Question

One of the complex ions below absorb the shortest wavelength of visible light equal to 429 nm.

(1) [CoI6]3-,   (2) [Co(H2O)6]3+,   (3) [Co(OH)6]3+,     (4) [Co(NH3)6]3+,     (5) [Co(en)3]3+.

Given the spectrochemical series, color(wavelength range), and the values of Plank's constant, h, and the speed of light, c, below;

I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < NO2- < CN-

Red(750-650)nm, Orange(650-580)nm, Yellow(580-560)nm,

Green(560-490)nm, Blue(490-430)nm, Violet(430-400)nm,

[h = 6.626 x 10-34 J·s, c = 2.998 x 108 m/s],

Place the answers to the following questions in the space provided.
If your answer(s) are in exponential form they should be entered as follows; 1.00 x 10-14 is entered as 1.00e-14.
Multiple colors may be input as blue-green, red-orange, etc.

The energy of absorption, ∆o=  J, the color observed=  ,

and the number of the complex ion from above is =

Answer 1

All the given complexes are octahedral.

Since the metal in is same all the five complexes ,that is, Co +3

Therefore we can use the spectrochemical series to get the idea about crystal field splitting energy or ∆o of each complex.

On arranging the ligand I-, OH-, H2O, NH3, en according to spectrochemical series, we observe that the maximum splitting of d orbitals into T25 and eg is observed in complex( 5).

Since energy

Thus, energy is inversely proportional to wavelength

Therefore the complex that has maximum crystal field splitting will have min wavelength absorbed. Since the absorbed wavelength is 429 nm and it belongs to violet region (430-400nm) the complex is (5). Since it shows maximumAbsorption.

Using artists color wheel, that gives the relationship between the color absorbed and complementary color reflected in visible region of light. We get that when violet color is absorbed , yellow color is reflected. This the complex (5)[ Co(en)3]3+ will be yellow in color.

The value of energy absorbed can be calculated by :

Co+3 has outer electronic configuration 3d6

t2g6 eg0 because en is a strong field ligand thus low spin complex is formed. Since t2g6 has 6 electrons and it is associated with -0.4 ∆o thus the complex has crystal field stabilisation energy energy =-0.4 ×6∆0= -2.4∆0.

Where ∆0 = 1/ wavelength=1/429 nm= 23310.023 cm-1

Thus CFSE = -2.4. * 23310.023 = 55944.055 cm-1

Enery of absorption= 55944.055 * h* c  

=1.11 * 10 raised to-18

1.11e -18 J

NOTE - c is converted into cm per s by multiplying the above value with 100.