Author Question: Rate of a reaction triples when the temperature is increased from 25C to 35C. Calculate the activation Energy? (Read 3399 times)

sadsdas

  • Newbie
  • *
  • Posts: 10
Rate of a particular reaction triples when the temperature is increased from 25C to 35C. Calculate the activation energy for this reaction?
How to approach the problem when there is no rate constant? What formula to use?



Yolanda

  • Hero Member
  • *****
  • Posts: 757
anytime you read "activation energy" and "temperature" in the same sentence you should immediately think "Arrhenius equation"
.. k = A x exp(-Ea / RT)

and since you have "rate" not "k" we can do this
.. rate = k x [A]^n.... .  <====.. typical rate equation
so that
.. rate1 = k1 x [A1]^n
.. rate2 = k2 x [A2]^n
and if we assume we start with the same concentration of [A] and just vary "T" and the problem indicates, then [A1]^n = [A2]^n = [A]^n.. so that
.. rate1 / k1 = [A]^n = rate2 / k2
rearranging
.. rate1 / rate2 = k1 / k2
i.e..
.. I can substitute (rate1 / rate2) for (k1 / k2)...  Capice?

***********
going back to the Arrhenius equation.. since we have 2 conditions
.. k1 = A exp(-Ea / RT1)
.. k2 = A exp(-Ea / RT2)
rearranging
.. k1 / exp(-Ea / RT1) = A
.. k2 / exp(-Ea / RT2) = A
since the both = A, they must = each other
.. k1 / exp(-Ea / RT1) = k2 / exp(-Ea / RT2)
rearranging
.. k1 / k2 = exp(-Ea / RT1) / exp(-Ea / RT2)

now.. since a^b / a^c = a^(b-c)
.. k1 / k2 = exp( (-Ea/RT1) - (-Ea/RT2) )
taking ln of both sides and rearranging a bit..
.. ln(k1 / k2) = (-Ea/R) x (1/T1 - 1/T2)

rearranging one last time and subbing in that rate1 / rate2 for k1 / k2
.. Ea = (-R) x ln(rate1/rate2) / (1/T1 - 1/T2)

and finally... considering rate2 = 3x rate1
.. Ea = (-8.314 J/molK) x ln(1 / 3) / (1/295K - 1/308K) x (1kJ / 1000J) = +63.8 kJ/mol

*******
do you understand all of this?



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question
 

Did you know?

Most strokes are caused when blood clots move to a blood vessel in the brain and block blood flow to that area. Thrombolytic therapy can be used to dissolve the clot quickly. If given within 3 hours of the first stroke symptoms, this therapy can help limit stroke damage and disability.

Did you know?

Your chance of developing a kidney stone is 1 in 10. In recent years, approximately 3.7 million people in the United States were diagnosed with a kidney disease.

Did you know?

The most common treatment options for addiction include psychotherapy, support groups, and individual counseling.

Did you know?

The strongest synthetic topical retinoid drug available, tazarotene, is used to treat sun-damaged skin, acne, and psoriasis.

Did you know?

Women are two-thirds more likely than men to develop irritable bowel syndrome. This may be attributable to hormonal changes related to their menstrual cycles.

For a complete list of videos, visit our video library