Alcohol-based fuels for automobiles lead to the production of for...

Question

Alcohol-based fuels for automobiles lead to the production of formaldehyde (CH2O) in exhaust gases. Formaldehyde undergoes photodissociation, which contributes to photo- chemical smog: CH2O + hn ¡ CHO + H The maximum wavelength of light that can cause this reac- tion is 335 nm. (b) What is the maximum strength of a bond, in kJ>mol, that can be bro- ken by absorption of a photon of 335-nm light?

Accepted Answer

Hi everyone for this problem. We're told the photo dissociation of ozone happens in the troposphere. A light with a maximum wavelength of 320 nm can initiate this reaction, calculate the maximum bond strength and killing joules per mole. That can be broken by the absorption of 320 nm of light. So our goal here is to calculate the maximum bond strength and killer joules per mole. What this means is we're calculating energy and we're also given the wavelength. Okay, so the relationship between the energy of a photon and the wavelength of the light is described by this equation. Energy is equal to H. C. Over lambda. So let's go ahead and define some of these variables. H is Planck's constant and this value is 6.626 times 10 to the negative 34 Jules. Time seconds. Okay see is our speed of light and that value is 3.00 times 10 to the 8th m/s. And Lambda is our wavelength. We're told that we have a wavelength of nm. So we have everything that we need to solve for our energy. So we can go ahead and plug these values in so that we can figure out what is our energy. So let's go ahead and do that. So energy is equal to plank's constant times the speed of light over our wavelength. Okay, So if you take a look, our speed of light is in meters per second but our wavelength is in nanometers. So we need to go ahead. And convert our wavelength from nanometers two m. So let's go ahead and do that. So I'll move this here and one nanometer, We have 10 to the negative nine meters. Okay so our nanometers cancel and we're left with the unit of meters. So we get Our wavelength is 3.20 times 10 to the - m. So let's plug that in. Okay, so once we do this calculation we're going to get our energy is equal to 6.211 8 7. 5 times 10 To the - jewels. Perfect time. Okay. Okay so but what we want to do is we want to convert this jules per photon to kill a jules Permal. Okay so let's go ahead and rewrite this so that we can convert it properly. So I moved this wavelength conversion up here. So our 6. 875 times 10 to the negative 19 jewels per photon needs to be converted to kill a jules Permal. Okay so we can convert the jewels to kill a jules We have in one, kill a jewel there is 1000 jewels. So let's go ahead and cancel out our jewels unit. And now we need to go from photon to mole. Okay so another conversion that we should know is that in one mole? There is 6.022 times 10 to the 23 photons. So let's go ahead and plug that in. So on one more We have 6.022 times 10 to the photons. Now our Photons cancel and we're left with killer joules per mole, which is exactly what we need. So let's go ahead and finish this off by doing the calculation. And when we do the calculation, we'll get a final answer of kg jewels per mole. And this is going to be our final answer. Okay, so this is going to be The maximum bond strength and kill a jewels per mole that can be broken by the absorption of nm of light. That's the end of this problem. I hope this was helpful.

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