A metal element (M) forms a hexadentate complex with the ligand ethylenediammine (en). Its formula is M(en)32+. The metal ion and the ligand do not absorb in the visible region of spectrophotometer and a 1.00 cm cuvette, the following absorbances were measured for various concentrations of the metal and the ligand:
[M2+] M---------[en] M-----------Absorbance at 450 nm
1.0 x 10-5------1.0 x 10-5------------0.03
2.0 x 10-5------4.0 x 10-5------------0.12
3.0 x 10-5------9.0 x 10-5------------ 0.27
4.0 x 10-5------6.0 x 10-5------------ 0.18
5.0 x 10-5------10.0 x 10-5---------- 0.30
6.0 x 10-5------18.0 x 10-5---------- 0.54
7.0 x 10-5------25.0 x 10-5---------- 0.63
8.0 x 10-5------20.0 x 10-5---------- 0.60
a.) Calculate the absorbance (same as extinction) coefficient for the complex at 450 nm
b.) What would be the absorbance of a solution with [M2+] = 2.5 x 10-5 M and [en] = 7.0 x 10-5 M ?
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To calculate the absorbance coefficient for the complex at 450 nm, we need to use the Beer-Lambert Law, which states that absorbance (A) is directly proportional to the concentration (c) of the absorbing species and the path length (l) of the cuvette. Mathematically, it can be expressed as:
A = ε l c
where ε is the molar absorptivity (also known as the absorbance coefficient), l is the path length (given as 1.00 cm), and c is the concentration.
To calculate the molar absorptivity (ε), we can rearrange the formula to:
ε = A / (l x c)
For this question, we can use the data provided to calculate the molar absorptivity (ε) at 450 nm.
We can choose any set of concentrations and their corresponding absorbance values to calculate the molar absorptivity.
Let's choose the set [M2+] = 1.0 x 10-5 M and [en] = 1.0 x 10-5 M. The absorbance at 450 nm is 0.03.
Plugging in the values, we have:
ε = 0.03 / (1.00 cm x 1.0 x 10-5 M)
ε = 3.0 x 10^3 (M^-1 cm^-1)
Therefore, the absorbance coefficient for the complex at 450 nm is 3000 M^-1 cm^-1.
b.) To calculate the absorbance of a solution with [M2+] = 2.5 x 10-5 M and [en] = 7.0 x 10-5 M, we can use the absorbance coefficient calculated in part a and the Beer-Lambert Law.
A = ε l c
Plugging in the values, we have:
A = (3000 M^-1 cm^-1) x (1.00 cm) x (2.5 x 10-5 M)
A = 0.075
Therefore, the absorbance of the solution with [M2+] = 2.5 x 10-5 M and [en] = 7.0 x 10-5 M would be 0.075.