Question

what is the activation energy(Ea) of a first order reaction is the reaction rate constant(k) increases from 0.0300 min to 0.500 min as the temperature increases from 20.0 C to 45.0 C?

Answer #1

The temperature dependency of rate constant is given by Arrhenius equation.

According to Arrhenius equation,

k = k_{0}e^{-Ea/RT} Where Ea is the activation
energy and k0 is the frequency factor. Applying logarithm both
sides and applying for two different states, we get the relation
independant of frequency factor.

ln(k1/k2) = - Ea/R * [(1/T1)-(1/T2)]

Substituting the values at two different states,

We get

ln(0.3/0.5) = -Ea/8.314 [ 1/293 - 1/318]

Ea comes out to be = 15.828 kJ/mol

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There are several factors that affect the rate of a reaction.
These factors include temperature, activation energy, steric
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rate can be summarized in an equation called the Arrhenius
equation:
k=Ae−Ea/RT
where k is the rate constant, A is the
frequency factor, Ea is the activation energy,
R=8.314 J/(mol⋅K) is the universal gas constant, and
T is the absolute temperature.
__________________________________________________
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