Chemical equilibrium refers to the final mixture of a chemical reaction, where the reactants and products are done changing. In a chemical reaction, reactants are converted into products. A general belief is that all chemical reactions proceed to completion (where all reactants are converted into product). But this is not true in all cases. A lot of chemical reactions proceed only to a certain extent, i.e. the reactants are not fully converted into products and the resulting mixture contains both reactants and products. After sometime, the concentration of reactants or products becomes constant and we get a state of equilibrium for the system.
For example, in Haber's process for ammonia () manufacture, ammonia is only 15% of the equilibrium mixture, even at optimized temperature and pressure condition:
A chemical reaction which proceeds only in forward direction so that the reactants are converted into products and products do not react with each other to reform reactants is called an irreversible reaction.
Neutralization reaction like is an example of an irreversible reaction.
A chemical reaction in which reactants react together to form products and products formed react with each other directly to reform the original reactant back is known as a reversible reaction.
Reaction of hydrogen with iodine is an example of a reversible reaction.
Consider an elementary reversible reaction taking place in a closed container:
Where A and B react to produce C and D, while the products C and D can also react to produce A and B back.
Initially only the reactants A and B are present, and thus their concentration is maximum. As the reaction proceeds forward, C and D are produced. Thus in the beginning, the rate of forward reaction is very high. But as the reaction progresses, concentration of A and B decreases and on the other hand concentration of C and D increases. Hence the rate of forward reaction slows down and the rate of backward reaction goes on increasing.
Ultimately a state is reached when the rate of forward reaction becomes equal to the rate of backward reaction and the system attains equilibrium. After that, there will be no change in concentration of any of the species.
These are some of the characteristics of chemical equilibrium.
- The chemical reaction should be reversible.
- The equilibrium can be attained only if the system is closed, i.e. the reaction should be carried out in a closed vessel.
- The opposing processes (i.e. forward and backward reactions) occur at the same rate and there is a dynamic but stable condition.
- The observable properties of the system such as concentration, pressure, color, etc. becomes constant at equilibrium and remains unchanged thereafter.
- By bringing a change in conditions such as temperature, pressure or concentration, the equilibrium point can be shifted to the right or left hand side as required. Thus the reaction can be controlled to get more yield of products.
- The equilibrium can be approached from either direction.
- A catalyst does not alter the equilibrium point. It only increases the rate of reaction. The equilibrium is attained however.
Statement: For a homogeneous system at a constant temperature, the rate at which a substance reacts is proportional to its active mass and the rate of a chemical reaction is proportional to the product of active masses of the reacting substances at that moment.
The term active mass means molar concentration per unit volume, i.e. .
The reaction quotient () measures the relative amounts of products and reactants. It is given by
The rate of forward reaction is and the rate of backward reaction is Equating the forward and backward rates at equilibrium, we obtain
The ratio is called equilibrium constant of reaction and is denoted by
Equilibrium constant is independent of initial concentrations and pressure and is a function of temperature alone. Higher values of or mean that more products are formed and equilibrium is tilted towards the right hand side. Lower values of or mean reaction does not proceed much from left to right (equilibrium is tilted towards the left hand side) even though equilibrium has been attained.
For a reaction involving gaseous reactants and products, a new equilibrium constant in terms of partial pressure can be expressed as
If all gases are assumed to be ideal, then
Since it follows that
This can be used for deriving the relationship between and as follows:
where denotes the difference between the number of moles of products and the number of moles of the reactants.
Temperature dependence of
Van't Hoff's equation relates equilibrium constant of reaction with temperature as follows:
where is the heat of reaction at temperature .
When in an equilibrium reaction, if all the reactants and products are present in the same phase (gaseous or liquid), then it is called homogeneous equilibrium.
Equilibrium constant expression:
Note: denotes concentration of .
If reactants and products are found in two or more phases, the equilibria describing them are called heterogeneous equilibrium.
Note: and do not include concentration of solids. The concentration of solid substances is taken as unity.
As we know
So higher values of equilibrium constant indicate that the equilibrium concentration of the product(s) is high and its lower values indicate that the equilibrium concentration of products is low.
Large values of or , larger than about , favour the products strongly.
For intermediate values of or , in range of to , concentration of reactions and products are comparable.
Small values of favour the reactants strongly.
Le Chatelier's principle tells us what will happen when equilibrium is disturbed qualitatively. This numerical problem is designed to explain the same principle quantitatively. This problem is large and its very purpose is to clear doubts regarding chemical equilibrium.
If this reaction would be irreversible, we would have of and of
Remember Van't Hoff equation! That will give equilibrium constant at a particular temperature. For this, we need to solve the following differential equation:
Separating variables, we have
We will use this relation to find at
This will give .
From equilibrium constant formula
We see that is increased when temperature is lowered.
Similarly, one can calculate at
We notice that is increased when temperature is lowered.
These results prove Le chatelier's principle: An exothermic reaction is favoured at low temperature as equilibrium concentration of increases from to when temperature is lowered from to
We know at If we can relate concentration of with time, the problem can be easily solved by finding for this . For this we proceed as follows:
Material balance for
Since reaction is taking place in closed vessel, both input=0 and output=0.
Putting these terms in matrial balance equation gives
Writing in terms of we have
Substituting in the values and gives
The above equation can be solved using the method of integration factor:
where is the constant of integration. Its value can be found out by the following initial condition:
which gives Therefore,
Now, we have the relation between and
To find time required for equilibrium, put then
This is not good. We did such a lengthy calculation and got infinity as a result. This may predict that equilibrium cannot be achieved in finite time. But if we find time required for to become 33.34, it will be only This strange behavior can be explained by the nature of the function which becomes asymptotic to the line . For practical purpose, time required for is enough.
We know a catalyst increases rate of reaction without itself actually getting consumed. But here the question is whether it will change the equilibrium concentrations of and The answer is simply no. It increases both rate constants to the same extent so that the ratio of rate constants that is is the same as in non-catalytic reaction. For a proof see How does catalyst work.
For finding time required for equilibrium, we proceed as follows:
We have increased rate constants for both forward and backward reactions in catalytic reaction as
Now writing the material balance for we have
Substituting in the values and gives
Try to solve this equation by integration factor method as we did above and get the final equation
Putting and solving for t, we will get same result as we did above in case of non-catalytic reaction. i.e. . This time we know how to avoid this problem. We proceed to find time for and get
We see that time required for concentration to reach is half of what we get in case of non catalytic reaction.
For non catalytic equation, we had
In general, one can easily show that time required will be less in catalytic reaction than non-catalytic reaction for the same concentration.
Here is the graph of concentration of in two cases.
Since one mole of gives one mole of there is no increase or decrease of pressure during reaction.Hence changing pressure at equilibrium will not change the equilibrium concentration of and
At equilibrium, we have of and of Now we are adding another of How will this disturb the equilibrium? Adding this extra at previous equilibrium will result in same equilibrium as if it will be if we start with of Another way to think is that of will give and will remain unreacted. So in total we will have and Hence we will have more at equilibrium.
You can point out that percentage of in equilibrium mixture is the same in both cases (%). But this is not the case in general.
You can look into some related topics. Though these are related to physics, you can understand the meaning of equilibrium in different branches of science.