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Question

For the following sequential reaction:


Aλ1Bλ2C,

If the λ1=1.8×105s1 and λ2=1.1×102s1 and initial molar concentration of A is 1.8 M, the concentration of C at time t=1day is :

A
1.20M
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B
1.42M
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C
4.12M
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D
None of these
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Solution

The correct option is C 1.42M
We know, Aλ1Bλ2C

Given, [A]0=1.8M,λ1=1.8×105s1andλ2=1.1×102s1.

Since, λ1<<λ2, thus, B will be converted to C at higher rate than A is converted to B. Thus, sequential reaction may therefore, be written as:

Aλ1C

[A]0=[A]t+[C]t ... (i)

For 1st order reaction, rate expression in integrated form gives:
[A]t=[A]0eλ1t ... (ii)

Thus, by eqs. (i) and (ii),
[A]0=[A]0eλ1t+[C]t

or [C]t=[A]0[1eλ1t]

=1.8[1e1.8×105×24×3600]

[C]t=1.42M

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