It takes 338 kJ/mol to break an carbon chlorine single bond calculate the maximum wavelength of light which an carbon chlorine single bond could be broken by absorbing a single photon

Question

Be sure your answer has correct number of significant digits in nm

Answer 1

To find the maximum wavelength of light which a carbon-chlorine single bond could be broken by absorbing a single photon, we can use the equation:

E = hc/λ

Where:
E = energy required to break the bond (in joules)
h = Planck's constant (6.62607015 × 10^-34 J·s)
c = speed of light (2.998 × 10^8 m/s)
λ = wavelength of light (in meters)

First, let's convert the energy required to break the bond from kJ/mol to joules per molecule:
338 kJ/mol = 338,000 J/6.022 × 10^23 molecules

Now, we can calculate the energy required to break a single bond:
Energy per molecule = 338,000 J/ 6.022 × 10^23 molecules = 5.612 × 10^-19 J

Next, we need to convert this energy into electron volts (eV) by dividing it by the elementary charge, which is 1.602176634 × 10^-19 C:
Energy in eV = (5.612 × 10^-19 J) / (1.602176634 × 10^-19 C) = 3.5 eV

Now, we can rearrange the energy equation to solve for the wavelength:
λ = hc / E

Plugging in the values:
λ = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (3.5 eV * 1.602176634 × 10^-19 J/C)

Calculating this equation gives us:
λ ≈ 1.769 × 10^-7 meters

Finally, let's convert this into nanometers:
λ ≈ 1.769 × 10^-7 meters * 10^9 nm/m = 176.9 nm

So, the maximum wavelength of light which a carbon-chlorine single bond could be broken by absorbing a single photon is approximately 176.9 nm.