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The rate of a reaction increases with an increase in the concentration of the reactants. But sometimes, the reaction rate would not be doubled even though the concentration is doubled. Sometimes, the reaction rate increases significantly when the concentration of the reactants increases in small amounts.
Also, the concentration of some reactants in a chemical reaction does not affect the reaction rate at all. This explains that the concentration of each reactant is not directly proportional to the reaction rate. The reaction rate is always proportional to some power of the concentration of a reactant. This power is known as the order of the reaction with respect to that reactant.
Let’s consider the following hypothetical reaction where reactants A and B react to form the product C. The rate of the reaction is directly proportional to some power of the concentration of A and B.
Where x and y are the order of the reaction with respect to the reactants A and B, respectively. The value of x and y can be 0, 1, 2, … The overall order of the reaction is given by x + y. The above expression can be written as follows using a proportional constant. This constant is known as the reaction constant. And this expression is known as the “Rate law expression”
Where,
If the order is zero with respect to a reactant, it is called a zeroth-order reaction with respect to that reactant. As the zeroth order of any number is 1, the rate is equal to the rate constant. That means the change in concentration of that reactant does not affect the rate of the reaction.
If the order is 1 with respect to a reactant, the reaction is called a first-order reaction with respect to that reactant. As the first order of any number is the same number, the rate is equal to the product of the rate constant and the concentration. That means when the concentration is doubled, the reaction rate would also be doubled.
If the order is 2 with respect to a reactant, the reaction is called a second-order reaction with respect to that reactant. In the third-order reactions, the rate shows a significant change when the concentration is changed by a small amount.
Consider the following reaction,
The initial rates have been measured by changing the concentrations of NO and H2. The obtained results are shown in the table below.
| Experiment number | [NO] (mol dm-3) | [H2] (mol dm-3) | Initial rate (mol dm-3 s-1) |
| 1 | 0.005 | 0.002 | 1.3 × 10-5 |
| 2 | 0.010 | 0.002 | 5 × 10-5 |
| 3 | 0.010 | 0.004 | 10 × 10-5 |
Solutions
Let’s assume that the order with respect to NO is “x” and the order with respect to H2 is “y”. If the rate constant is “k”, the rate law for the above reaction can be written as follows.
By substituting the experimental data into the above equation, we can obtain three simultaneous equations. The order of the reaction (x and y) can be found by solving them.
The reaction order with respect to NO(g) is 2.
The order of the reaction with respect to H2(g) is 1. Using the values obtained for the x and y, the rate law can be written as follows.
The value of the rate constant can be found by substituting x and y values for either of the reactions.
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