The familiar form for the Arrhenius equation for two different absolute temperat

Question

The familiar form for the Arrhenius equation for two different absolute temperatures T1 and T2 is:

ln k2?/?k1 = ?Ea?/?R (1?/?T2 ? 1?/?T1?)
Equations relating several parameters can usually be expressed in any of several algebraically equivalent expressions.
Which of the following is an algebraically equivalent expression of the Arrhenius equation?

A. ln k2?/?k1 = Ea?/?R (1?/?T1 ? 1?/?T2?)

B. ln k2?/?k1 = R?/?Ea (1?/?T1 ? 1?/?T2?)

C. ln k1?/?k2 = Ea?/?R (1?/?T1 ? 1?/?T2?)

D. ln k1?/?k2 = R?/?Ea (1?/?T1 ? 1?/?T2?)

Explanation / Answer

the given reaction is

ln(K2/K1) = (-Ea/R) ( 1/T2 - 1/T1)

this can be rearranged as

ln(K2/k1) = ( -Ea/R) [-(1/T1 -1/T2)]

as - x - becomes + , the equation now becomes

ln(k2/K1) =( Ea/R) ( 1/T1 -1/T2)

so

the algebrically equivalent expression of the arhenius equation is

ln k2 / k1 = Ea / R (1 / T1 ? 1 / T2 )

so

the answer is option A) ln k2 / k1 = Ea / R (1 / T1 ? 1 / T2 )

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