Chemical Equilibrium, Law of Mass Action & Applications | Physical Chemistry PDF Download

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. 

State of Chemical Equilibrium

• 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 Reactions

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

For example:

Irreversible Reactions:

•  Always goes for completion. 
•  Reactants are completely consumed in these reactions
• Precipitation reaction, NaCl + AgNO₃→AgCl(s) + NaNO₃ 
• 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.

Examples:

But when Fe_(s) is heated and water vapor is passed over it in an open vessel, it is converted to Fe₃O_4(s) along with the evolution of hydrogen gas.

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

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

Reversible reactions:

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

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

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

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.

Physical Equilibrium (e.g., Vaporization of Water):

• Water evaporates, and vapor concentration increases.
• The rate of evaporation equals the rate of condensation.
• Concentrations of liquid water and vapor remain constant.
• Molecules continue to transition between liquid and vapor phases, but there is no net change in their amounts.

Chemical Equilibrium (e.g., Dissociation of PCl₅):

• PCl₅ dissociates into PCl₃ and Cl₂.
• The rates of the forward reaction (PCl5 dissociating) and the reverse reaction (PCl₃ and Cl₂ recombining) become equal.
• Concentrations of PCl₅, PCl₃, and Cl₂ remain constant.
• Reactions continue in both directions, but the net concentration of each substance does not change.

Key Characteristics of Equilibrium:

• Reactant and product concentrations do not change at equilibrium.
• Molecules continue to react in both directions at the same rate.
• The system can adjust if disturbed, shifting to re-establish equilibrium.

Le Chatelier's Principle:

• If equilibrium is disturbed (by changes in concentration, pressure, or temperature), the system will shift to restore equilibrium.

This can be shown graphically.

So, “state of chemical equilibrium can be defined as the state when the rate of forward reaction becomes equal to the 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, 

Applying law of mass action, 

Rate of forward reaction, 

Where k_f = rate constant of forward reaction 

Similarly, 

Rate of reverse reaction

Where k_r = rate constant of the reverse reaction.

At equilibrium, 

Rate of forward reaction = Rate of reverse reaction

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

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

Illustration:The rate of disappearance of A is given asCalculate the value of the equilibrium constant.

Solution: 

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

Equilibrium Constant (Kp) in terms of Partial Pressure: 

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

From the law of mass action, 

From the ideal gas equation 

PV = nRT

At constant temperature,

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

P ∝[A]

Similarly, P ∝ [B]

So, equation (1) can be rewritten as

All Equilibrium constants (Keq)-

• Kc 
• Kp
• Kx
• Kn

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

Relationship Between K_p and K_c

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

 And                                            

From the ideal gas equation,

PV = nRT

So, P_B = [B] RT; P_D = [D]RT

Similarly, P_A = [A]RT; P_C = [C]RT

Substituting the values of P_A, P_B, P_C, and P_D in equation (2), we get 

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.

Illustration: The value of K_p for the Reactionis 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 K_p.

Homogeneous  Reactions:

• All reactants and products are in the same phase (gas, liquid, or solid).
• Example:$\mathrm{ N}\mathrm{<sub\; style="word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 13px\; !important;\; letter-spacing:\; inherit;\; color:\; black">2</sub>}\left(g\right)+3H\mathrm{<sub\; style="word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 13px\; !important;\; letter-spacing:\; inherit;\; color:\; black">2</sub>}\left(g\right)\rightleftharpoons 2NH\mathrm{<sub\; style="word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 13px\; !important;\; letter-spacing:\; inherit;\; color:\; black">3</sub>}\left(g\right)N\_2\; (g)\; +\; 3H\_2\; (g)\; \backslash rightleftharpoons\; 2NH\_3\; (g)$
  

Heterogeneous Reactions:

• Reactants and products are in different phases (solid, liquid, or gas).
• Example:$CaCO\mathrm{<sub\; style="word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 13px\; !important;\; letter-spacing:\; inherit;\; color:\; black">3</sub>}\left(s\right)\rightleftharpoons CaO\left(s\right)+CO\mathrm{<sub\; style="word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 13px\; !important;\; letter-spacing:\; inherit;\; color:\; black">2</sub>}\left(g\right)CaCO\_3\; (s)\; \backslash rightleftharpoons\; CaO\; (s)\; +\; CO\_2\; (g)$

Equilibrium Constant for Homogeneous Reversible Reactions

Products and reactants are in the 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

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

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 P_T also remains constant and we will get the curve mention below.

Case II: Homogeneous:Δng > 0

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 P_T also increases and becomes constant at equilibrium as shown below.

Case III: Homogeneous and Δng < 0

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

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.

Initial concentration (mol L^–1)

Equilibrium concentration (mol L^–1)

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

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

 P_HI = mole fraction of HI × Total pressure

Similarly, 

Substituting these values in equation (iii) we get

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

K_p = K_c 

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

Thermal Dissociation of Phosphorus Pentachloride

PCl_5(g) dissociates thermally according to the reaction,

Let us consider that 1 mole of PCl₅ has been taken in a container of volume V litre and at equilibrium x moles of PCl_5(g) dissociates. Thus 

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

Equilibrium concentration (mol L^–1)

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

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

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

Mole fraction of PCl₃ = Mole fraction  

And mole fraction of PCl₅ 

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

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

Equilibrium Constant for Heterogeneous Reversible Reactions

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

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

Initial moles                           1               0            0 

Moles at equilibrium             1- x          x             x

Applying law of mass action, K_c

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

K_c = [NH₃] [HCl]

And K_p =P_NH3 * P_HCl

Thermal Dissociation of Ag₂CO₃:

A_g2CO_3(s) dissociates thermally according to the equation.

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

Now, let us consider that 1 mole of Ag₂CO_3(s) is heated in a closed container of volume V and x mo l of Ag₂CO_3(s) dissociates at equilibrium, then

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

Significance of magnitude of Equilibrium Constant 

• A very large value of K_c or K_p signifies that the forward reactions has gone to completion or very nearly so.
•  A very small value o f K_c or K_p signifies that the forward reaction has not occur to any significant extent.
•  If the numerical value of K_c or K_p 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

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: 

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

The Extent of Reaction

Case I: 

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

(The concentration of product is very low and the concentration of reactant is very high) It clearly explains that the 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 reaction has just started.

Case II: 

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

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

Hence, it explains that reaction has almost completed.

Illustration:Initial mole of reactant is 1 mole and the 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. 

x = 10^–25

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

Solution:                

At any time concentration  

Since Q_C> K_C, so reaction will move in backward direct ion to attain equilibrium.

Equilibrium concentration  

Equilibrium concentration of A(g) = 0.16 

Equilibrium concentration of B(g) = 0.04 

Equilibrium concentration of C(g) = 0.04

Illustration: Calculate K_P for the reaction. When NO₂ is 30% dissociated and total pressure at equilibrium is 2 bar.

Solution: 

Given, α = 0.3

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

Partial Pressure      

_{Put α = 0.3}

K_P = 0.79

Dealing with Degree of Dissociation (α)

In terms of moles

In terms of α

Applications of Chemical Equilibrium

• Industrial Chemistry: Chemical equilibrium principles are widely used in industrial processes to optimize reaction yields and product purity. Examples include the Haber-Bosch process for ammonia synthesis and the production of methanol and sulfuric acid.

• Environmental Chemistry: Equilibrium concepts play a role in understanding environmental processes, such as the behavior of pollutants in air, water, and soil. Equilibrium calculations help assess factors like pH in natural waters and the equilibria involved in acid rain formation.

• Chemical Analysis: Equilibrium-based methods are employed in analytical chemistry for quantitative analysis. Techniques like spectrophotometry and titration rely on equilibria between analytes and reagents to determine concentrations.

• Pharmaceuticals: Drug formulations often involve equilibrium-based principles. For example, the solubility of a drug in a particular solvent can be crucial for drug delivery systems.

• Biological Systems: Equilibrium concepts are relevant in biological systems, such as the binding of oxygen to hemoglobin in blood. Understanding the equilibrium between reactants and products is essential for comprehending biochemical reactions.

• Corrosion Prevention: Equilibrium considerations are important in preventing corrosion. By controlling the conditions in which metals are exposed to moisture and oxygen, it is possible to establish conditions that hinder the corrosion process.

• Food Chemistry: Equilibrium reactions are crucial in food chemistry, such as controlling the pH of food products and ensuring the stability of emulsions and suspensions.

• Fertilizer Production: In the production of fertilizers, equilibrium principles are applied to optimize the synthesis of nutrients like ammonium nitrate.