Respuesta :
Answer : The rate law for the following mechanism is [tex]Rate=k'[A]^2[B][/tex]
Explanation :
Rate law : It is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.
As we are given the mechanism for the reaction :
Step 1 : [tex]A+B\rightleftharpoons C[/tex] (fast)
Step 2 : [tex]C+A\rightarrow D[/tex] (slow)
Overall reaction : [tex]2A+B\rightarrow D[/tex]
The rate law expression for overall reaction should be in terms of A and B.
As we know that the slow step is the rate determining step. So,
The slow step reaction is,
[tex]C+A\rightarrow D[/tex]
The expression of rate law for this reaction will be,
[tex]Rate=k[C][A][/tex] ............(1)
Now applying steady state approximation for [tex]C[/tex], we get:
[tex]K=\frac{[C]}{[A][B]}[/tex]
[tex][C]=K\times [A][B][/tex] ...........(2)
Now substituting equation 2 in 1, we get:
[tex]Rate=k[A]\times K\times [A][B][/tex]
[tex]Rate=K\times k[A]^2[B][/tex]
[tex]Rate=k'[A]^2[B][/tex]
Hence, the rate law for the following mechanism is [tex]Rate=k'[A]^2[B][/tex]
The reaction is processed in two steps. The rate law for the reaction is, [tex]\rm Rate=\textit k^" [A]^2\;[B][/tex].
Which step in reaction determines rate law?
The rate law is determined by the product of the reactant concentration in the reaction that formulates the rate of reaction with the rate constant.
The rate law is followed by the slow step in the reaction. The slow step in the reaction is, [tex]\rm C+A\rightarrow D[/tex]
Thus, the rate law for the reaction is,
[tex]\rm Rate= \textit k \;[C]\;[A][/tex]
The rate constant for the reaction is given in terms of A and B, as the overall reaction is, [tex]\rm 2A+B\rightarrow D[/tex].
The rate constant for the slow reaction is given as:
[tex]K=\rm \dfrac{[C]}{[A]\;[B]} \\\\C = K\;[A]\;[B][/tex]
Substituting the value of [C] in the rate law of the reaction:
[tex]\rm Rate=\textit K\;[A][B]\;\times\;k[A]\\Rate=k^" [A]^2[B][/tex]
The overall rate for the reaction is, [tex]\rm Rate=\textit k^" [A]^2\;[B][/tex].
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