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## Q. 4.6

One way to determine the concentration of $Fe^{2+}$ in an environmental sample is to add  solution of phenanthroline (phen) molecules that will bond to the metal ions, creating an intensely orange-red solution (Figure 4.10). The absorbance of a $5.00 × 10^{-5} M$ solution is measured as 0.55 in a 1.00 cm cell. (a) Calculate the molar absorptivity, ε, and (b) determine the concentration of such a solution whose absorbance is 0.36. ## Verified Solution

Collect and Organize Given the concentration and absorbance of a solution, we are asked to calculate the molar absorptivity (ε).

Analyze (a) We can rearrange Beer’s law to solve for ε and then use this value to find the concentration of the unknown solution. (b) Concentration and absorbance are linearly related by Beer’s law, so we predict that a smaller absorbance for the unknown solution should correspond to a lower concentration. (In fact, a concentration of zero would correspond to zero absorbance.)

Solve
a. Rearranging Equation 4.4 and substituting for A, b, and c:

$\varepsilon =\frac{A}{bc} =\frac{0.55}{(1.00 cm)(5.00\times 10^{-5} M)} =1.1\times 10^{4} M^{-1} cm^{-1}$

b. Solving Beer’s law for concentration and substituting for A, b, and ε:

$c=\frac{A}{\varepsilon b}=\frac{0.36}{(1.1\times 10^{4} M^{-1} \cdot \sout{cm^{-1}})(1.00 \sout{cm})}=3.3 \times 10^{-5} M$

Think About It As predicted, the concentration of the unknown solution is lower than $5.00\times 10^{-5} M$