Question

it takes 242 kj/mol to break a chlorine - chlorine single bond. calculate the maximum wavelength of light for which a chlorine - chlorine single bond could be broken by absorbing a single photon. be sure your answer has the correct number of significant digits.

Explanation:

Step1: Calculate energy per photon

Given energy to break \(Cl - Cl\) bond is \(E = 242\space kJ/mol\).
First, convert energy per mole to energy per photon.
We know that \(1\space mol=6.022\times 10^{23}\) photons.
\(E=\frac{242\times 10^{3}\space J/mol}{6.022\times 10^{23}\space photons/mol}\)
\(E=\frac{242\times 10^{3}}{6.022\times 10^{23}}\space J\)
\(E = 4.019\times 10^{-19}\space J\)

Step2: Use the formula \(E = h

u=\frac{hc}{\lambda}\) to find \(\lambda\)
where \(h = 6.626\times 10^{-34}\space J\cdot s\) (Planck's constant), \(c = 3\times 10^{8}\space m/s\) (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 \(E = 4.019\times 10^{-19}\space J\)
\(\lambda=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{4.019\times 10^{-19}}\space m\)
\(\lambda=\frac{19.878\times 10^{-26}}{4.019\times 10^{-19}}\space m\)
\(\lambda = 4.946\times 10^{-7}\space m\)
Convert to \(nm\): \(1\space m = 10^{9}\space nm\)
\(\lambda=494.6\space nm\approx495\space nm\)

Answer:

\(495\space nm\)