# Need help finding magnitude of K.?

A particular first-order reaction has a rate constant of 1.35x10^2s−1 at 25.0∘C . What is the magnitude of k at 41.0∘ C if Ea = 55.5 kJ/mol .

Options:

1.23×10^4

1.35×10^2

154

2.60×10^47

4.23×10^2

Thanks in advance!

### 1 Answer

Relevance

- Dr WLv 72 months ago
from the arrhenius equation

.. k = Ao exp(-Ea / RT)

for 2 conditions of different T with Ea held constant

.. k1 = Ao exp(-Ea / RT1)

.. k2 = Ao exp(-Ea / RT2)

dividing the 2nd by the first

.. k2 / k1 = (Ao / Ao) * exp(-Ea / RT2) / exp(-Ea / RT1)

rearranging

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

where

.. k1 = 1.35x10^2 / sec

.. Ea = 55500 J/mol

.. R = 8.314 J/molK

.. T1 = 298.15K

.. T2 = 314.15K

you get to finish

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Thank you! Was confused with the exp in the equation but figured it was e^ and got the right answer, thanks!