Question

The activation energy of one of the reactions in a biochemical process is 532611 J mol^–1. When the temperature falls from 310 K to 300 K, the change in rate constant observed is k₃₀₀ = x × 10^–3 k₃₁₀. The value of x is ______.

[Given: ln 10 = 2.3, R = 8.3 J K^–1 mol^–1]

Options

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Answer 1

The activation energy of one of the reactions in a biochemical process is 532611 J mol^–1. When the temperature falls from 310 K to 300 K, the change in rate constant observed is k₃₀₀ = x × 10^–3 k₃₁₀. The value of x is 1.

Explanation:

`ln  "k"_2/"k"_1 = "E"_"a"/"R" [1/"T"_1 - 1/"T"_2]`

`ln  310/300 = 532611/8.3 [1/300 - 1/310]`

`ln  "k"_310/"k"_300 = 532611/8.3 (10/93000)`

`ln  "k"_310/"k"_300` = 6.9

`ln  "k"_310/"k"_300` = 3 × ln 10

`"k"_310/"k"_300` = 10³

k₃₀₀ = k₃₁₀ × 1 × 10⁻³

i.e., k₃₀₀ = 1 × 10⁻³ k₃₁₀ 

So, x = 1