Question

Ozone (O3) absorbs radiation from the sun and is decomposed into O2 and O. Calculate the maximum wavelength of light (in nm) that would provide enough energy to promote this decomposition. Hint: First calculate the H for the reaction.

O3 + hv O2 + O

Hrxn = ?

Answer 1

E = hv
v= c/(wavelength symbol)
c = 3.00 x 10-8
h = 6.626 x 10-34
Enthalpies of formation:

O2 (g) Hf = 0
O (g) Hf = 249.4 kJ/mol
O3 (g) Hf = 142.2 kJ/mol

Answer 2

Hrxn = H prod- H rec
Hrxn = 249.4-142.2 = ??? kJ/mol

E = hv => v= E/h
v=??? kJ/6.626 x 10-34

c= vλ => λ = c/v

Answer 3

Okay so now I need to find E. How do I go about that? I'm assuming it has to do with the 107.2 kJ/mol found for Hrxn?

Answer 4

And the speed of light was also given : 300,000,000 m/s

Answer 5

And doesn't E need to be in J not kJ? so v= 107200/ 6.626 x 10^-34

Answer 6

Yes but even after getting an answer I've been trying to find out why I'm wrong. I keep getting an answer of about 1000nm when the correct amount is around 290nm.

Answer 7

Here's what I've attempted so far. 107200 joules is per mole. So we'll divide by avogadro's number to get per molecule. This is 1.78x10^0-19. I then combined the two equations and solved for wavelength getting w = hc/E. Plugging in all the values for h,c and e and converting to nm I still get 1116nm which I know to be incorrect from experience.

Answer 8

c = 3.00 x 10^8 m/s

Answer 9

107200 J/mol / 6.022 x 10^23 = 1.78 x 10^27
1.78x10^27 / 6.626 x 10^-34 = 2.7 x 10^-8
3.00x10^8/ 2.7x10^-8 =1.1 wavelength

Answer 10

your first division is incorrect. 107,200/ avogadro's number. Either way something else is off. Not sure what's going on.

Answer 11

All though I believe the steps your taking are the correct ones. I think somehow the kilo joules value in the beginning is whats wrong. We would be correct if we started with a Kj/mol of around 450.

Answer 12

AAahhhhhhh I think I 've found it out. So we shouldn't be using the heats of formation. We should be finding the amount of energy it takes to break the ozone molecule. If we use the bond energy of 495kj/mol of breaking a double bonded oxygen then we get the correct answer.

Answer 13

But the 495 wasn't given and I don't remember ever being to told to memorize that.

Answer 14

How was this question assigned? Lab, quiz, ...?

Answer 15

Its a take home quiz. All the info given is all we need to finish the question

Answer 16

I'm still getting 1.1 x 10^9 nm for my answer

Answer 17

Welp that's all you can do then. I agree with the method you did it as well.

And you should be getting 1.11e-6m or 1110nm

Answer 18

\[\frac{1.78\times10^{-19}}{6.626\times10^{-34}} =2.686\times10^{14}\]
\[wavelength = \frac{3.00\times 10^8}{2.686\times10^{14}} = 1.116\times10^{-6}meters = 1116nm\]

Answer 19

How did you get 1.78 x 10^-19?

Answer 20

107200joules/ avocados number

Answer 21

107200 / 6.022 x 10^23 = 1.78 x 10^27

Answer 22

Oh wait sorry calculation error