=) is replaced by two half arrow ( ⇌ ) pointing the reaction in both the directions. This sign (⇌) represents the reversibility of the reaction

3Fe +4H₂O ⇌ Fe₃O₄ + 4H₂

Some examples of reversible reactions are given below: 

 CaCO₃  ⇌ CaO + CO₂

CH₃COOH + C₂H₅OH ⇌ CH₃COOC₂H₅ +H₂O

Heterogeneous Reactions: The reversible reaction in which more than one phase is present is called heterogeneous reaction.

CaCO₃(s) ⇌ CaO(s) +CO₂(g)

MgCO₃(s) ⇌ MgO(s) + CO₂(g)

2Na2O2(s)+ 2H2O(𝓁) ⇌ 4NaOH(𝓁) +O₂(g)

3Fe(s) +4H₂O(𝓁)⇌ Fe₃O₃ (s) +4H₂(g) 

Homogeneous Reactions: The reversible reaction in which only one phase is present, i.e. all the reactions and products are in the same physical state is called homogeneous reaction.

H₂(g) +I₂(g) ⇌ 2HI(g)

CH₃ COOH(𝓁)+ C₂H₅OH(𝓁) ⇌ CH₃COOC₂H₅ (𝓁)+H₂O(𝓁)

 

Dynamic Nature of Chemical Equilibrium 

Dynamic nature is characterized by constant change, activity, or progress. Thus, chemical equilibrium is dynamic in nature. In a reversible reaction, the state in which both forward and backward reactions or two opposing reactions occur at the same speed is called as chemical equilibrium. The measurable properties of the system such as pressure, density, colour or concentration remain constant under a certain set of conditions.

 

 

Characteristics of Equilibrium State 

1. A system needs to be always closed to achieve equilibrium since an open system allows the escape of the formed products which prevents the backward reaction. 
2. Chemical equilibrium, at a given temperature, is characterized by constancy of certain properties such as pressure, concentration, density or colour. 
3. Chemical equilibrium can be attained from either side, i.e., from the side of reactants or products. 
   N₂ + 3H₂ ⇌  2NH₃                      
4. Aequilibrium, each reactant and each product has a fixed concentration and this is independent of the fact whether we start the reaction with the reactants or with the products. This reaction can be graphically represented as,
                  
5. resence of catalyst never affects the equilibrium but it helps in attaining it rapidly. 
6. The reactions move with the same speed exhibiting the dynamic nature

At equilibrium:

• Rate of forward reaction = rate of backward reaction
• Concentration (mole/litre) of reactant and product becomes constant.
• ΔG = 0
• Q = Keq

Law of mass action:

The rate at which a substance reacts is directly proportional to its active mass raised to suitable powers, and the rate of reaction is directly proportional to the product of all such active masses of reactants.

Factors influencing equilibrium constant (K_p or K_c):

• Stoichiometric representation of a reaction
• Mode of representing the change
• Temperature
• Units of pressure

Units of K_p and K_c 

• Units of K_p = (unit of pressure)^∆n
• Units of K_c = (unit of concentration)^∆n 

Prediction of direction at reaction and reaction quotient

• If Q = K, the reaction is in equilibrium.
• If Q > K, the reaction moves from right to left.
• If Q < K, the reaction moves from left to right.

Le Chatelier's Principle:

If a system at equilibrium is subjected to a disturbance or stress which changes any of the factors that determine the state of equilibrium, the system will react in such a way as to minimise the effect of the disturbance.

 

Effect of concentration:

• If the concentration of reactant is increased at equilibrium, then the reaction shifts in the forward direction.
• If the concentration of product is increased, then the equilibrium shifts in the backward direction.

Effect of volume:

• If the volume is increased, the pressure decreases; hence, the reaction will shift in the direction in which pressure increases,
  i.e. in the direction in which the number of moles of gases increases and vice versa.
• If the volume is increased, then for
  Δn > 0, the reaction will shift in the forward direction
  Δn < 0, the reaction will shift in the backward direction
  Δn = 0, the reaction will not shift

Effect of pressure:

If the pressure is increased at equilibrium, then the reaction will try to decrease the pressure; hence, it will shift in the direction in which less number of moles of gases is formed.

Effect of inert gas addition:

1. Constant pressure:
   If the inert gas is added, then to maintain the pressure constant, volume is increased. Hence, the equilibrium will shift in the
   direction in which larger number of moles of gas is formed.
   Δn > 0, the reaction will shift in the forward direction
   Δn < 0, the reaction will shift in the backward direction
   Δn = 0, the reaction will not shift
2. Constant volume:
   Inert gas addition has no effect at constant volume.

Effect of temperature:
Equilibrium constant is only dependent on the temperature.

• For an endothermic (ΔH > 0) reaction, the value of the equilibrium constant increases with increase in temperature.
• For an exothermic (ΔH < 0) reaction, the value of the equilibrium constant decreases with increase in temperature.
• For ΔH > 0, the reaction shifts in the forward direction with increase in temperature.
• For ΔH < 0, the reaction shifts in the backward direction with increase in temperature.
• If the concentration of reactant is increased at equilibrium, then the reaction shifts in the forward direction.
• If the concentration of product is increased, then equilibrium shifts in the backward direction.