Question

The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy

=Ea80.0/kJmol

. If the rate constant of this reaction is

×4.510−6·M−1s−1

at

40.0°C

, what will the rate constant be at

65.0°C

?

Round your answer to

2

significant digits.

Answer 1

According to Arrhenius equation,

$k=Ae^{-E_a/RT}$

k - the rate constant for a given reaction
A- the pre-exponential factor, specific to a given reaction
Ea - the activation energy of the reaction
R - the universal gas constant, useful here as 8.314J mol−1K−18.314J mol-1K-1
T - the absolute temperature at which the reaction takes place

As you can see, the Arrhenius equation establishes a relationship between the rate constant and the absolute temperature at which the reaction takes place.

In other words, this equation allows you to determine how a change in temperature affects the rate of the reaction.

Let the rate constant for T1= 40oC be K1 and rate constant at T2=65oC be K2

So, you know that at T, the rate constant for your reaction takes the form C Em ki = A. expl CAPRT Likewise, at T2 the rate constant takes the form k2 = A. exp( - RET) Divide these two equations to get rid of the pre-exponential factor, A ki k A exp( - A exp( - ) )

Ea /RT₂ k eE/RT

After Putting the value,

(4.5E-6/k2)=(e28.468)/(e30.742)

k2=43.731 x 10-6 at 65oC