The complex ion, [Ni(NH3)6]2+, has a maximum absorption near 580 nm. Calculate the crystal field splitting
energy (in kJ/mol) for this ion.
206 kJ/mol
To calculate the crystal field splitting energy for the complex ion [Ni(NH3)6]2+, we need to use the relationship between the absorption wavelength and the crystal field splitting energy.
The absorption wavelength, λ, is related to the crystal field splitting energy, Δ, by the equation:
Δ = hc / λ
Where:
- Δ is the crystal field splitting energy
- h is Planck's constant (6.62607015 × 10^-34 J·s)
- c is the speed of light (2.998 × 10^8 m/s)
- λ is the absorption wavelength in meters
To calculate the crystal field splitting energy, we first need to convert the absorption wavelength from nanometers (nm) to meters (m). We know that 1 nm = 1 × 10^-9 m, so:
λ = 580 nm × (1 × 10^-9 m/nm) = 580 × 10^-9 m = 5.8 × 10^-7 m
Next, we can substitute the values of Planck's constant (h) and the speed of light (c) into the equation:
Δ = (6.62607015 × 10^-34 J·s) × (2.998 × 10^8 m/s) / (5.8 × 10^-7 m)
Calculating this expression will give us the crystal field splitting energy in joules (J). However, the question asks for it in kJ/mol. To convert from joules to kJ/mol, we need to divide the calculated energy by Avogadro's number (6.02214076 × 10^23).
Finally, we can convert the energy from joules to kilojoules (kJ) by dividing by 1000.
Let's calculate it!
Calculate E from the wavelength, w.
E = hc/w which is E/ion
Then convert to kJ/mol
J/ion x 6.02E23 J/mol and convert to kJ/mol.