SME
Inorganic Chemistry · Problem type
Splitting from the color absorbed
Use this for “[Ti(H₂O)₆]³⁺ absorbs most strongly at 500 nm. Find Δₒ in cm⁻¹ and in kJ/mol. What color does the solution look?”
Diagram
λ
=
c/f
=
3 ×
10
8
/(6
×
10
14
)
λ = 500 nm
E
=
hf
=
6.626 ×
10
-34
×
6 ×
10
14
E
=
3.98 ×
10
-19
J
In
electronvolts:
3.98 ×
10
-19
/(1.602
×
10
-19
)
=
2.48
eV
Higher frequency, shorter wavelength, more energy per photon: blue photons carry more than red.
This is an example. Type your own values to start a new problem.
Δₒ
cm⁻¹
=
10⁷
÷
λ
nm
Eₘ
Energy per mole of photons
calculated · kJ/mol
Formulas
Δₒ
=
10
7
λ
20,000
=
10
7
500
Eₘ = 0.011963 × Δₒ
239.26 = 0.011963 × 20,000
Assumptions
•
A d¹ ion has one d–d band: the photon absorbed lifts its electron from t₂g to eg, so its energy is Δₒ.
•
Δₒ in cm⁻¹ is the wavenumber 1 ÷ λ, so 10⁷ ÷ λ with λ in nm (1 cm is 10⁷ nm).
•
One cm⁻¹ per mole of photons is hcNA = 0.011963 kJ/mol (c = 2.998 × 10¹⁰ cm/s).
•
The color seen is the light left over: the complement of the color absorbed.
Step-by-step
WE KNOW
λ = 500 nm
FIND
splitting (Δₒ), energy per mole of photons (Eₘ)
Step 1 · Find splitting (Δₒ)
Use Δₒ = 10⁷ ÷ λ
The
wavenumber
is
1
λ
;
with
λ
in
nm,
10
7
nm
make
1
cm.
Δₒ
=
10
7
500
Δₒ
=
10,000,000
500
Δₒ = 20,000 cm⁻¹ → It absorbs green light, so it looks red-violet, the light left over.
Step 2 · Find energy per mole of photons (Eₘ)
Use Eₘ = 0.011963 × Δₒ
Each cm⁻¹ is hc per photon, times NA for a mole, in kJ.
Eₘ = 0.011963 × 20,000
Eₘ = 239.26 kJ/mol
Check
Put the numbers back in. Both sides should match.
20,000
=
10
7
500
✓
239.26 = 0.011963 × 20,000 ✓
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