It takes 146kJ/mol to break a oxygen oxygen single bond calculate the maximum wavelength of light for which a oxygen oxygen single bond could be broken by absorbing a single photon

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

1 answer

To calculate the maximum wavelength of light for which an oxygen-oxygen 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 (convert kJ to J by multiplying by 1000)
h = Planck's constant (6.62607015 × 10^-34 J·s)
c = speed of light in a vacuum (3.00 × 10^8 m/s)
λ = wavelength of light in meters (convert nm to m by dividing by 10^9)

First, let's convert the energy required to break the bond to joules:

146 kJ/mol * (1000 J/kJ) = 146,000 J/mol

Now we need to convert this to energy required per molecule. Since there is Avogadro's number (6.02214076 × 10^23) of molecules in a mole:

146,000 J/mol / (6.02214076 × 10^23 molecules/mol) = 2.42 × 10^-19 J/molecule

Now, we can substitute the values into the equation:

2.42 × 10^-19 J = (6.62607015 × 10^-34 J·s)(3.00 × 10^8 m/s) / λ

Rearranging the equation to solve for λ:

λ = (6.62607015 × 10^-34 J·s)(3.00 × 10^8 m/s) / (2.42 × 10^-19 J)

λ ≈ 8.21 × 10^-7 meters

Converting this value to nanometers:

λ ≈ 8.21 × 10^-7 meters * (10^9 nm/1 meter) ≈ 821 nm

Therefore, the maximum wavelength of light for which an oxygen-oxygen single bond could be broken by absorbing a single photon is approximately 821 nm.