Question

i'm stumped on how to write this in mathematical form. it says the rate increased by a factor of 2000, I am supposed to determine by what percent the Energy of activation will be reduced. The answer is 25% in the book. I don't know how they get the answer using this formula: k1/k2=Ae^-Ea/RT. A is constant for both reactions. T = 298 K, R = 8.3145

Answer 1

I am not sure, and someone can come along after I am done and check what I am telling you, but I believe you are missing some information like the temperature change. The question seems to be incomplete.

Answer 2

yeah I'm not sure...an example in the book just equates them, its for a catalyzed reaction by saying k1/k2=(Ae^-Ea/RT)/(Ae^-Ea/Rt)=e^-Ea/RT but I'm not sure about that way.

Answer 3

Is this a multipart problem; i.e., is there another part of the problem in which Ea is calculated? or given? If so, what is the value of Ea in that part of the problem?

Answer 4

no they didn't give anything else

Answer 5

[AI-generated answer — Explain Bot]

To determine the percent reduction in energy of activation, let's break down the steps using the given formula:

1. Start by considering two reactions, let's call them Reaction 1 and Reaction 2.

2. The given information states that the rate of Reaction 2 increased by a factor of 2000 compared to Reaction 1. Mathematically, this can be expressed as:
Rate of Reaction 2 = 2000 * Rate of Reaction 1

3. Now, let's apply the formula k1/k2 = Ae^(-Ea/RT), where k1 and k2 represent the rate constants of Reaction 1 and Reaction 2, respectively. A is a constant for both reactions, T is the temperature (298 K), R is the gas constant (8.3145 J/(mol*K)), and Ea is the energy of activation.

4. Substituting the given information into the formula, we have:
Rate of Reaction 1 / Rate of Reaction 2 = Ae^(-Ea/RT) / (2000 * Ae^(-Ea/RT))

5. We can simplify the expression by canceling out the A's, resulting in:
1 / 2000 = e^(-Ea/RT) / e^(-Ea/RT)

6. Since the exponential functions on both sides have the same base (e), the exponents must be equal. Therefore:
-Ea/RT = -Ea/RT

7. From here, we can solve for the energy of activation Ea. Divide both sides of the equation by -RT:
Ea = Ea / 2000

8. Now, to determine the reduction in the energy of activation, we calculate the difference:
Reduction in energy of activation = Ea - Ea / 2000

9. Simplifying the equation, we have:
Reduction in energy of activation = Ea(1 - 1/2000)

10. To express the reduction as a percentage, we divide the reduction in energy of activation by the original energy of activation and multiply by 100:
Percent reduction = Reduction in energy of activation / Ea * 100

11. Substituting the simplified equation from step 9, we get:
Percent reduction = (Ea(1 - 1/2000)) / Ea * 100

12. Canceling out the Ea's, we obtain:
Percent reduction = (1 - 1/2000) * 100

13. Evaluating the expression, we find that the percent reduction is 99.95%.

Therefore, it seems there might be an error in the book. The correct percent reduction in the energy of activation should be approximately 99.95% instead of 25%.