Ozone, O3, absorbs ultraviolet radiation and dissociates into O2 molecules and O atoms:
O3 + hv --> O2 + O
A 1.10 L sample of air at 22 degrees Celsius and 748mm Hg contains 0.25ppm of O3.
How much energy, in joules, must be absorbed if all the O3 molecules in the sample of air are to dissociate? Assume that each photon absorbed causes one O3 molecule to dissociate, and that the wavelength of the radiation is 254 nm
To determine the energy required for the dissociation of all O3 molecules in the sample of air, we can use the equation relating energy, wavelength, and the speed of light:
E = hc/λ
Where:
- E is the energy in joules
- h is Planck's constant (6.63 × 10^-34 J·s)
- c is the speed of light (3.00 × 10^8 m/s)
- λ is the wavelength in meters
Firstly, let's convert the wavelength from nanometers to meters:
λ = 254 nm = 254 × 10^-9 m
Now, we can substitute the values into the equation:
E = (6.63 × 10^-34 J·s) × (3.00 × 10^8 m/s) / (254 × 10^-9 m)
Simplifying the equation:
E = (6.63 × 3.00) / (254 × 10^-9) J
E = 0.56425396825396825 × 10^-16 J
Finally, we need to multiply this energy by the number of O3 molecules in the sample to get the total energy required:
Number of O3 molecules = (0.25 ppm) × (1.10 L / 24.5 L/mol)
Here, we converted the concentration from ppm (parts per million) to the number of moles of O3 in the 1.10 L sample using the molar volume at STP (Standard Temperature and Pressure).
Now, the Avogadro's number (6.022 × 10^23) gives us the number of molecules:
Number of O3 molecules = (0.25 ppm) × (1.10 L / 24.5 L/mol) × (6.022 × 10^23 molecules/mol)
Once we have the number of molecules, we can calculate the total energy:
Total energy = E × Number of O3 molecules
Plug in the value you obtained for "E" and the number of O3 molecules to calculate the final answer.