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The plots of k versus 1 T for two different reactions are straight lines that intersect exactly at the y-axis. The slope of the line for the first reaction is -4600 K and that for the second reaction is -3100 K . If k₁ and k₂ are the rate constants of the first and second reactions respectively at 300 K , then the value of ( k₂ k₁ ) is _____.

Correct answer

5

Step-by-step solution

The Arrhenius equation is given by k = A e^ -E_a/RT . Taking the natural logarithm on both sides, we get: k = A - E_a R ( 1 T ) This is the equation of a straight line ( y = mx + c ) where: y-intercept ( c ) = A Slope ( m ) = - E_a R Since the plots for the two reactions intersect exactly at the y-axis, their y-intercepts are equal: A₁ = A₂ A₁ = A₂ = A For the first reaction: k₁ = A - E_ a1 RT Given slope = -4600 K - E_ a1 R = -4600 K So, k₁ = A - 4600 T For the second reaction: k₂ = A - E_ a2 RT Given slope = -310

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