Question

it takes 412. kj/mol to break a carbon - hydrogen single bond. calculate the maximum wavelength of light for which a carbon - hydrogen single bond could be broken by absorbing a single photon.
round your answer to 3 significant digits.

nm

Explanation:

Step1: Calculate energy per photon

We know that \(E = \frac{E_{\text{mol}}}{N_A}\), where \(E_{\text{mol}}=412\space kJ/mol = 412\times10^{3}\space J/mol\) and \(N_A = 6.022\times 10^{23}\space mol^{-1}\)

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Step2: Use the formula \(E = h

u=\frac{hc}{\lambda}\) to find \(\lambda\)
We know that \(h = 6.626\times 10^{-34}\space J\cdot s\) and \(c = 3\times 10^{8}\space m/s\)

From \(E=\frac{hc}{\lambda}\), we can solve for \(\lambda\): \(\lambda=\frac{hc}{E}\)

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Since \(1\space m = 10^{9}\space nm\), \(\lambda=2.91\times 10^{-7}\space m\times10^{9}\space nm/m = 291\space nm\)

Answer:

\(291\space nm\)