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## Q. 5.3

A second spectrophotometric method for the quantitative determination of $Pb^{2+}$ levels in blood gives a linear normal calibration curve for which

$S_{stand} = (0.296 ppb^{–1}) × C_S + 0.003$

What is the $Pb^{2+}$ level (in ppb) in a sample of blood if $S_{samp}$ is 0.397?

## Verified Solution

To determine the concentration of $Pb^{2+}$ in the sample of blood, we replace $S_{stand}$ in the calibration equation with $S_{samp}$ and solve for $C_A$

$C_A=\frac{S_{samp}-0.003}{0.296 ppb^{-1}} =\frac{0.397-0.003}{0.296 ppb^{-1}}=1.33 ppb$

It is worth noting that the calibration equation in this problem includes an extra term that is not in equation 5.3.

$k = \frac{S_{\text{stand}}}{C_s}$        5.3

Ideally, we expect the calibration curve to give a signal of zero when $C_S$ is zero. This is the purpose of using a reagent blank to correct the measured signal. The extra term of +0.003 in our calibration equation results from uncertainty in measuring the signal for the reagent blank and the standards.