If you were only given this info, could you calculate the Activation energy?

Question

Problem: A simple rule states that the reaction rate changes by a factor of 2 or 3 due to a temperature increase of10K. Calculate EA using this rule.
Thats all it says... is this a typo in my script or is my professor really just whack?

Answer 1

The equation you are looking for is Arrhenius equation, In short, the Arrhenius equation is an expression that shows the dependence of the rate constant k of chemical reactions on the temperature T and activation energy Ea, as shown below:

k=A* exp(-Ea/RT)

where A is the pre-exponential factor or simply the prefactor and R is the gas constant

We can write two equations because of this

At temp1., k1=A* exp(-Ea/RT1)

At temp 2., k2=A* exp(-Ea/RT2)

if temp2 is greater than temp 1, then the ratio of the two yields

(k2/k1)= exp(-Ea/RT1)/exp(-Ea/RT2)= exp(-Ea/(R(1/T1-1/T2)))

= exp(-Ea/(R(T2-T1)/T2*T1))

if k2/k1=2, then exp(-Ea/(R(T2-T1)/T2*T1))= 2

Taking natural logs we have

Ln 2 = -Ea/(R(T2-T1)/T2*T1))= But T2= T1 +10

Ln 2= -Ea/(R(10/(T1*(T1+10))

Ea = - Ln(2)*(T1*(T1+10))/10R.

Just knowing the initial temperature allows Ea to be calculated for example the temperature is 373K, using the above expression the rate constant doubles when

Ea = - Ln(2)*(373*383)/10R = -1191.03.

Answer 2

It's going to take a little algebra, but this is a perfectly reasonable question.

The equation you need is a form of the Arrhenius equation that relates rate constants at two different temperatures to the activation energy and temperature.

I can't write the equation properly here, but hopefully you can understand it. The equation will look something like:

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

In your case, the ratio k1/k2 will be 1/2 or 1/3, and the temperatures will be T and T+10. Eventually, T will disappear from the equation, and you can solve for Ea.

Good luck.

Answer 3

Use of a catalyst can change the required activation energy by providing another route for the reaction.