Question

it takes 151. kj/mol to break an iodine - iodine single bond. calculate the maximum wavelength of light for which an iodine - iodine single bond could be broken by absorbing a single photon.
round your answer to 3 significant digits.

Explanation:

Step1: Calculate the energy per photon

The energy required to break one mole of iodine - iodine bonds is \(E_{mol}=151\space kJ/mol = 151\times10^{3}\space J/mol\).
Using Avogadro's number \(N_{A}=6.022\times 10^{23}\space mol^{-1}\), the energy per photon \(E\) is \(E=\frac{E_{mol}}{N_{A}}\).

$$E=\frac{151\times 10^{3}\space J/mol}{6.022\times 10^{23}\space mol^{-1}}$$

$$E\approx2.51\times 10^{-19}\space J$$

Step2: Use the photon energy formula \(E = h

u=\frac{hc}{\lambda}\) to find the wavelength \(\lambda\)
We know that \(h = 6.626\times 10^{-34}\space J\cdot s\) (Planck's constant) and \(c = 3\times 10^{8}\space m/s\) (speed of light).
From \(E=\frac{hc}{\lambda}\), we can solve for \(\lambda\): \(\lambda=\frac{hc}{E}\)
Substitute \(h = 6.626\times 10^{-34}\space J\cdot s\), \(c = 3\times 10^{8}\space m/s\) and \(E = 2.51\times 10^{-19}\space J\) into the formula:

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Convert meters to nanometers: Since \(1\space m = 10^{9}\space nm\), \(\lambda=7.92\times 10^{-7}\times10^{9}\space nm = 792\space nm\)

Answer:

\(792\space nm\)