## Chapter 17

## Q. 17.4

**Serum Iron Analysis**

Serum iron and standard iron solutions were analyzed as follows:

**Step 1** To 1.00 mL of sample, add 2.00 mL of reducing agent and 2.00 mL of acid to reduce and release Fe from transferrin.

**Step 2** Precipitate proteins with 1.00 mL of 30 wt% trichloroacetic acid. Centrifuge the mixture to remove protein.

**Step 3** Transfer 4.00 mL of supernatant liquid to a fresh test tube and add 1.00 mL of solution containing ferrozine and buffer. Measure the absorbance after 10 min.

**Step 4** To establish each point on the calibration curve in Figure 17-9, use 1.00 mL of standard containing 2–9 μg Fe in place of serum.

The blank absorbance was 0.038 at 562 nm in a 1.000-cm cell. A serum sample had an absorbance of 0.129. After the blank was subtracted from each standard absorbance, the points in Figure 17-9 were obtained. The least-squares line through the standard points is

Absorbance = 0.067_{0} × (μg Fe in initial sample) + 0.001_{5}

According to Beer’s law, the intercept should be 0, not 0.001_{5}. We will use the small, observed intercept for our analysis. Find the concentration of iron in the serum.

## Step-by-Step

## Verified Solution

Rearranging the least-squares equation of the calibration line and inserting the corrected absorbance (observed − blank = 0.129 − 0.038 = 0.091) of unknown, we find

μg Fe in unknown = \frac{absorbance − 0.001_{5}}{0.067_{0}} = \frac{0.091 − 0.001_{5}}{0.067_{0}} = 1.33_{6} μg

The concentration of Fe in the serum is

[Fe] = moles of Fe/liters of serum

= (\frac{1.33_{6} × 10^{−6} g Fe}{55.845 g Fe/mol Fe})/(1.00 × 10^{−3} L) = 2.39 × 10^{−5} M

* Test Yourself* If the observed absorbance is 0.200 and the blank absorbance is 0.049, what is the concentration of Fe (μg/mL) in the serum? (

*2.23 μg/mL)*

**Answer:**To find the uncertainty in μg Fe, use Equation 4-27.

Uncertainty in x (= s_{x}) = \frac{s_{y}}{\left|m\right| }\sqrt{\frac{1}{k} + \frac{1}{n} + \frac{(y − \overline{y} )^{2}}{m² \sum{(x_{i} − \overline{x} )^{2}} }} **(4-27)**