Question 5.5: A fourth spectrophotometric method for the quantitative dete...
A fourth spectrophotometric method for the quantitative determination of the concentration of Pb²^+ in blood yields an S_{samp} of 0.712 for a 5.00-mL sample of blood. After spiking the blood sample with 5.00 mL of a 1560-ppb Pb²^+ standard, an S_{spike} of 1.546 is measured. Determine the concentration of Pb²^+ in the original sample of blood.
The concentration of Pb²^+ in the original sample of blood can be determined by making appropriate substitutions into equation 5.9 and solving for C_A.
\frac{s_{samp}}{C_A} =\frac{S_{spike}}{C_A[V_0/(V_0+V_s)]+C_S[V_s/(V_0+V_s)]} (5.9)
\frac{0.712}{C_A} =\frac{1.546}{C_A\left[\frac{5.00 ml}{\left(5.00 ml+5.00\times 10^{-3} ml\right) }\right] +1560 ppb\left[\frac{ 5.00 \times 10^{-3 ml}}{(5.00 ml + 5.00\times 10^{-3} ml)}\right] }
\frac{0.712}{C_A} =\frac{1.546}{0.9990C_A+1.558 ppb}
0.7113C_A+1.109 ppb=1.546C_A
C_A = 1.33 ppb
Thus, the concentration of Pb²^+ in the original sample of blood is 1.33 ppb.