Chemical Equilibrium at a Glance

Chemical Equilibrium at a Glance

Equilibrium Constant for a general reaction and its multiples

Le Chatelier’s principles

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Le Chatelier’s principle: Temperature change

In the last post we have seen how the system dealt with the concentration change and pressure change, today we will see what happens if we change the temperature or add some foreign substances like catalyst or noble gases to the system.

You know that equilibrium constant depends on temperature, if we change the temperature, system will no longer be in equilibrium. How can a system control its temperature itself? Energy is released when new bonds are formed and this provides heat to the system. And energy is needed when a bond is broken which is supplied by the system in the form of heat. Now you can guess how the system can deal with it.

When reactants combine to form products, some old bonds are broken and some new bonds are formed. And when we subtract the energies involved, we get to know how much energy is used or released in that particular reaction. If the energy of the reactants is more than that of the products, then energy will be released in the reaction, such reactions are called exothermic reactions. And its opposite is called endothermic reactions, here energy is required.

N_2(g) + 3H_2(g) ⇌ 2NH_3(g)  ......... ∆E = 92.38 kJ mol^-1

The above reaction is an example of exothermic reaction, which means some amount of energy is released. If we increase the temperature of the system, then the system will shift the reaction in backward direction so that it can consume some of the heat. And if we lower the temperature then system will make the forward reaction faster to produce more heat. That means if we want to produce more ammonia we have to keep the temperature low.  

Effect of Temperature change on Equilibrium

Effect of catalyst addition

Catalysts are those substances which speed up the reaction without being involved it in. Suppose you are participating in a race and suddenly you find that a furious dog is chasing you, then what will happen? Naturally you will run like hell. Here the dog is neither participating in the race nor is it involved the race, but its presence speeds up your running. So dog acts as a catalyst.

Catalysts can help a system to achieve equilibrium sooner but their presence don’t create any disturbance because they don’t participate in the reaction.

Similarly addition of noble gases don’t alter the equilibrium because they are noble in nature and do not participate in reaction.

So you have learnt how Le Chatelier’s principle help us to predict the direction of the reaction and help us to understand how a system deals with the changes. Now you will be able to understand what Le Chatelier’s principle states, it states that “a change in any of the factors that determine the equilibrium conditions of a system will cause the system to change in such a manner so as to reduce or to counteract the effect of the change”.

In the next post we will try to sum up all the findings of equilibrium.​

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What Is the Relation between Kc and Kp?

In the last post we learned about equilibrium constant Kc, for which we expressed concentration of reactants and products in terms of molarity (mols/L). If all species in a reaction mixture are gases, it becomes difficult to measure their concentration in molarity. For such a reaction mixture, it is convenient to measure concentration of their participants in terms of Partial Pressure.

You are quite familiar with the gases and you know how they exert pressure. If two or more types of gas molecules are present in a container, how will you decide which gas exerts maximum pressure? And how much pressure is exerted by each gas?

Let's try a different example, imagine that 4 members of yellow team, 6 members of green team and 10 members of orange team are jumping on the stage. Their combined efforts exert pressure on the floor of the stage. So what do you think which team contributes more? Obviously orange team contributes more because 10 out of 20 members are from Orange team. It means the team with larger fraction (team members/ total members) contributes more. Or, we can say that fraction of team members is proportional to the pressure exerted by team. Pressure exerted by an individual team is called the partial pressure of that particular team. Total pressure exerted on the stage is the sum of partial pressure of all teams.

P_total = P₁+ P₂+ P_3........

Similarly, when all participants in a reaction vessel are in gaseous state, their concentration is determined by their partial pressure. Let’s find out how we can relate partial pressure to the concentration.

From Ideal gas equation we know that:

PV= nRT

P= nRT/V

n/V is concentration in moles per litre, so

P= cRT

So we can say that:

P = [concentration of gas] RT

At constant temperature we can say that pressure of gas is proportional to its concentration:

P is proportional to c

Let’s take a reaction as example:

H_2(g) + I_2(g) ↔ 2HI_(g)           ....................(1)

For this reaction equilibrium constant will be:

K_c= [HI]² / [H] [I]

Or, if we write in terms of partial pressure, then K_c will become K_p

K_p= (P_HI)² / (P_H) (P_I)

Since P = cRT we can write:

K_p= (P_HI)² / (P_H) (P_I) = [HI]² (RT)²/ [H]RT [I]RT

K_p= K_c

Here you have seen that K_p = K_c but, it doesn't happen always. If it is not true then what is the relation between them. Let’s try to find out their relation:

a A + b B ↔ c C + d D

K_c  = [C]^c [D]^d / [A]^a [B]^b

K_p= (P_C) (P_D) / (P_A) (P_B)

K_p= (P_C) (P_D) / (P_A) (P_B) = [C]^c(RT)^c [D]^d(RT)^d / [A]^a (RT)^a[B]^b (RT)^b

K_p= K_c (RT)^(c+d)-(a+b)

K_p= K_c (RT)^Δn

Relation between Kp and Kc

Where Δn = (number of moles of gaseous products - number of moles of gaseous reactants) in a balanced chemical equation.

In equation (1) number of moles of reactants 2 and number of moles of gaseous product is 2, that’s why for this reaction K_p= K_c.

Let’s check this relation for another reaction:

N_2(g) + H_2(g) ↔ 2NH_3(g)

It is not a balanced equation since number of H isn’t equal on both sides of arrow. First we write the balanced equation:

N_2(g) + 3H_2(g) ↔ 2NH_3(g)             .................(2)

This reaction has total 4 moles of reactants and 2 moles of product, thus we get

Δn = 2-4 = -2

If the above relation is correct, we would get:

K_p = K_c(RT)^-2

Let’s try to find out:

K_c= [NH₃]² / [N] [H]³

And

K_p= (P_NH3)² / (P_N) (P_H)³

K_p= (P_NH3)² / (P_N) (P_H)³ = [NH₃]² (RT)² / [N]RT [H]³ (RT)³

K_p = K_c(RT)^-2

Yes, we have successfully proved it.

Like K_c, K_p is also a unit-less constant and since it is the ratio of pressures, its unit depends on it. For equation 1, it is unit-less quantity but for equation 2 its unit is bar^-2.

I hope you have understand the concept of K_p and its relation with K_c. Let’s try to solve a problem:

For reaction 2NOCl_(g) ↔ 2NO_(g) + Cl_2(g) value of K_c is 3.75×10^-6 at 1069K. Calculate the K_p for the reaction at the same temperature.

You know that:  K_p = K_c (RT)^Δn 

This reaction has 2 moles of reactants and total 3 moles of product, thus we get

Δn = 3-2 = 1

So,

K_p= K_c (RT)

K_p= 3.75×10^-6 (0.0831)(1069)

K_p= 0.033

Now we have learnt how to calculate equilibrium constants, but we don't know its significance. What information can we draw from it? In the next post we will explore its significance.

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Le Chatelier’s Principle: Concentration and Pressure Change

Now you are familiar with the term ‘equilibrium’. In this post we will try to understand its nature. You know that equilibrium is established under particular conditions of temperature, pressure and concentration. If you change any of these conditions it gets disturbed. But it has a peculiar quality that when anything disturbs it, it tries to overcome that disturbance and regain its peace. How does it overcome disturbances? Let’s try to learn it.

Equilibrium happens in reversible reactions or systems. When equilibrium gets disturbed due to any change, the system works to nullify those changes and regain its equilibrium. It is known as Le Chatelier’s principle (I am not giving its proper definition). In this post we will see how a system deals with the change in concentration and pressure?

Effect of Concentration Change

H_2(g) + I_2(g) ⇌ 2HI_(g)

If we add some H₂ or I₂ in above reaction mixture, system will no longer be in equilibrium. To regain its equilibrium, the system will work to reduce the concentration of H₂ or I₂. So it works in forward direction to consume excess H₂ or I₂and regain its equilibrium.

If we add some HI, then the system will start working in backward direction and regain its equilibrium. If we remove some HI then what will it do? It will work in forward direction and produce more HI to cancel out the changes. And if we frequently remove some HI from the system it will continually produce HI.

Effect of concentration change on equilibrium

Effect of Pressure Change

In previous post (Ideal Gas Equation) we have seen that pressure is inversely proportional to the volume and directly proportional to the number of moles. Pressure change affects only those systems or reactions which involve gaseous reactants and products but has no effect on solid and liquid reactants or products because pressure change does not cause much effect on them.

Pressure change affects those reactions in which total number of moles of reactants and total number of moles of product are different. Let’s take an example:

CO_(g) + 3H_2(g) ⇌ CH_4(g) + H₂O_(g)

As you can see, in this reaction 4 moles of reactants are being converted into 2 moles of products.
If we reduce the volume of the reaction vessel by half then pressure of the system will be doubled (P∝V^-1). By doing this, we have disturbed the equilibrium of the system. So it shifts the reaction in forward direction (pressure ∝ number of moles), thus it can reduce the number of moles and the pressure of the system.

Le Chatelier’s Principle: effect of pressure change

Similarly if we reduce the pressure of the system, it will shift the reaction in backward direction and by increasing the number of moles the system will cancel the effect of pressure and resume its equilibrium.  

Now you have seen how smartly a system reacts and regains its equilibrium. In the next post we will see how it deals with the other changes.

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What is The Difference Between Reaction Quotient and Equilibrium Constant?

In the previous post we have learnt about equilibrium constant. Let’s revise it quickly.

• Equilibrium constant is a ratio of product and reactant’s molar concentration at equilibrium.
• It is independent of initial concentration of reactants.
• It is specific for a particular reaction.
• It is a temperature dependent constant.
• It is unit less constant because it is the ratio of concentrations.

Equilibrium is a state when reaction seems to be seized because both forward and backward reactions go on at the same rate and no change in the concentration of reactant and product is seen . So what information can we draw by equilibrium constant?

Equilibrium constant is the ratio of molar concentration of product to the molar concentration of reactant and its value gives general information about the extent of reaction. Larger value of equilibrium constant shows that reaction is nearer to the completion when equilibrium is established, as it means product concentration is larger than reactant. Similarly smaller value shows that equilibrium is established at the beginning of the reaction, because reactant concentration is much larger than product concentration. And if its value is equal to 1, it means reaction has finished half way through because product and reactant concentrations are equal at this point.

From above discussion one more concept about equilibrium has been clarified that equilibrium can be established at any point of reaction. It is the situation when rate of forward and backward reaction becomes equal. These are the general applications of equilibrium constant but how do we get information about a particular reaction? For this we need another parameter known as “Reaction Quotient” (Q_c). We can predict the direction of the particular reaction by comparing it with the equilibrium constant.

Reaction Quotient is similar to the equilibrium constant, the only difference is that in reaction quotient, concentrations of product and reactants are at a given time not necessarily at the time of equilibrium. Let’s take an example:

a A + b B ↔ c C + d D
Q_c  = [C]^c [D]^d / [A]^a[B]^b

Here concentration of products and reactants are taken in mole/L at the time t. At the time of equilibrium Q_c becomes equal to the K_c. Let’s see how Qc and Kc help us to predict the direction of the reaction. We will take an example to explain it:

H_2(g) + I_2(g) ↔ 2HI_(g)
K_c = 57.0 at 700K.

At time t molar concentration of H₂ = 0.10M, I₂ = 0.20M and HI = 0.40M so reaction quotient will be:

Q_c = (0.40)2 / (0.10) (0.20)
Q_c = 8.0

At the time t, Q_c is less than K_c and Q_c has to upgrade itself to reach to  K_c. In order to increase the value of Q_c reaction has to produce more product which means reaction will be shifted in forward direction.

If at a certain time t₂ you find Q_cis greater than K_c, then Q_c has to downgrade itself by increasing the concentration of reactants, that means reaction will be shifted in backward direction.

In the above discussion, we have seen that reversible reactions have a tendency to achieve equilibrium state, they adjust themselves either in backward or forward direction to do so. If we want to produce more HI in the above reaction, how can we take advantage of equilibrium. Can we fool it and get more HI? In the next post we will learn it.

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