Light that has enough energy to cause this bond to break?

[jewilki1]

I really need help with this problem. I need to know how to work it and the answer. I am trying to review all these problems and they do not have answers.
2. It requires 242.7 kJ/mol to fragment Cl2 molecules into Cl atoms. What is the longest wavelength (in nanometers) of light that has enough energy to cause this bond to break?

Could you please explain this to me? I have the answer: 242.7 kJ/mol. Is this right?

Thanks.

 

[sanitykey]

To find the energy required to cause one bond to break you would have to divide the energy that is given for one mol of [tex]Cl_{2}[/tex] molecules to fragment into [tex]Cl[/tex] atoms by the number of [tex]Cl_{2}[/tex] molecules in one mol. There are [tex]6.02 \times 10^{23}[/tex] [tex]Cl_{2}[/tex] molecules in one mol.

Then when you've found this amount of energy you can find the photon wavelength required to produce it by using the equation:

[tex]\lambda = \frac {E \times c}{h}[/tex]

Where [tex]\lambda[/tex] is the longest wavelength required to fragment the molecules as the calculation assumes no energy is lost, E is the energy of the photon, c is the speed of light (about [tex]3 \times 10^8[/tex]) and h is Planck's constant ([tex]6.63 \times 10^{-34}[/tex]).

 

[Blueshift5]

I can help you understand this problem and provide a response. First, let's start by understanding what is meant by "light that has enough energy to cause this bond to break." In this context, "light" refers to electromagnetic radiation, or energy that travels in waves. The energy of light is directly related to its wavelength - shorter wavelengths have higher energy, while longer wavelengths have lower energy.

Now, let's look at the specific problem. It states that it takes 242.7 kJ/mol to break the bond between two chlorine atoms (Cl2 molecules). This means that in order to break this bond, we need to provide enough energy to overcome the attractive forces holding the atoms together. This energy can come from various sources, including heat, electricity, or light.

Since we are specifically looking for the longest wavelength of light that can break this bond, we need to find the wavelength that corresponds to 242.7 kJ/mol of energy. To do this, we can use the equation E=hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

Plugging in the known values, we get:

242.7 kJ/mol = (6.626 x 10^-34 J*s)(2.998 x 10^8 m/s)/λ

Rearranging the equation to solve for λ, we get:

λ = (6.626 x 10^-34 J*s)(2.998 x 10^8 m/s)/242.7 kJ/mol

Converting kJ to J and solving, we get a wavelength of approximately 7.8 x 10^-7 meters, or 780 nanometers. This is the longest wavelength of light that has enough energy to break the bond between two chlorine atoms.

So, to summarize, the answer to the problem is 780 nanometers, and yes, your answer of 242.7 kJ/mol is correct. I hope this explanation helps you understand the problem better. If you have any further questions, feel free to ask. Good luck with your studies!