Question

it takes 146. kj/mol to break an oxygen - oxygen single bond. calculate the maximum wavelength of light for which an oxygen - oxygen single bond could be broken by absorbing a single photon. round your answer to 3 significant digits.

Explanation:

Step1: Convert bond - energy per mole to energy per photon

The energy per mole of bonds is $E_{mol}=146\ kJ/mol$. First, convert this to joules per mole: $E_{mol}=146\times10^{3}\ J/mol$. Then, use Avogadro's number $N_A = 6.022\times 10^{23}\ mol^{-1}$ to find the energy per photon $E$. The formula is $E=\frac{E_{mol}}{N_A}$.
$E=\frac{146\times 10^{3}\ J/mol}{6.022\times 10^{23}\ mol^{-1}}\approx2.424\times 10^{-19}\ J$

Step2: Use the photon - energy formula to find the wavelength

The energy of a photon is given by $E = h
u=\frac{hc}{\lambda}$, where $h = 6.626\times 10^{-34}\ J\cdot s$ is Planck's constant, $c = 3.00\times 10^{8}\ m/s$ is the speed of light, and $\lambda$ is the wavelength. Rearranging the formula for $\lambda$ gives $\lambda=\frac{hc}{E}$.
Substitute the values of $h$, $c$, and $E$:
$\lambda=\frac{6.626\times 10^{-34}\ J\cdot s\times3.00\times 10^{8}\ m/s}{2.424\times 10^{-19}\ J}\approx8.20\times 10^{-7}\ m$

Step3: Convert the wavelength to nanometers

Since $1\ m = 10^{9}\ nm$, then $\lambda = 8.20\times 10^{-7}\ m\times10^{9}\ nm/m = 820\ nm$

Answer:

$820\ nm$