The O−H bond enthalpy is 463 kJ/mol. What is the wavelength of light that will cause dissociation of H2O into the hydrogen atom and the hydroxyl radical
A proton in a linear accelerator has a de Broglie wavelength of 141 pm, what is the speed of the photon?
To determine the wavelength of light required for the dissociation of H2O into the hydrogen atom (H) and the hydroxyl radical (OH•), we need to consider the bond enthalpy and the energy associated with the dissociation reaction.
The dissociation of H2O can be represented by the following equation:
H2O → H + OH•
In this reaction, the O−H bond is broken, and the dissociation energy is equal to the O−H bond enthalpy.
The bond enthalpy is the amount of energy required to break one mole of a specific bond in a compound. In this case, the O−H bond enthalpy is given as 463 kJ/mol.
Now, to find the energy associated with the dissociation reaction, we need to convert the bond enthalpy from kJ/mol to joules:
Bond enthalpy = 463 kJ/mol = 463,000 J/mol
Since energy can be related to wavelength using the equation:
E = hc/λ
where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of light.
We can rearrange this equation to solve for λ:
λ = hc/E
Substituting the values:
λ = (6.626 x 10^-34 J·s) × (3.00 x 10^8 m/s) / (463,000 J/mol)
Now, the given bond enthalpy is in joules per mole, so we need to convert it to joules per molecule, which is done by dividing by Avogadro's number (6.022 x 10^23 molecules/mol):
λ = (6.626 x 10^-34 J·s) × (3.00 x 10^8 m/s) / (463,000 J/mol) × (1 mol / 6.022 x 10^23 molecules)
Evaluating this expression will give us the wavelength of light required for the dissociation of H2O into H and OH•.