A minimum energy of 225 kJ/mol is required to break a certain chemical bond in a compound. What is the

longest wavelength of radiation (in nm and angstroms, Å; 1 Å = 10−10 m) necessary to break the bond? In
which region of the electromagnetic spectrum does this radiation lie?

You want 225,000 J/mol or

225,000 x (1 mol/6.02E23) = ? J/atom
Then E = hc/wavelength.
Substitute and solve for wavelength in meters, convert to A and nm.

To find the longest wavelength of radiation required to break the chemical bond, we need to use the equation relating energy and wavelength called the energy-wavelength equation:

E = hc/λ

Where:
E is the energy (in Joules),
h is Planck's constant (6.626 x 10^(-34) J.s),
c is the speed of light (2.998 x 10^8 m/s),
λ is the wavelength (in meters).

First, we need to convert the minimum energy required to break the bond from kJ/mol to Joules. Since 1 kJ = 1000 J, we have:

Minimum energy = 225 kJ/mol * (1000 J/1 kJ) = 225,000 J/mol

Next, we divide this energy by Avogadro's number (6.022 x 10^23 mol^(-1)) to find the energy per molecule:

Energy per molecule = 225,000 J/mol / (6.022 x 10^23 mol^(-1)) ≈ 3.74 x 10^(-19) J/molecule

Now, we can solve the energy-wavelength equation for the wavelength:

λ = hc/E

Substituting the known values:

λ = (6.626 x 10^(-34) J.s * 2.998 x 10^8 m/s) / (3.74 x 10^(-19) J/molecule)

Calculating this division gives us the wavelength in meters. However, we want the wavelength in nanometers (nm) and angstroms (Å).

To convert from meters to nanometers, we multiply by 10^9:

λ(nm) = λ(m) * 10^9

To convert from meters to angstroms, we multiply by 10^10:

λ(Å) = λ(m) * 10^10

Finally, we can calculate the values:

λ(m) = (6.626 x 10^(-34) J.s * 2.998 x 10^8 m/s) / (3.74 x 10^(-19) J/molecule)

λ(m) ≈ 1.68 x 10^(-6) m

λ(nm) = 1.68 x 10^(-6) m * 10^9 ≈ 1680 nm

λ(Å) = 1.68 x 10^(-6) m * 10^10 ≈ 16800 Å

Therefore, the longest wavelength of radiation necessary to break the bond is approximately 1680 nm or 16800 Å.

To determine which region of the electromagnetic spectrum this radiation lies in, we can match the wavelength range with the corresponding region:

- Radiation with a wavelength of 1680 nm falls in the infrared region of the electromagnetic spectrum.
- Radiation with a wavelength of 16800 Å falls in the ultraviolet (UV) region of the electromagnetic spectrum.