Chapter 5 - Analytical Sciences Digital Library

162 Analytical Chemistry 2.0
add V o of C A
add V std of C std
Figure 5.5 Illustration showing the method of standard
additions. The volumetric flask on the left contains
a portion of the sample, V o , and the volumetric
flask on the right contains an identical portion of the
sample and a spike, V std , of a standard solution of the
analyte. Both flasks are diluted to the same final volume,
V f . The concentration of analyte in each flask is
shown at the bottom of the figure where C A is the analyte’s
concentration in the original sample and C std is
the concentration of analyte in the external standard.
Concentration
of Analyte
C
A
dilute to V f
Vo
× C
V
f
A
V V
o
× + C ×
std
V V
f
std
f
The ratios V o /V f and V std /V f account for
the dilution of the sample and the standard,
respectively.
S
k C V o
= 5.7
V
samp A A
f
V V
o
std
S k C C
spike
=
Af A
+ V
std
p V 5.8
f
f
As long as V std is small relative to V o , the effect of the standard’s matrix on
the sample’s matrix is insignificant. Under these conditions the value of k A
is the same in equation 5.7 and equation 5.8. Solving both equations for
k A and equating gives
S
samp
C V A
V
o
f
=
C V A
V
o
f
S
spike
+ C
which we can solve for the concentration of analyte, C A , in the original
sample.
Example 5.3
A third spectrophotometric method for the quantitative analysis of Pb 2+ in
blood yields an S samp of 0.193 when a 1.00 mL sample of blood is diluted
to 5.00 mL. A second 1.00 mL sample of blood is spiked with 1.00 mL of
a 1560-ppb Pb 2+ external standard and diluted to 5.00 mL, yielding an
std
V V
std
f
5.9