Arrhenius Equation Problem Involving a Biological Reaction?

Question

If the activation energy, Ea, for a certain biological reaction is 50 kJ/mol.  By what factor, or in other words, how many times will the rate of this reaction increase when the body temperature increases from 37°C (normal) to 40°C (fever)?

(A) 1.15

(B) 1.20

(C) 2.0x10^5

(D) 1.0002

(E) 2.0

Soooo.....I thought I was on the right track using the following equation:

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

I plugged all the values in that were given to me and solved for the (k2/k1) ratio and boom....my calculator displayed the value 1.0002.  And so I circled (D).  According to the practice test key my answer is wrong and stupid.  If anyone can point me in the right direction that would be awesome cuz I really don't know where else to go on this one.

Thanks everyone :-p

Jan · Accepted Answer

Hey Adam, let's  try noch einmal;

ln(k2/k1) = (50*10^3/R)*[(1/310) - (1/313)] = 0.186
thus
k2/k1 = exp(0.186) = 1.20
=> (B)

is it correct?

Steve · Answer

I think the equation should work fine, but there are a couple of possible traps:
1) Make sure the units of Ea and R are appropriate - if you are using R in J/mol/K, make sure Ea is in J/mol not kJ/mol 
2) Make sure the temperatures are converted to Kelvin

Adam Hess · Answer

Jan!  (B) is totally the right answer!!  You used the same equation?!?  What did I do different!?

OMG!!  Careless, careless, careless.  I kept the Ea in units of kJ when I should've converted it to Joules.  I did get 1.20.

Okay, I've been doing problems all morning and I guess that means it's time for a break.

Thanks Jan.  As always you're the best :-D

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Arrhenius Equation Problem Involving a Biological Reaction?

3 Answers