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Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

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11. Disturbance in equilibrium: The Le-Chatelier’s Principle

This principle, which is based on the fundamentals of a stable equilibrium, states that “When a chemical reaction at equilibrium is subjected to any stress, then the equilibrium shifts in that direction in which the effect of the stress is reduced”.

Confused with “stress” Well by stress here what we mean is any change of reaction conditions e.g. in temperature, pressure, concentration etc.

This statement will be explained by the following example.

Let us consider the reaction:   Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Let the moles o f N2, H2 and NH3 at equilibrium be a, b and c moles respectively. Since the reaction is at equilibrium,

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Where, 

X terms denote respective mole fractions and PT is the total pressure of the system.

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Here,

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Now, let us examine the effect of change in certain parameters such as number of moles. Pressure, temperature etc.

If we increase a or b, the left hand side expressio n becomes QP (as it is disturbed from equilibrium) and we can see that Q> KP

 The reaction therefore moves backward to make QP = KP

 If we increase c, QP < KP and the reaction has to move forward to revert back to equilibrium.

If we increase the volume of the container (which amounts to decreasing the pressure), QP < KP and the reaction moves forward to attain equilibrium.

If we increase the pressure of the reaction, then equilibrium shifts towards backward direction since in reactant side we have got 2 moles and on product side we have got 4 moles. So pressure is reduced in backward direction.

However from the expression if we increase the temperature of the reaction, the left hand side increase (QP) and therefore does it mean that the reaction goes backward (since QP > KP

Does this also mean that if the number of moles of reactant and product gases are equal no change in the reaction is observed on the changing temperature (as T would not exist on the left hand side)?. The answer to these quest ions is No. This is because KP also change with temperature. Therefore we need to know the effect of temperature on both QP and KP to decide the course of the reaction.


1. Effect of Concentration on Equilibrium:

If the concentration of a component is increased, reaction shifts in a direction which tends to decrease its concentration

For exmaple: Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

At equilibrium: Moles        1        1        1           1          KC = 1

If added 1 mole of D at equilibrium:

                                               1       1          1         1        QC = 2

QC> KC react ion implies reaction proceeds in backward direct ion.

At new equilibrium: 1 +x          1+ x           1-x           2-x

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Note: Here KC will remain constant even after addition of D Because KC depends on temperature only. 

2. Effect of change of pressure / volume on equilibrium

Three cases arises

· Δng = 0 

· Δng > 0 

· Δng < 0

Case I:Δng = 0 

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

At equilibrium 1 atm 1 atm 2 atm       1 

When we double the pressure or half the volume at equilibrium at t

                           2 atm 2 atm 4 atm      1

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Here, K= QP

 Hence reaction will not move in any direction. It resembles the reaction is still at equilibrium. 

Case II: Δng> 0

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

At equilibrium  1 atm          1 atm          1 atm             3       1 

When we double the pressure or half the volume 

At t                     2 atm           2 atm          2 atm            6      2

At this time, Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

QP = 2

QP>KP; hence reaction will move in backward direction.

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

At new equation 2+P          2-P          2-P

Case III:Δng < 0

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

At t = teq           1 atm        1 atm          1 atm       3           1

When we double the pressure or half the volume at equilibrium

At t                     2 atm        2 atm       2 atm    6         2

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Since, QP< KP React ion will move in forward direction

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

New equilibrium      2–P        2–P         2+P

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Table to calculate

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

3. Effect of Temperature on Equilibrium:

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Now we will derive the dependence of KP on temperature.

Starting with Arrhenius equation of rate constant

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Where, k= rate constant for forward reaction, A= Arrhenius constant of forward reaction, 

Eaf = Energy of activation of forward reaction

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Dividing (i) by (ii) we get,

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

We know that Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry (equilibrium constant)

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

At temperature T1

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

At temperature T2

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Dividing (iv) by (iii) we get 

The enthalpy of a reaction is defined in terms of activation energies as Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

For and exothermic reaction, ΔH would be negative. If we increase the temperature of the system (T2 > T1), the right hand side of the equation (V) becomes negative.

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry 

that is, the equilibrium constant at the higher temperature would be less than that at the lower temperature.

Now let us analyse our question. Will the reaction go forward or backward?

Before answering this, we must first encounter problem. If temperature is increased. The new KP would either increase or decrease or remain unchanged. If Kp increase and QP decreases. 

Then Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry therefore the reaction moves forward. If Kincrease and QP remains same then Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry Again, the reaction moves forward. What, if KP increase and QP also increase?

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry This can be answered by simply looking at the dependence of QP and KP on temperature. You can see from the equation that KP depends on temperature exponentially. While Q’s dependence on T would be either to the power g, l, t………..Therefore the variat ion in KP would still be greater QP and the reaction moves forward again. Therefore, to see it decreases, reaction moves backward and if it remains fixed, then no change at all.

Therefore, two cases arises:

(1) ΔH is +ve (Endothermic Reactions)

(2) ΔH is -ve (Exothermic Reactions)


Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Endothermic Reaction:

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

As we increase temperature, it is clearly understood by equation (1). That Keq also increase. Hence, with increase in temperature Keq increases in endothermic reactions.

Reactions will shift in forward direction.

Exothermic Reaction (ΔH = -ve)

As temperature is increased, the magnitude o f Keq decreases. Hence, increase in temperature leads to decrease in Keq. React ion will shift in backward direction.

4. Effect of addition of inert gases to a reaction at equilibrium

1. Addition at constant pressure

Let us take a general reaction

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

We know,  

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Where,

nC , nD , n A , n B denotes the no. of moles of respective components and PT is the total pressure and ∑n = total no. of moles of reactants and products.

Now, rearranging, Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Where Δn = (c + d) - (a + b)

Now, Δn can be = 0, < 0 or > 0

Let us take each case separately.

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

Addition of inert gas increases the Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry is decreased and so is Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

So products have to increase and reactants have to decrease to maintain constancy of KP. So the equilibrium moves forward.

Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry

In this case Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry decreases but Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry increases. So products have to decrease and reactants have to increase to maintain constancy of KP. So the equilibrium moves backward.

2. Addition at Constant Volume:

Since at constant volume, the pressure increases with addition of inert gas and at the same time ∑n also increases, they almost counter balance each other. So Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry can be safely approximated as constant. Thus addition of inert gas has no effect at constant volume.

The document Le-Chatelier’s Principle & Factors Affecting Equilibrium Constant (K) Notes | Study Physical Chemistry - Chemistry is a part of the Chemistry Course Physical Chemistry.
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