It takes 157kJ/mol to break a nitrogen oxygen single bond calculate the maximum wavelength of light for which a nitrogen oxygen 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 calculate the maximum wavelength of light, we'll use the equation:

E = hc/λ

Where:

E = energy of the photon
h = Planck's constant (6.626 x 10^-34 J · s)
c = speed of light (2.998 x 10^8 m/s)
λ = wavelength of light (in meters)

First, we need to convert the energy from kJ/mol to J/mol and then to J:
1 kJ = 1000 J
1 mol = 6.022 x 10^23 molecules

Energy per molecule = 157 kJ/mol / (6.022 x 10^23 molecules/mol)
Energy per molecule = 2.61 x 10^-22 J

Now we can calculate the maximum wavelength using the equation:

E = hc/λ

λ = hc / E

λ = (6.626 x 10^-34 J · s) / (2.61 x 10^-22 J)

λ = 2.53 x 10^-12 m

Lastly, let's convert the wavelength from meters to nanometers:
1 m = 1 x 10^9 nm

λ = 2.53 x 10^-12 m * 1 x 10^9 nm/m
λ = 2.53 nm

Therefore, the maximum wavelength of light for which a nitrogen oxygen single bond could be broken by absorbing a single photon is 2.53 nm.