It takes 348kJ/mol to break a carbon carbon single bond calculate the maximum wavelength of light for which a carbon carbon 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 that can break a carbon-carbon single bond, we will use the equation:

E = hc/λ

where:
E is the energy required to break the bond (348 kJ/mol),
h is Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light (2.998 x 10^8 m/s),
and λ is the wavelength of light we are trying to calculate.

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

E = 348 kJ/mol × (1000 J/1 kJ) = 348,000 J/mol

Now, we need to convert the energy per mole into energy per photon:

Avogadro's number (N_A) = 6.022 x 10^23 mol^-1

Energy per photon (E_photon) = E / N_A

E_photon = (348,000 J/mol) / (6.022 x 10^23 mol^-1) = 5.778 x 10^-19 J/photon

Now, we can rearrange the equation to solve for the wavelength:

λ = hc/E_photon

λ = (6.626 x 10^-34 J·s) × (2.998 x 10^8 m/s) / (5.778 x 10^-19 J/photon)

λ ≈ 3.84 x 10^-7 m or 384 nm

Therefore, the maximum wavelength of light for which a carbon-carbon single bond could be broken by absorbing a single photon is approximately 384 nm.