Question 5.7: A fifth spectrophotometric method for the quantitative deter...
A fifth spectrophotometric method for the quantitative determination of the concentration of Pb^{2+} in blood uses a multiple-point standard addition based on equation 5.6. The original blood sample has a volume of 1.00 mL, and the standard used for spiking the sample has a concentration of 1560 ppb Pb^{2+}. All samples were diluted to 5.00 mL before measuring the signal. A calibration curve of S_{spike} versus V_s is described by
S_{spike} = 0.266 + 312 mL^{–1} × V_s
Determine the concentration of Pb^{2+} in the original sample of blood.
S_{spike}=k\left\lgroup C_A\frac{V_0}{V_\mathrm{f}}+C_S\frac{V_s}{V_\mathrm{f}} \right\rgroup (5.6)
To find the x-intercept we let S_{spike} equal 0
0 = 0.266 + 312 mL^{–1} × (\text{x-intercept})
and solve for the ×-intercept’s absolute value, giving a value of 8.526 × 10^–4 mL.
Thus
\text{x-intercept}=8.526\times 10^{-4} ml =\frac{C_AV_0}{C_S} =\frac{C_A\times (1.00 ml)}{1560 ppb}
and the concentration of Pb^{2+} in the blood sample, C_A, is 1.33 ppb.