2nd order terms in purity calculations of reference standards
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jbladon! 1!
Second Order Terms in Purity Calculations of
Pharmaceutical Reference Standards!
jbladon! 2!
CASE I!
%Purity = 100% − %Water − %HPLC Impurities
Protocol requires using HPLC purity and! the water content to determine analyte purity!
?!
jbladon! 3!
CASE I!
%Purity = F
1F
2100%
Protocol requires using HPLC purity and! the water content to determine analyte purity!
F1 is the fraction of entire sample that is not water.
F2 is the fraction of sample excluding water that is analyte.
jbladon! 4!
Let,
A = Analyte*
Im = Impurities*
W = Water
Then,
F1 =A + Im
A + Im+W
⎛⎝⎜
⎞⎠⎟
, F2 =A
A + Im
⎛⎝⎜
⎞⎠⎟
F1F2 =A + Im
A + Im+W
⎛⎝⎜
⎞⎠⎟
A
A + Im
⎛⎝⎜
⎞⎠⎟=
A
A + Im+W
⎛⎝⎜
⎞⎠⎟
____________________ • Where each response factor is known or it is assumed they are identical
jbladon! 5!
%HPLC Impurities
100%=
Im
A + Im
⎛⎝⎜
⎞⎠⎟
Rearrange F2
F2 =A
A + Im
⎛⎝⎜
⎞⎠⎟=
A + Im− Im
A + Im
⎛⎝⎜
⎞⎠⎟= 1−
Im
A + Im
⎛⎝⎜
⎞⎠⎟
F2 = 1−%HPLC Impurities
100%
⎛⎝⎜
⎞⎠⎟
jbladon! 6!
%Water
100%=
W
A + Im+W
Rearrange F1
F1 =A + Im
A + Im+W
⎛⎝⎜
⎞⎠⎟=
A + Im+W −WA + Im+W
⎛⎝⎜
⎞⎠⎟
=A + Im+W
A + Im+W−
W
A + Im+W
⎛⎝⎜
⎞⎠⎟
F1 = 1−%Water
100%
⎛⎝⎜
⎞⎠⎟
jbladon! 7!
jbladon! 8!
%Purity = 1−%Water
100%
⎛⎝⎜
⎞⎠⎟
1−%HPLC Impurities
100%
⎛⎝⎜
⎞⎠⎟
100%
%Purity = 1−%Water
100%−
%HPLC Impurities
100%+
%Water
100%
⎛⎝⎜
⎞⎠⎟
%HPLC Impurities
100%
⎛⎝⎜
⎞⎠⎟
⎧⎨⎪
⎩⎪
⎫⎬⎪
⎭⎪100%
The Second Order Term
jbladon! 9!
Example
Let %Water = 2.5%
%HPLC Impurities = 5.0%
Then %Purity = {1- 0.025 - 0.050 + (0.025)(0.050)}100%
%Purity = 92.6%
If the second order term is omitted, %Purity = 92.5%
jbladon! 10!
CASE II
Protocol requires using the HPLC purity,!the water and solvent content, and!
the inorganic ion content !to determine analyte purity!
jbladon! 11!
1. Water Content by TGA!2. Solvent Content by Gas
Chromatography!3. Inorganic Ions by Ion Chromatography!4. Fraction of what is left by HPLC Purity!
jbladon! 12!
%Purity = 100% − %Water − %Solvent
− %Inorganic − %HPLC Impurities
?!
jbladon! 13!
%Purity = F
1F
2100%
F1 is the fraction of sample that is
not water/solvent/inorganic
F2 is the fraction of sample
excluding water/solvent/inorganic
that is analyte.
jbladon! 14!
Let,
A = Analyte*
IMP = Impurities*
W = Water
S = Solvent
IN = Inorganic
Then,
F1 =A + IMP
A + IMP + IN +W + S
⎛⎝⎜
⎞⎠⎟
, F2 =A
A + IMP
⎛⎝⎜
⎞⎠⎟
____________________ • Where each response factor is known or it is assumed they are identical
jbladon! 15!
F1F2=
A + IMP
A + IMP +W + S + IN
⎛⎝⎜
⎞⎠⎟
A
A + IMP
⎛⎝⎜
⎞⎠⎟
F1F2=
A
A + IMP +W + S + IN
⎛⎝⎜
⎞⎠⎟
jbladon! 16!
%HPLC Impurities
100%=
IMP
A + IMP
Rearrange F2
F2 =A
A + IMP
⎛⎝⎜
⎞⎠⎟=
A + IMP − IMPA + IMP
⎛⎝⎜
⎞⎠⎟
F2 =A + IMP
A + IMP−
IMP
A + IMP
⎛⎝⎜
⎞⎠⎟
F2 = 1−%HPLC Impurities
100%
jbladon! 17!
%Water / Solvent
100%=
W + S
A + IMP +W + S + IN
%IN
100%=
IN
A + IMP +W + S + IN
Rearrange F1
F1 =A + IMP
A + IMP +W + S + IN
⎛⎝⎜
⎞⎠⎟=
F1 =A + IMP +W + S + IN −W − S − IN
A + IMP +W + S + IN
⎛⎝⎜
⎞⎠⎟
F1 =
A + IMP +W + S + IN
A + IMP +W + S + IN−
W + S
A + IMP +W + S + IN
−IN
A + IMP +W + S + IN
⎛
⎝
⎜⎜⎜
⎞
⎠
⎟⎟⎟
F1 = 1−%Water / Solvent
100%−
%IN
100%
jbladon! 18!
%Purity = 1−%Water / Solvent
100%−
%IN
100%
⎛⎝⎜
⎞⎠⎟
x 1−%HPLC Impurities
100%
⎛⎝⎜
⎞⎠⎟
100%
jbladon! 19!
%Purity =
1−%Water/Solvents
100%−
%IN
100%−
%HPLC Impurities
100%
+%Water/Solvents
100%
⎛⎝⎜
⎞⎠⎟
%HPLC Impurities
100%
⎛⎝⎜
⎞⎠⎟
+%IN
100%
⎛⎝⎜
⎞⎠⎟
%HPLC Impurities
100%
⎛⎝⎜
⎞⎠⎟
⎧
⎨
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎫
⎬
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
100%
The Second Order Terms
jbladon! 20!
Example
Let %Water/Solvent = 2.5%
%Inorganic = 5.0% %HPLC Impurities = 5.0%
Then
%Purity = {1- 0.025 - 0.050 - 0.050 + (0.025)(0.050) + (0.050)(0.050)}100%
%Purity = 87.9%
If both second order terms are omitted, %Purity = 87.5%
jbladon! 21!
Dr. Wiley and the Division of Chemistry Staff in 1883.
Wiley, third from right, was 37. Courtesy Wallace F. Janssen FDA Historian
Meet the Boys of the FDA
jbladon! 22!
If you have a question about an equation to calculate the purity of a reference standard in a protocol or method, see your supervisor and
bring my handouts for this presentation
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