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Question

Under the same reaction condition, initial concentration of 1.386 mol dm−3 of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics respectively. Ratio (k1/ko) of the rate constant for first order (k1) and zero order (k0) of the reaction is:

A
0.5 mol1 dm3
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B
1.0 mol dm3
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C
1.5 mol dm3
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D
2.0 mol1 dm3
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Solution

The correct option is A 0.5 mol−1 dm3The values of rate constants ko,k1 for zero order and first order reaction, respectively, are given by the following equation: ko=Ao2×t1/2k1=0.693t1/2 Substituting the various values we get, ko=1.386 mol litre−12×20 s ..(i)k1=0.69340 s ...(ii) Dividing (ii) by (i), we get k1ko=0.69340×2×201.386 mol−1 litre =0.6931.386 mol−1 litre =0.5 mol−1 dm3

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