Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemistry: Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

The document Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry is a part of the Chemistry Course Physical Chemistry.
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Chemical Equilibrium

In a chemical reaction, chemical equilibrium is the state in which both reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

  • Usually, this state results when the forward reaction proceeds at the same rate as the reverse reaction. 
  • The reaction rates of the forward and backward reactions are generally not zero, but equal. Thus, there are no net changes in the concentrations of the reactant(s) and product(s). Such a state is known as dynamic equilibrium.

Irreversible and Reversible Reactions

Irreversible Reactions

Those reactions which proceed in forward direction and reaches almost to completion are called Irreversible reactions.

For example:

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Irreversible Reactions:

  •  Always goes for completion. 
  •  Reactants are completely consumed in these reactions

Ex.: Ppt. reaction, NaCl + AgNO3→AgCl(s) + NaNO3

case, if we remove AgCl (which is the product), reaction will move in forward direction].

Reversible Reactions

Those reactions which proceed in both forward and backward directions and never reaches completion are called Reversible reactions.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

But when Fe(s) is heated and water vapor is passed over it in an open vessel, it is converted to Fe3O4(s) along with the evolution of hydrogen gas.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

And when Fe3O4 is reduced with hydrogen gas, it gives Fe(s) and H2O

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

But, if the reaction is carried out in closed vessel, this reaction becomes reversible.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Reversible reactions:

  •  Never goes for completion
  •  Irrespective of the fact whether the reaction has started by reactants or products.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

If we remove C (which is product), the reaction will again start and moves in forward direction to attain equilibrium again. 

  • These reactions can be initiated in any direction. 
  • Always takes place in a closed vessel.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

State of Equilibrium

Equilibrium is a state in which the rate of the forward reaction equals the rate of the backward reaction. Although some chemical reactions reach completion, some other reactions do not completely occur.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

  • It has generally been observed that many changes (physical and chemical) do not proceed to completion when they are carried out in a closed container. Consider, for example, vaporisation of water,

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

  • At any temperature, vapourisation of water takes place, initially the concentration of water is much greater than the concentration of vapour, but with the progress of time, concentration of vapour increases whereas that of water remains constant and after a certain interval of time. 
  • There is no change in concentration of vapour, this state is known as state of physical equilibrium. In a similar way, this has also been found for chemical reactions, for example. 
  • When PCl5(g) is heated in a closed continue, its dissociation starts with the formation of PCl3(g) and Cl2(g) are formed due to dissociation of PCl5(g). After a certain interval of time, the concentration of PCl5(g), PCl3(g), and Cl2(g) each become constant. 
  • It does not mean that at this point of time, dissociation of PCl5(g) and its formation from m PCl3(g) and Cl2(g) has been stopped. Actually, the rate of dissociation of PCl5 and the rate of formation of PCl5(g) becomes equal. 
  • This state is called the state of chemical equilibrium. So, the state of chemical equilibrium is dynamic.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

This can be shown graphically.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry        Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

So, “state of chemical equilibrium can be defined as the state when the rate of forward reaction becomes equal to rate of reverse reaction and the concentration of all the species becomes constant”.


Law of Mass Action

Guldberg and Waage in 1807 gave this law and according to this law, “At constant temperature, the rate at which a substance reacts is directly proportional to its active mass and the rate at which a chemical reaction proceeds is directly proportional to the product of active masses of the reacting species”.

The term active mass of a reacting species is the effective, concentration or its activity (a) which is related to the molar concentration (C) as

a = f C

where f = activity coefficient. F < 1 but f increases with dilution and as V → ∞ i.e. C → 0, f → 1 i.e., a → C Thus at very low concentration the active mass is essentially the same as the molar concentration. It is generally expressed by enclosing the formula of the reacting species in a square bracket.

To illustrate the law of mass action, consider the following general reaction at a constant temperature, 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Applying law of mass action, 

Rate of forward reaction, 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Where k= rate constant of forward reaction 

Similarly, 

Rate of reverse reaction

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Where k= rate constant of reverse reaction.

At equilibrium, 

Rate of forward reaction = Rate of reverse reaction

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

So, from equation (i) and (ii), we get

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

where, Kc is the equilibrium constant in terms of molar concentration.

Illustration:

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

The rate of disappearance of A is given as:

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry  Calculate the value of the equilibrium constant.

Solution: 

We know, at equilibrium concentration of each species present in the given equilibrium. Become constant.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Equilibrium Constant (Kp) in terms of Partial Pressure: 

Consider the same general reaction taking place at a constant temperature,

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

From the law of mass action, 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

From ideal gas equation 

PV = nRT

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

At constant temperature,

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Thus, we can say in a mixture of gases, Partial pressure of any component (say A)

P ∝[A]

Similarly, P ∝ [B]

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

So, equation (1) can be rewritten as

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

All Equilibrium constants (Keq)-

  • Kc 
  • Kp
  • Kx
  • Kn

Kx and Kn are not considered equilibrium constants, because these can be varied without change in temp. for gases. 

Relationship Between Kp and Kc

From the above, for the same general reaction at constant temperature.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry 

 And                                            Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

From the ideal gas equation,

PV = nRT

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

So, PB = [B] RT; PD = [D]RT

Similarly, PA = [A]RT; PC = [C]RT

Substituting the values o f PA, PB, PC, and PD in equation (2), we get 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Where, Δn = (c + d) - (a + b)

i.e;, Δn = sum of no. of moles of gaseous products-sum of no. of moles of gaseous reactants.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Illustration: The value of Kp for the Reaction

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

is 0.03 atm at 4270C, when the partial pressure is expressed in atm. What is the value of Kc.

Solution: Firstly, consider species that are present in gaseous phase only. So, we can write Kp.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Application of Law of Mass Action: 

Reversible Reactions:

  • Homogeneous 
  • Heterogeneous 

Equilibrium Constant for Homogeneous Reversible Reactions: 

Products and reactants are in same phase. Homogeneous gaseous equilibria are best classified into three categories i.e., in which no. of moles of product and reactant varies. 

Case I: Homogeneous; Δng = 0

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

In this reaction, each and every species present are in same phase. That’s why this reaction is under the category of homogeneous equilibria. 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

PV = nRT (Ideal gas equation)

Here, V is constant. R is also constant.

P α n

Since no. of moles are constant i.e.  Initial = a

Final = a

Hence Palso remains constant and we will get the curve mention below.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Case II: Homogeneous:Δng > 0

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

You will easily get these expressions in the same way we did in last.

Here, no. of moles increases at equilibrium i.e. from a to (a+x). Hence PT also increases and becomes constant at equilibrium as shown below.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Case III: Homogeneous and Δng < 0

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

This graph clearly resembles that first pressure is decreasing and then becomes constant at equilibrium.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Synthesis of Hydrogen Iodide:

Suppose ‘a’ moles of H2 and ‘b’ moles o f I2 are heated at 444°C in a closed container of volume ‘V’ litre and at equilibrium, 2x moles of HI are formed.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Initial concentration (mol L–1)

Equilibrium concentration (mol L–1)

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Substituting the equilibrium concentrations of H2, I2 and HI in equation (i), we get 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Suppose the total pressure of the equilibrium mixture at 444°C is P, then

 PHI = mole fraction of HI × Total pressure

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Similarly, 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Substituting these values in equation (iii) we get

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

So, one can see from equations (iii) and (iv), that

Kp = K

This is so because Δn = 0 for the synthesis of HI from H2 and I2.

Thermal Dissociation of Phosphorus Pentachloride

PCl5(g) dissociates thermally according to the reaction,

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Let us consider that 1 mole of PCl5 has been taken in a container of volume V litre and at equilibrium x moles of PCl5(g) dissociates. Thus 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Initial concentration (mo l L–1) 1                        0              0                 0

Equilibrium concentration (mol L–1)                   Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

According to law of mass action, at a constant temperature,

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Substituting the values of equilibrium concentration, in equation (1), we have 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Now, total number of moles at equilibrium = 1 – x + x + x = 1 + x

Mole fraction of PCl3 = Mole fraction Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry 

And mole fraction of PCl5Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry 

Suppose total pressure at equilibrium is P, then we have from equation (2),

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Similarly, we can apply law of mass action on any reaction at equilibrium.    

Equilibrium Constant for Heterogeneous Equilibria

The equilibrium which involves reactants and products in different physical states. The law of mass action can also be applied on heterogenous equilibria as it was applied for homogenous equilibria (involving reactants and products in same physical states).

Thermal Dissociation of Solid Ammonium Chloride:

The thermal dissociat ion of NH4Cl(s) takes place in a closed container according to the equation

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Let us consider 1 mole of NH4Cl(s) is kept in a closed container of volume ‘V’ litre at temperature TK and if x mole of NH4Cl dissociates at equilibrium then


Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Initial moles                           1               0            0 

Moles at equilibrium             1- x          x             x

Applying law of mass action, Kc Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

As NH4Cl is a pure solid, so there is no appreciable change in its concentration. Thus, 

K= [NH3] [HCl]

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

And Kp =PNH* PHCl

Thermal Dissociation of Ag2CO3:

Ag2CO3(s) dissociates thermally according to the equation.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Applying law of mass action, at constant temperature, we get,

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Now, let us consider that 1 mole of Ag2CO3(s) is heated in a closed container of volume V and x mo l of Ag2CO3(s) dissociates at equilibrium, then

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Initial moles                                    1             0          0 

Equilibrium moles                          1 - x        x           x

Now, as Ag2CO3 and Ag2O are solids, so their concentration can be assumed to be constants Thus

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Significance of magnitude of Equilibrium Constant: 

  • A very large value of Kc or Kp signifies that the forward reactions has gone to completion or very nearly so.
  •  A very small value o f Kc or Kp signifies that the forward reaction has not occur to any significant extent.
  •  If the numerical value of Kc or Kp is neither very large or very small, a reaction is most likely to reach a state of equillibrium in which both reactants and products are present

Predictions of Direction of the Reaction:

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry 

QC is called Reaction Quotient: 

QC is the ratio of the concentration of products and reactants each raised to their schoitiometric  coefficient as in balanced chemical equation. 

Hence, three cases arises: 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Note: While dealing wit h KP and α, take initial moles of reactant as 1 because ultimately they will be cancelled out.

The Extent of Reaction:

Magnitude of equilibrium constant tells us the extent of reaction. It resembles the extent by which the reactant has been reacted or product has been formed at equilibrium.

Case I: 

If equilibrium constant (say KC) is very-very small.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

(Concentration of product is very low and concentration of reactant is very high) It clearly explains that numerator is very small and denominator is very-very high.

Hence, by this we can infer that reaction has a very low approach in forward direction and reactions has just started.

Case II: 

If equilibrium constant (i.e. KC) is very-very high.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry 

(Concentration of product is very high and concentration of reactant is very low).

Hence, it explains that reaction has almost completed.

Illustration:Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Initial moles of reactant is 1 mole and volume of the container is 1L. Calculate the moles of B(g) at Equilibrium Kc = 10–50

Solution: Since the value of KC is very low. 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

x = 10–25

Illustration: If initially 1 mole of all the species present one taken in 10 L closed vessel, find equilibrium concentration of each species. 

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Solution:                 Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

At any time concentration   Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Since QC> KC, so reaction will move in backward direct ion to attain equilibrium.

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Equilibrium concentration  Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Equilibrium concentration of A(g) = 0.16 

Equilibrium concentration of B(g) = 0.04 

Equilibrium concentration of C(g) = 0.04

Illustration: Calculate KP for the reaction

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

When NO2 is 30% dissociated and total pressure at equilibrium is 2 bar.

Solution:

Given, α = 0.3

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

We are dealing with KP and α. Hence initial mole of N2O4 = 1

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Partial Pressure       Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Put α = 0.3

KP = 0.79

Dealing with Degree of Dissociation (α)

In terms of moles

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

In terms of α

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry

The document Chemical Equilibrium, Law of Mass Action & Applications Notes | Study Physical Chemistry - Chemistry is a part of the Chemistry Course Physical Chemistry.
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