Page 130 - Modern Analytical Chemistry

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Chapter 5 Calibrations, Standardizations, and Blank Corrections 113

S samp S spike
= 5.9
A [
[
/
(
V s
C A C V o /( V o + V s )] + C V V o + )]
s
S
5
EXAMPLE .5
A fourth spectrophotometric method for the quantitative determination of the
concentration of Pb 2+ 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 Pb 2+
2+
standard, an S spike of 1.546 is measured. Determine the concentration of Pb in
the original sample of blood.
SOLUTION
The concentration of Pb 2+ in the original sample of blood can be determined
by making appropriate substitutions into equation 5.9 and solving for C A .
.
0 712 1 546
.
=
é ù é 3 – ù
.
.
C A 500 mL 500 ´ 10 mL
C A ê ú + 1560 ppb ê ú
–3
3 –
.
500 mL +
ë (. 5 00 ´10 mL) û ë (5.00 mL + 5.00 ´ 10 mL) û
.
0 712 1 546
.
=
.
0 9990C A + 1 558 ppb
.
C A

.
.
0 7113C A + 1 109 ppb = 1 546C A
.
.
C A = 133 ppb
2+
Thus, the concentration of Pb in the original sample of blood is 1.33 ppb.
The single-point standard additions outlined in Examples 5.4 and 5.5 are easily
adapted to a multiple-point standard addition by preparing a series of spiked sam-
ples containing increasing amounts of the standard. A calibration curve is prepared Colorplate 2 shows an example of a set of
by plotting S spike versus an appropriate measure of the amount of added standard. standard additions and their corresponding
Figure 5.7 shows two examples of a standard addition calibration curve based on standard additions calibration curve.
equation 5.6. In Figure 5.7(a) S spike is plotted versus the volume of the standard so-
lution spikes, V s . When k is constant, the calibration curve is linear, and it is easy to
show that the x-intercept’s absolute value is C A V o /C S .
5
EXAMPLE .6
Starting with equation 5.6, show that the equations for the slope, y-intercept,
and x-intercept in Figure 5.7(a) are correct.
SOLUTION
We begin by rewriting equation 5.6 as

kC V kC S
Ao
S spike = + ´ V s
V f V f
which is in the form of the linear equation
Y = y-intercept + slope ´X