The rate constant k₁ and k₂ for two different reactions are 10¹⁶. e^-2000/T and 10¹⁵.e^-1000/T respectively. The temperature at which k₁ = k₂

1000 K

2000/2.303 K

2000 K

1000/2.303 K

Solution

1000/2.303 K

The Arrhenius equation is represented as;
k = Ae^-Ea/RT
In the given equations first, take log and then compare them.

k₁ = 10¹⁶ e^-2000/T
k₂ = 10¹⁵ e^-1000/T
On taking log, we get

log space straight k subscript 1 space equals space space log space space 10 to the power of 16 space minus fraction numerator 2000 over denominator 2.303 space end fraction straight T space... space left parenthesis straight i right parenthesis log space straight k subscript 2 equals space log space 10 to the power of 15 space minus fraction numerator 1000 over denominator 2.303 end fraction space straight T......... space left parenthesis ii right parenthesis thin space straight k subscript 1 space equals space straight k subscript 2 Hence comma space from space eqs space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space straight T space equals fraction numerator space 1000 over denominator 2.303 end fraction straight K space

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