Arrhenius Equation - Chemical Kinetics

[vertciel]

Hello everyone,

I am having trouble with determining where I erred in the following exercise. If someone could point out my mistake, I would appreciate the help.

Thank you!

---

1. The decomposition of N₂O₅ has an activation energy of 103 kJ/mol and a frequency factor of $$4.3E13 s^-1$$. What is the rate constant for this decomposition at 20°C?

---

I simply substituted the given values into the Arrhenius Equation (omitting units to save time in typing):

$$k = Ae^{\frac{-E_a}{RT}}$$

$$k = 4.3E13 \times e^{\cfrac{-103}{8.314 \times 293 K}}$$

$$k = 4.1E13 1/s$$

---

However, the given answer is:

Spoiler

1.9E-5 1/s

.

 

[Mike H]

Are you *sure* you're using the right units, since you omitted them in your original post? What units are you using for the gas constant? Activation energy? Temperature?

I would go back and check them again.

P.S. - I think these sorts of questions belong in the Homework Help section (even if it's not technically a homework question, it very strongly resembles one, at least IMO.)

 

[vertciel]

Thanks for your reply, Mike H.

I apologise; I didn't realize that this was the correct forum. If someone could please move this to the Homework Help section, that would be appreciated.

I have rewritten my work with units:

$$k = 4.3E13 \frac{1}{s} \times e^{\cfrac{-103 \frac{kJ}{mol}}{8314 \frac{kJ}{K mol} \times 293 K}}$$

$$k = 4.3E13 \frac{1}{s}$$

I get a different answer, but one that is still incorrect.

 

[Ygggdrasil]

R is 8.314J K^-1 mol^-1 = 0.008314 kJ K^-1 mol^-1.

[edit: thanks GCT]

 

[GCT]

You're one decimal place off.

 

[vertciel]

Thank you very much for your help!