Page 128 - Modern Analytical Chemistry

1400-CH05 9/8/99 3:59 PM Page 111

Chapter 5 Calibrations, Standardizations, and Blank Corrections 111

Add V of C A Add V of C A Add V of C S
S
o
o

Dilute to V f Dilute to V f

Figure 5.5
Illustration showing the method of standard
Total concentration Total concentration additions in which separate aliquots of
of analyte of analyte sample are diluted to the same final volume.
One aliquot of sample is spiked with a
V o V o V S
C C + C known volume of a standard solution of
A
V f A V f S V f analyte before diluting to the final volume.

tion is shown in Figure 5.5. A volume, V o , of sample is diluted to a final volume,
V f , and the signal, S samp is measured. A second identical aliquot of sample is aliquot
spiked with a volume, V s , of a standard solution for which the analyte’s concen- A portion of a solution.
tration, C S , is known. The spiked sample is diluted to the same final volume and
its signal, S spike , is recorded. The following two equations relate S samp and S spike to
the concentration of analyte, C A , in the original sample

V o
S samp = kC A 5.5
V f
æ V o V s ö
S spike = k C A + C S ÷ 5.6
ç
è V f V f ø
where the ratios V o /V f and V s /V f account for the dilution. As long as V s is small rela-
tive to V o , the effect of adding the standard to the sample’s matrix is insignificant,
and the matrices of the sample and the spiked sample may be considered identical.
Under these conditions the value of k is the same in equations 5.5 and 5.6. Solving
both equations for k and equating gives

S samp S spike
=
S ( /
A (
A (
o /
o /
CV V f ) CV V f ) + C V V f ) 5.7
s
Equation 5.7 can be solved for the concentration of analyte in the original sample.