Difference between rate law expression and law of mass action

Law is the instruction on how things should work. Hey! but here we are not talking about governmental law in science we deal with something bigger than that "Law of nature", sounds exciting ?

Well, control your excitement because it's not as interesting as it seems at the start and can be a bit confusing. So in this article, I am here to deal with one of the confusion you may have regarding different laws of nature.

Difference between rate law and the law of mass action
You see, in chemical kinetics which is a study on measurement of how fast a chemical reaction occurs you will deal with two such laws, rate law expression and the law of mass action. 

If you are just starting out with chemical kinetics then you may get confused between both of them because they look almost similar but in reality, they are not. 

Rate law expression and law of mass action are different from each other and one of the main differences is that in the rate law expression the concentration of the reactant is raised to some power which may or may not be equal to stoichiometric coefficient of reactant but in case of law of mass action, concentration of reactant is raised to the power which is equal to the stoichiometric coefficient of reactants. 

I know, both these laws can confuse you a bit because they both seem similar. Don't worry I got your back and will clear the concept of both and how they both differ with each other. 

Refer to this table for a brief difference between rate law expression and law of mass action: 

Difference between rate law expression and the law of mass action
S.no On the basis of Rate law expression Law of mass action
1 Definition It expresses the rate of chemical reaction Equation which represents the ratio between the mass of products and reactant raised to the power of the stoichiometric coefficient.
2 Equation components The rate law is composed of rate constant and concentration of the reactants with the order of overall reaction The law of mass action equation consists of a concentration of reactants and products raised to the power of the stoichiometric coefficient.
3 Product The product is not included in the rate law The product of the reaction is included in the equation of the law of mass action.
4 Proportionality constant Rate law has proportionality constant 'K' The law of mass action does not have a proportionality constant.
5 Stoichiometric coefficient Concentrations of reactants are raised to some power which may or may not be equal to the stoichiometric coefficient of the reaction. Concentrations of reactants and products are raised to the power of their stoichiometric coefficient.

This was a brief difference between rate law and law of mass action but still, if it's not clear to you that how they both are different when both of the laws conclude the same thing and I understand it can be a bit confusing.

So to clear your doubt completely, let's see the meaning of both the laws and what they both state.

Before going straight into the topic of rate law or law of mass action, we need to learn some basics.

So in any chemical reaction, the rate of a chemical reaction depends on the concentration of reactants or in simpler terms, "amount of reactant in a chemical equation decides the rate of reaction."

Both the rate law and law of mass action convey the same meaning in some way or the other but with a slight difference and therefore people get confused between the two.

So first we will look at what is rate law and law of mass action and then will differentiate between both of them on various factors such as product, equation, proportionality constant just how we did it in the table above but in more depth.

What is rate law ?  

So as I mentioned earlier, both the laws signify that the rate of reaction depends on the concentration of reactant but in different ways.

Rate law or rate equations is a mathematical expression that describes the relationship between the rate law and concentration of reactants in the equation.

So, here is the equation of rate law:



Here [A] is the concentration of reactant A, [B] is the concentration of reactant B and [C] is the concentration of reactant C with raise to the power of 'm', 'n' and 'p' which may or may not be equal to the stoichiometric coefficient of reactant respectively and this goes on depending upon the number of reactant in a chemical equation.

Well, I know you may be wondering that what does stoichiometric coefficient mean, so let me tell you for a general chemical equation: "aA+bB → cC+dD"

In the above equation, the stoichiometric coefficient of reactant 'A' and 'B' will be 'a' and 'b' respectively.

What is the law of mass action ?

Somewhat similar to the rate law, the law of mass action also conveys the same thing but as I mentioned earlier with a slight difference. 

The law of mass action states that the rate of chemical equation is directly proportional to the product of the active mass of the reactants, with each active mass term raised to the power equal to its respective stoichiometric coefficient in a balanced equation with a constant temperature. 
As I told you earlier, they both look the same but, the main difference is in the rate law expression, the concentration of reactants are raised to the power of something which may or may not be equal to the stoichiometric coefficient

But in the case of the law of mass action, the concentration of reactant will be raised to the power of the stoichiometric coefficient of a chemical reaction. 

Why in rate law expression the concentration of reactant, power is not always the stoichiometric coefficient ?

You may wonder, that both the law conveys the same thing still one says the concentration will be raised to the power of the stoichiometric coefficient but the other one does, why this way ? 

The reason for this is, rate law doesn't say that concentration cannot be raised with the power of the stoichiometric coefficient, in fact, you will find that in many examples of your book, the power raised with the concentration of reaction is same as the stoichiometric coefficient of reactant. 

But the only reason here is that the rate of chemical reaction not only depends on the concentration of reactant but instead, it depends on a variety of other factors as well. Such as temperature, pressure, etc. 

So, therefore, it will not be appropriate to calculate the rate of an equation only on the concentration of reactant but we need to consider other factors as well which will affect the value and the power of concentration of reactant will raised to. 

Conclusion:

So I hope, now that the difference between both the rate law expression and the law of mass action is clear to you, as now you know both the laws convey the same message that the rate of chemical reactions depends on the concentration of reactants. 

But law of mass action only considers the concentration of reactant as the factor for the rate of reaction but in reality rate of a chemical reaction depends on many other factors as well and the reason why rate law and law of mass action are almost the same has a slight difference.

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