Analytical Chem istry - DePauw University

166 Analytical Chemistry 2.0where Y is S spike and X is V std . The slope of the line, therefore, is k A C std /V fand the y-intercept is k A C A V o /V f . The x-intercept is the value of X whenY is zero, orkCV kCA A o A std0 = + × x-interceptV VffkCVA A oV CVfAx-intercept=− =−kCA stdCstdVfoPractice Exercise 5.2Beginning with equation 5.8 show that the equations in Figure 5.7b forthe slope, the y-intercept, and the x-intercept are correct.Click here to review your answer to this exercise.Because we know the volume of the original sample, V o , and the concentrationof the external standard, C std , we can calculate the analyte’s concentrationsfrom the x-intercept of a multiple-point standard additions.Example 5.6A fifth spectrophotometric method for the quantitative analysis of Pb 2+in blood uses a multiple-point standard addition based on equation 5.8.The original blood sample has a volume of 1.00 mL and the standard usedfor spiking the sample has a concentration of 1560 ppb Pb 2+ . All sampleswere diluted to 5.00 mL before measuring the signal. A calibration curveof S spike versus V std has the following equationS spike = 0.266 + 312 mL –1 × V stdWhat is the concentration of Pb 2+ in the original sample of blood.So l u t i o nTo find the x-intercept we set S spike equal to zero.0 = 0.266 + 312 mL –1 × V stdSolving for V std , we obtain a value of –8.526 × 10 –4 mL for the x-intercept.Substituting the x-interecpt’s value into the equation from Figure 5.7a− × =− =− ×−4CV C 100 . mLA oA8.526 10 mLC 1560 ppband solving for C A gives the concentration of Pb 2+ in the blood sampleas 1.33 ppb.std