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Question

Select the equation for [B] at any time t in the following reaction. Let the initial concentration of A be [A0] and B and C be 0.


A
[B]=[B]0(k1[A]k1+k2)(1e(k1+k2)t)
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B
[B]=k1[A]k1+k2(1e(k1+k2)t)
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C
[B]=k1[A]0k1+k2(1e(k1+k2)t)
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D
[B]=k1[A]0k1+k2(1e(k1+k2)t)
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Solution

The correct option is C [B]=k1[A]0k1+k2(1e(k1+k2)t)
The overall net rate of consumption of A or net rate reaction

=d[A]dt=(d[A]dt)1+(d[A]dt)2d[A]dt=k1[A]+k2[A]d[A]dt=[k1+k2][A]d[A]dt=koverall[A]Where=koverall = k1+k2

Integrating Eq. (i), we get

[A]=[A]0e(k1+k2)t

Also, from the rate equation:

d[B]dt=k1[A] and d[C]dt=k2[A]


Substituting the value of [A] (t) in the differential equation for [B] and [C] and integrating, we get

[B]=[B]0+t0k1[A]0e(k1+k2)t)dt

[B]=k1[A](k1+k2)(1e(k1+k2)t), since[B]0=0

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