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Question: A hypothetical reaction \(\mathop A\nolimits_2 + \mathop B\nolimits_2 \to 2AB\)follows the mechanism...

A hypothetical reaction A2+B2→2AB\mathop A\nolimits_2 + \mathop B\nolimits_2 \to 2ABfollows the mechanism as given below:
A2⟷A+A\mathop A\nolimits_2 \underset{{}}{\overset{{}}{\longleftrightarrow}}A + A
A+B2→AB+BA + \mathop B\nolimits_2 \to AB + B
A+B→AB+BA + B \to AB + B(slow)
A+B→ABA + B \to AB(fast)
The order of the overall reaction is:
A. 2
B. 1
C. 1.5
D. 0

Explanation

Solution

Order of reaction is defined as the number which relates rate of chemical reaction by determining the concentration of reactants. Order and molecularity of reactions are not the same term. Molecularity of reaction cannot be determined experimentally for a complex reaction. Molecularity of a reaction cannot be more than three for an elementary reaction.

Complete step by step answer: The order of reaction is determined by the slow steps in the reaction.
Now first we will take the slow step of the reaction
A+B2→AB+BA + \mathop B\nolimits_2 \to AB + B
The reaction rate will be r=k[A][B2]r = k[A] [B_2] ____________ equation 1
Now the A is an intermediate substance so its concentration will be determined from the equilibrium step.
A2⟷A+A\mathop A\nolimits_2 \underset{{}}{\overset{{}}{\longleftrightarrow}}A + A [𝐴]2
Now the equilibrium constant Keq will be [A]2[A2]\dfrac{{\mathop {[A]}\nolimits^2 }}{{\left[ {\mathop A\nolimits_2 } \right]}}

Now A will become = Keq[A2]12\mathop K\nolimits_{eq} \mathop {[\mathop A\nolimits_2 ]}\nolimits^{\dfrac{1}{2}}
Now put this value of A in equation 1
r=K[A][B2]r=kKeqr = K[A][\mathop B\nolimits_2 ]r = k\mathop K\nolimits_{eq}
[A2]12[B2]\mathop {[\mathop A\nolimits_2 ]}\nolimits^{\dfrac{1}{2}} [\mathop B\nolimits_2 ]
Now order of reaction will be sum of both the powers
12+1=32=1.5\dfrac{1}{2} + 1 = \dfrac{3}{2} = 1.5
So, the correct answer is “Option C”.

Note: Order of reaction is defined as the number which relates rate of chemical reaction by determining the concentration of reactants. There are zero order reactions , first order reactions etc. The first order reaction is the reaction that occurs in the linear relation with concentration of reactants. The reaction that does not depend on the concentration of reactants is known as zero order reaction.