Question

it takes 498. kj/mol to break an oxygen - oxygen double bond. calculate the maximum wavelength of light for which an oxygen - oxygen double bond could be broken by absorbing a single photon.
be sure your answer has the correct number of significant digits.

Explanation:

Step1: Find energy per photon

First, we know the energy to break one mole of bonds is \( 498 \, \text{kJ/mol} = 498000 \, \text{J/mol} \). Using Avogadro's number \( N_A = 6.022 \times 10^{23} \, \text{mol}^{-1} \), the energy per photon \( E \) is:
\( E = \frac{498000 \, \text{J/mol}}{6.022 \times 10^{23} \, \text{mol}^{-1}} \approx 8.27 \times 10^{-19} \, \text{J} \)

Step2: Relate energy to wavelength

The formula relating energy \( E \), Planck's constant \( h = 6.626 \times 10^{-34} \, \text{J·s} \), speed of light \( c = 3.00 \times 10^8 \, \text{m/s} \), and wavelength \( \lambda \) is \( E = \frac{hc}{\lambda} \). Rearranging for \( \lambda \):
\( \lambda = \frac{hc}{E} \)
Substitute \( h \), \( c \), and \( E \):
\( \lambda = \frac{(6.626 \times 10^{-34} \, \text{J·s})(3.00 \times 10^8 \, \text{m/s})}{8.27 \times 10^{-19} \, \text{J}} \approx 2.40 \times 10^{-7} \, \text{m} = 240 \, \text{nm} \)

Answer:

\( 240 \, \text{nm} \) (or \( 2.40 \times 10^{-7} \, \text{m} \))