Calculate the CFSE in kJmol-1 for an [Ti (H2o)6]3+ octahedral complex for which d – dtransition is the single broad absorption peak with a maximum at 20300 cm -1 . Draw thesplitting energy ?

To calculate the CFSE (Crystal Field Stabilization Energy) in kJmol-1 for the [Ti(H2O)6]3+ complex, we first need to convert the absorption peak wavelength from cm-1 to nm.

20300 cm-1 is equal to 1/20300 m-1 = 4.926 x 10^-5 m-1
This is equal to 4.926 x 10^4 cm-1

Now, we convert this to nm:
1 cm-1 = 10,000 nm
Therefore, 4.926 x 10^4 cm-1 = 4.926 x 10^4 x 10,000 nm = 492,600 nm

Now, we can calculate the splitting energy (?):
E = hc/λ
where:
E = energy in Joules
h = Planck's constant = 6.626 x 10^-34 J s
c = speed of light = 3.00 x 10^8 m/s
λ = wavelength in meters

Converting the wavelength to meters:
492,600 nm = 492,600 x 10^-9 m = 4.926 x 10^-4 m

Now, calculate the energy:
E = (6.626 x 10^-34 J s * 3.00 x 10^8 m/s) / 4.926 x 10^-4 m
E = 4.03 x 10^-19 J

Now, convert this energy to kJ:
1 J = 1 x 10^-3 kJ
4.03 x 10^-19 J = 4.03 x 10^-19 x 10^3 kJ = 4.03 x 10^-16 kJ

Therefore, the CFSE for the [Ti(H2O)6]3+ complex is 4.03 x 10^-16 kJmol-1.

The crystal field stabilization energy (CFSE) is a measure of the stability of a metal complex in a particular oxidation state and geometry. It is calculated using the following equation:

CFSE = -0.4 - n(t2g) - Δo + 0.6 - n(eg) - Δo

where n(t2g) and n(eg) are the number of electrons in the t2g and eg orbitals, respectively, and Δo is the crystal field splitting energy.

In the case of an [Ti(H2O)6]3+ complex, the d-d transition is the single broad absorption peak with a maximum at 20300 cm-1. This corresponds to a Δo value of 20300 cm-1. The complex has three d electrons, which will occupy the t2g orbitals. Therefore, the CFSE can be calculated as follows:

CFSE = -0.4 - 3 - 20300 cm-1 = -24360 cm-1

The negative sign indicates that the complex is more stable in the octahedral geometry than in the free ion state.

The splitting energy diagram for an octahedral complex is shown below. The t2g orbitals are lower in energy than the eg orbitals, and the CFSE is determined by the number of electrons in each set of orbitals. In the case of an [Ti(H2O)6]3+ complex, the three d electrons will occupy the t2g orbitals, resulting in a CFSE of -24360 cm-1.

[Image of splitting energy diagram for octahedral complex]