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EPA 903/9-80-004
U.S. ENVIRONMENTAL PROTECTION AGENCY
METHOD OF STANDARD ADDITIONS
AND EFFECTS OF DILUTION
May 1980
Annapolis Field Office
Region III
U.S. Environmental Protection Agency
EPA Report Collection
Information Resource Center
US EPA Region 3
Philadelphia, PA 19107
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Method of Standard Additions
and Effects of Dilution
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• May 1980
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£ Joseph Lee Slayton
E. Ramona Trovato
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Annapolis Field Office
I Region III
U.S. Environmental Protection Agency
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The method of standard additions is useful when the matrices
P of standards and samples differ significantly. The method of additions
Mm may involve additions of small quantities of the analyte to the sample
with no significant dilution of the sample or cases which involve
• significant sample dilution. In general, a plot is made of absorbance
versus added concentration and the value of the X-intercept is taken
'| as the analyte concentration.
. The method of standard addition eliminates interferences that
cause constant multiplicative errors in the concentration of analyte
I measured. As an example of this type of interference, consider a
sample with a true analyte concentration of 1.0 ppm. The analyst
| assays the sample and determines a concentration of 0.5 mg/1 indicating
_ an interference factor of .5. (This is a. negative interference since
™ the interference factor is "less than 1.) The sample is spiked with
I small quantities of the analyte to produce an added concentration of
1.0 ppm and 2.0 ppm and values of 1 ppm and 1.5 ppm, respectively,
• are obtained. From these results the analyst decides there is an
_ interference and plots the data (Figure 1).
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Figure 1. Data and Plot of Method of Standard Additions
Concentration of analyte
added after dilution
by sample
(mg/1)
0
1
2
*Measured
Concentration
Ong/1)
.5
1.0
1.5
**Measured
Absorbance
.05
.10
.15
*This represents an interference factor of .5.
**The standard curve had a slope of .1 and a /-intercept of zero.
t Absorbance
.3
.2
.1
-2.0 -1.0
1.0 2.0
Amount Added
(Concentration, mg/1)
Scale of negative concentration
values and positive concentration
values must be' the same.
The extrapolation of the line to the X-intercept generates the actual
concentration of the sample (ignoring the negative sign).
The addition of small known quantities of the analyte or "spiking"
to determine sample concentration is based upon the Beer's Law
relationship: the absorbance is directly proportional to the concentration
of the analyte present (Figure 2) .
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Figure 2. Plot of Absorbance vs Concentration with Application of Beer's Law
1
1
!• Absorbance Ab^-^
*5^^
^^ Concentration
[ t
0 IX+ISo IX+ISi
I Beer's Law:
Abo Abi
• IX -f IS0 = IX f ISi
: or
KX = (Ab0) (Si) I
Abi -Ab0 I
;
or
where: Abo = Absorbance of solution
with concentration =
IX + IS0
Abi = Absorbance of solution with
concentration = IX + ISi
I = Interference factor (constant
multiplicative error)
S0 s 0 spike addition = 0
Si - Concentration of analyte added
after dilution by the
volume (sample volume
total
+ spike
X = Ab0Si / (Abi - Ab0) volume)
.
The sample concentration may
• proportion (Figure 2) . The
X = Concentration of analyte in
sample
be determined by solving for x in the
method of standard additions plot
may be generalized (Figure 3) :
1 Figure 3. Generalized Plot of Method of Standard Additions
1
1 ^>
^^^
• Absorbance
^^^'"
^^^
Amount Added
M, X1 S0 Si (Concentration)
y = mX + b
Iat y = o
X1 = -b/m
b = Ab0
_ m =(Abi - Ab0)/ Si
• X1 = -Ab0Si / (Abi ~ Abo)
where: Abo = Absorbance of solution with
zero analyte addition
Abi = Absorbance of solution
associated with addition of
spike of Si
S0 = 0 spike addition
•" Si = Concentration of analyte added
1
after dilution by the
volume (sample volume
volume)
total
+ spike
X1 = Method of standard addition
determined concentration of
analyte in sample
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• Again, a linear relationship based upon Beer's Law is assumed. A linear
relation is defined: y = mX+b; where y is the absorbance, X is the concentration,
J m is the slope, and b is the y-intercept. At the X-intercept, y = o and X1 =
^ -b/m, or X1 = -AboSi/Abi-Abo- The extrapolation generates the same numerical
• value (but negative in sign) as the true result and is therefore apol-icable to
• additions of small volumes of analyte. The interference free (true) result
was obtained from the Beer's Law relation because of the constant nature of
• the interference.
_ A problem arises in using the extrapolation method when significant
* and varying dilutions of the sample by the addition of the spike are involved.
• The spiked samples are prepared by adding a significant volume of analyte and
diluting to a pre-set volume with the sample (i.e., 1. establish a pre-set
£ volume, for example, 100 ml; 2. for the first spiked sample, add 2 ml of
analyte of a known concentration and add 98 ml of sample to bring the total
• volume to 100 ml; 3. for the second spiked sample, add 4 ml of analyte of the
• same known concentration and add 96 ml of sample to bring the total volume
to 100 ml; etc.).The results obtained from this method of standard additions
• are incorrect because the concentration of the interferent varies in each
spiked sample aliquot. In order to accurately determine the analyte
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concentration, the concentration of the interferent must be kept constant.
This can be accomplished by following the EPA method of standard additions.
4.
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The results of the EPA method of standard additions outlined in the
1974 and 1979 editions of the EPA Manual of. Methods of. Chemical Analysis
• of Water and Wastes* may be effected by dilution. The EPA method requires
that a constant volume of sample be added to a constant volume of standards
I and blank. If the volume of sample consistently used is V and the volume
m of standards and blank is consistantly v where V f v, this experiment may
be generalized to that presented in Figures 4(1) and 4(2).
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Petal's section page 12, 1979 EPA Manual of Methods of Chemical Analysis
m of Water and Wastes
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Figure 4(1). Correct result obtained using Beer's Law coupled with
the Dilution and Interference Factors and Using the
Procedure outlined by EPA
V
1 v blk
V
v std #1
V
v std #2
V
v std #3 1
Absorbance
Ab]
Abc
Concentration
IFX+IZT0
IFX+IZTi
where:
Abr
Abj
IPX + IZTO IFX
or X = Z -AbpTj
F
but; Z/F = v/V
V
v
F
z
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T]_
Ab
therefore; X = v
True V
AbQTi
Abi-Abo
Volume of sample
Volume of standard or blank
V/CV+v)
V/CY+V)
Any interference factor
Concentration of the analyte
in the blank = 0
Concentration of the analyte
in standard #1 (S1=ZTi)
Absorbance associated with
the concentration:
IFX+JZT0
Absorbance associated with
the concentration:
X = Sample concentration
6.
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Figure 4(2). Incorrect result obtained using the Method of Standard
Additions as outlined by EPA, where V •£ v, (an example
is included in the appendix).
1
i v blk
V
v std #1
V
v std #2i
V !
v std #3i
•• Absorbance
where:
y - mXl+b
m = Ay/ AX
b = y-intercept
at y=o, X:=-b/m
therefore; X^C
Ab
V =
v =
TO =
TI =
Ab =
Abi-Ab0
Abj-Ab0
Amount Added
(Concentration)
Volume of sample
Volume of standard or blank
Concentration of the analyte
in the blank = 0
Concentration of the analyte
in standard #1
Absorbance associated with
zero analyte addition
Absorbance associated with
addition of a concentration
of Tj_
Method of standard addition
determined concentration of
analyte in sample
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These results indicate that if v jt V, this method of standard additions
does not yield accurate results. The results of extrapolation may
be corrected by a factor, -(v/V):
X -(Xl)Cv/VH-l)
True
If the "Amount Added" is interpreted as the concentration of
standard corrected for dilution by the sample, the true result remains:
X = Z Ab0Ti
True F Ab-A
the extrapolation becomes:
X1 = -Ab0
(See Figure 5)
Figure S. Incorrect result obtained using the Method of Standard
Additions when Dilution of the Sample by the Spike is
Disregarded (V ^ v)
h Absorbance
Amount Added
(Concentration)
where:
y = mX+b
m = Ay/AX =
b = Ab0
at y=o, X =-b/m
X^C-Abp ZTl)
V
v
F
Z
Ab
X1 =
Volume of sample
Volume of standard or blk
V/CV+v)
v/CV+v )
Concentration of the analyte
in standard #1 (Si=ZTi)
Absorbance associated with
zero standard addition
Afasorbance associated with
addition of a concentration
of ZTi
Method of standard addition
determined concentration of
analyte in sample
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1
fl The result of the extrs
by a factor: X =
• True
The EPA method of
ipolation, X1 = (-Ab0) (ZTi) , may be corrected
Abi -Ab0
[X^C-l ) , where F = V/(v+V).
F
standard additions yields accurate results
Iwhen v = V. In this case F = V - Z - v and Beer's Law with
v+V v-t-V
- correction for dilution yields the result:
•. Ab0 = Ab^ or X = AboTi
IPX IPX +IETi True Abi-Abo
1 which is the same result obtained from a plot of absorbance vs the
_~ concentration of the analyte in the added standard (See Figure 6) .
1
Figure 6. Plot of Absorbance vs Concentration Added when V=v
'•; Correct result
1
•A AD^,^-
1^
'
• Absorbance ~
^
Xa T0 TI (Concentration)
1
w
y = mX+b
at y = 0, X1 = -b/m
b = Ab0
where: V = Volume of sample
v = Volume of standard or blank
TI = Concentration of the analyte
in standard #1
Abo = Absorbance associated with
Im = Ay/ AX ~ (Abi - Ab0)/T^ zero standard addition
X1 = (-Abp) (Ti) / (Abi - Abo) Abl = Absorbance associated with
X (X*) (v/V) (-1)
ITrue
,
X = (X:)(-l)
True
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1
and v = V; addition of a concentration
of TI
X = True concentration of analyte
in sample
X1 = Method of standard addition
determined concentration of
analyte in sample
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The EPA method of standard additions does not account for the
'• dilution of sample by the standard except when:
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1. The volume of sample used is the same as the volume of standard,
V = v.
2, Zero analyte was initially present, Ab0 = 0.
• 3. No dilution of sample by standard occurs (insignificant
volumes, e.g. microliter of standard and blank are used and
£ diluted to a constant volume with sample).
« If the volumes of sample and standard are significant and unequal,
the extrapolation will only yield accurate results if a correction
M factor is employed (an example is included in the Appendix).
In conclusion, the method of standard addition does not necessarily
£ correct for dilutions resulting from the addition of the analyte.
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10.
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^B
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A 1.0 mg/1 phenol reference
antipyrine method. The results
and from the method of standard
Standard Calibration Curve
Concentration
(mg/1)
0
.2
.5
.7
1.0
2.0
3.0
4.0
The reference sample had an
1.0 mg/1 based upon the standard
Standard Method of Additions
Twenty milliliters of sampl
Appendix
sample was analyzed using the 4-amino
obtained from a standard calibration curve
additions follow.
Absorbance
.000
.029
.070
.098 correlation coefficient = .999
slope = .140
.142 y-intercept = -.000346
.272
.421
.562
absorbance of 0.142 which corresponds to
calibration curve.
e were placed into each of four flasks. To
flask #1, 80 ml of deionized water were added. To flask #2, 80 ml of a 0.5 mg/1
phenol solution were added. To
were added. To flask #4, 80 ml
flask #3, 80 ml of a 1.0 mg/1 phenol solution
of a 2.0 mg/1 phenol solution were added. The
concentrations added and absorbances obtained are tabulated in Table I.
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Table I
Flask No.
1
2
3
4
Concentration Added
(mg/1)
0
correlation coefficient
.084 slope = .112
y-intercept = .027
.138 at y = o, x = -.240
Absorbance
.027
.5
1.0
2.0 .252
The result obtained from a plot of the data in Table I is 0.240 rag
phenol/1. This value is incorrect due to the dilution of the sample by the
spike. The actual concentration may be obtained by multiplying the value
of the x-intercept by v/V (see Equation 1), where v is the spike volume and
V is the sample volume.
Actual Concentration = (Value of the x-intercept)(-1)(v/V) Equation 1
In this example, the actual concentration = (-.240)(-1)(80/20) = 0.96 mg/1.
, Alternatively, the concentrations of the standards added may be corrected
for dilution by the sample. In Table II, the added concentrations corrected
for dilution by the sample and corresponding absorbances are listed. (Tables I
and II are identical except that the concentrations added have been corrected
for dilution by the sample in Table II).
.9999
Flask No.
1
2
3
4
Table II
Added Cone. Corrected
for Dilution
(mg/1)
0
.4
1.6
Absorbance
.027
correlation coefficient = .999
.084 slope = .140
y-intercept = .027
.138 at y = o,x = -.192
.252
1.2.
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I The result obtained from a plot of the data in Table II is 0.192 mg/1.
— Again an incorrect result is generated. The actual value may be obtained by
multiplying the x-intercept by (v+V)/v, where v is the spike volume and V is
• the sample volume (see Equation 2).
f Actual Concentration = (Value of the x-intercept)(-1)(v+V)/v Equation 2
* In this example, the actual concentration = (-.192)(-1)(100/20) =0.96 mg/1.
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13,
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA 903/9-80-004
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
METHOD OF STANDARD ADDITIONS AND EFFECTS OF DILUTION
5. REPORT DATE
May 1980
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
J. L. Slayton
and E. R. Trovato
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME ANO ADDRESS
Annapolis Field Office, Region III
U.S. Environmental Protection Agency
Annapolis Science Center
Annapolis. Maryland 214Q1
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME ANO ADDRESS
same
13. TYPE OF REPORT ANO PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/903/00
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The basis and limitation of the Method of Standard Addition is discussed
with particular emphasis placed on the effects of dilution often encountered
in using this analytical tool. Dilutions employed when using Standard Additions
may effect the sample matrix. This problem may be avoided by maintaining a
constant sample dilution. If' significant dilution of the sample is involved,
a dilution factor must be applied to obtain the correct result by the Method
of Standard Additions.
17.
KEY WORDS ANO DOCUMENT ANALYSIS
DESCRIPTORS
b.lOENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Standard Addition
Beer's Law
Interference
Spike
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThaReport)
UNCLASSIFIED
21. NO. OF PAGES
13
20. SECURITY CLASS (This page/
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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