The dissociation energy of a carbon-bromine bond is typically abo...

Question

The dissociation energy of a carbon-bromine bond is typically about 276 kJ/mol. (a) What is the maximum wavelength of photons that can cause C-Br bond dissociation?

Accepted Answer

Hi everyone for this problem, we're told the nitrogen chlorine bond has an average bond dissociation energy of 200 kg per mole, calculate the highest wavelength of photons that can initiate the dissociation of the nitrogen chlorine bond. Okay, so our goal here is to calculate wavelength, and the relationship between energy of a photon and the wavelength of light is energy is equal to H. C. Over lambda. Okay, and so since we're being asked about wavelength here, we need to rearrange this equation so that it's solving for wavelength. When we rearrange this, it becomes wavelength is equal to H. C over E. So let's define some of these variables, H is Planck's constant, and this value is 6.626 times 10 To the negative 34 jewel seconds. And see is our speed of light. And that value is 3.00 times 10 to the 8th m/s. And E. Is energy. Okay, so energy per photon. And so we don't have this value. So we're going to need to calculate it in order to solve for wavelength, we can calculate the energy by using the bond association bond association energy that was given in the problem. So let's start there. So we know that We have 200 killer jewels per mole. So we need to figure out the energy per photon. So we need to go from kilo joules per mole to jules per photon. So let's start off by first going from killer jewels, two jewels and one killer jewel We have 1000 jewels. Okay, so our killer jewels cancel. And we're with left with jewels. Now remember we want to end with jewels per photon. So let's go ahead and go from jules from moles to photons by using avocados number and one more. There is 6.02, 2 times 10 to the 23 photons. Okay, so our moles cancel and we're left with photons. So we have jewels per photon, which is the units that we want. Okay, so when we do this calculation, we're going to get 3. times 10 to the negative 19 jewel per photon. And this is what we needed to plug in. So let's go ahead and plug in everything now. So plank's constant times our speed of light, divided by the energy per photon that we just calculated. Let me rewrite that. So this should be 3. 11 Times 10 to the negative 19th jewels. Okay, so when we calculate this, we're going to get our wavelength is equal to 5.99 Times 10 to the negative seven meters. So wavelength is usually written in nanometers. So let's go ahead and convert this from meters to nanometers and one nanometer, There is 10 to the -9 m. Okay, so our meters cancel and we're going to be left with a final wave length and meter and nanometers. And that value is 599 nm. And this is our final answer. This is the wavelength of photons that can initiate the dissociation of the nitrogen chlorine bond. That's the end of this problem. I hope this was helpful.

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