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Question: The reaction \[2NO+{{O}_{2}}\to 2N{{O}_{2}}\], follows the rate law=\[k{{[NO]}^{2}}[{{O}_{2}}]\]. Wh...

The reaction 2NO+O2→2NO22NO+{{O}_{2}}\to 2N{{O}_{2}}, follows the rate law=k[NO]2[O2]k{{[NO]}^{2}}[{{O}_{2}}]. What is the order of the reaction? If k=2.0×10−6mol−2L2s−1k=2.0\times {{10}^{-6}}mo{{l}^{-2}}{{L}^{2}}{{s}^{-1}}, what is the rate of the reaction when [NO]=0.04mol/L and O2=0.2mol/L{{O}_{2}}=0.2mol/L?

Explanation

Solution

Hint: The sum of the powers of the concentration of the reactants in the rate equation of that particular chemical reaction is called the order of the reaction. If rate of a reaction is given as k=[A]a[B]bk={{[A]}^{a}}{{[B]}^{b}} , where [A]a{{[A]}^{a}} is the concentration of the reactant A which is raised to the exponent a and [B]b{{[B]}^{b}} is the concentration of [B] which is raised to the exponent b, then the order of reaction =a+b. It is based on rate law or rate equation.
Complete step by step solution:
Order of a rate law is basically the sum of the exponents of its concentration terms. Rate law can be used to understand the composition of the reaction mixture. The order of the reaction is the exponent to which the concentration of that species is raised, and it indicates up to what extent the concentration of that species affects the rate of the reaction and also which species has the greatest effect. Consider the reaction
A+3B+2C→productsA+3B+2C\to products
The rate of the reaction will be
rate=k[A][B]2rate=k[A]{{[B]}^{2}}
The order of the reaction is = 1+2=3. The reaction is third order.
In the given reaction
2NO+O2→2NO22NO+{{O}_{2}}\to2N{{O}_{2}}
When we apply rate law we get
Rate=k[NO]2[O2]k{{[NO]}^{2}}[{{O}_{2}}], [NO] is the concentration of NO and [O2][{{O}_{2}}] is the concentration of oxygen.
Therefore, the order of the reaction is = 2+1= 3.
From the given values we can calculate the rate of the reaction
Rate=k[NO]2[O2]k{{[NO]}^{2}}[{{O}_{2}}]
From the question we know that [NO]= 0.04mol/L and [O2]=0.2mol/L[{{O}_{2}}]=0.2mol/L
So substituting these values, we get
Rate= 2.0×10−6×(0.04)2×0.2=0.00064×10−6L2mol−2s−12.0\times {{10}^{-6}}\times {{(0.04)}^{2}}\times 0.2=0.00064\times {{10}^{-6}}{{L}^{2}}mo{{l}^{-2}}{{s}^{-1}}

Thus, the rate of the reaction is 0.00064×10−6L2s−10.00064\times{{10}^{-6}}{{L}^{2}}{{s}^{-1}}.

Additional information:
-The reaction order is not always an integer.
-Zero-order means that the concentration of the species does not affect the rate of the reaction.
-Negative integer shows that the concentration of that species inversely affects the rate.
-Positive integer indicates that the concentration of the species directly affects the rate.

Note: Order of the reaction is often confused with the sum of coefficients of the reactant in a reaction. But this is not the case. It is the sum of the exponent of concentration of the reactant to which it is raised.