Q.36 An aqueous solution contains two compounds X and Y. This solution gave absorbance values of
1.0 and 0.4 at 220 and 280 nm, respectively, in a 1 cm path length cell.
Molar absorption coefficients (ε) of the compounds X and Y are as shown in the table below.
| Compound | ε220 (M−1 cm−1) | ε280 (M−1 cm−1) |
|---|---|---|
| Compound X | 1000 | 200 |
| Compound Y | 800 | 400 |
The concentration of Y in the solution is ________ mM.
Given Data
| Compound | ε220 (M−1 cm−1) | ε280 (M−1 cm−1) |
|---|---|---|
| X | 1000 | 200 |
| Y | 800 | 400 |
Path length, l = 1 cm
Concept: Beer–Lambert Law
The Beer–Lambert law is given by:
A = εlc
For a mixture of two absorbing species:
A = εXcX + εYcY
Step-by-Step Calculation
Equation at 220 nm
A220 = 1.0
1.0 = (1000)cX + (800)cY
Equation at 280 nm
A280 = 0.4
0.4 = (200)cX + (400)cY
Solving the Equations
Multiply the second equation by 5:
1000cX + 2000cY = 2
Subtract the first equation:
1200cY = 1
cY = 1 / 1200 = 8.33 × 10−4 M
Final Answer
Concentration of compound Y = 0.833 mM
Conclusion
By applying the Beer–Lambert law at two different wavelengths and solving the
simultaneous equations, the concentration of compound Y in the mixture is found
to be 0.833 mM. This method is essential for analyzing multi-component solutions
in spectroscopy.
