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Question

A substance, 'A' decomposes by a first order reaction. Starting initially with [A] = 2.00 M, after 200 min, [A] =0.250 M. The t1/2 and rate constant for the reaction, are respectively:

A
66.63 s and 0.0104 s1
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B
66.63 min and 0.0104 min1
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C
99.93 min and 0.0347 min1
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D
None of these
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Solution

The correct option is B 66.63 min and 0.0104 min1
For a first order reaction, rate law equation is as follows:
k=2.303tlog10aax
Here, if t=200 min,(ax)=0.250 M,a= initial concentration =2.0 M
So, k=2.303200log102.000.25
=2.303200log108
=0.0104 min1
For first order reaction, half life,
t1/2=0.693k=0.6930.0104
=66.63 min
Hence, (b) is the correct option.

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