Avaliação de Dados Analíticos

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23Chapter 4 Evaluating Analytical Data
nominal dosage z
% exceeding 
nominal dosage
100-mg 2.06 1.97
60-mg 2.15 1.58
30-mg 1.92 2.74
10-mg 7.21 —
 For tablets with a 10-mg nominal dosage, the value of z is suiciently 
large that efectively no tablet is expected to exceed the nominal dos-
age.
4. he mean and the standard deviation for the eight spike recoveries are 
99.5% and 6.3%, respectively. As shown in Figure SM4.3, to ind the 
expected percentage of spike recoveries in the range 85%–115%, we 
ind the percentage of recoveries that exceed the upper limit by calcu-
lating z and using Appendix 3 to ind the corresponding probability
.
. . . %z
X
6 3
115 99 5 2 46 0 695orv
n
=
-
=
-
=
 and the percentage of recoveries that fall below the lower limit
.
. . . %z
X
6 3
85 99 5 2 30 1 07orv
n
=
-
=
-
=-
 Subtracting these two values from 100% gives the expected probabil-
ity of spike recoveries between 85%–115% as 
% . % . % . %100 0 695 1 07 98 2- - =
5. (a) Substituting known values for the mass, the gas constant, the tem-
perature, the pressure, and the volume gives the compound’s formula 
weight as
( . ) ( . )
( . ) ( . ) ( . )
.FW
0 724 0 250
0 118 0 082056 298 2
16 0
atm L
g
mol K
L atm K
g/mol:
:
= =
 To estimate the uncertainty in the formula weight, we use a propaga-
tion of uncertainty. he relative uncertainty in the formula weight is
.
.
.
.
.
.
.
.
.
.
.FW
u 0 118
0 002
0 082056
0 000001
298 2
0 1
0 724
0 005
0 250
0 005
0 0271FW
2 2
2 2 2=
+ +
+ +
=
`
a
a
a a
j
k
k
k k
 which makes the absolute uncertainty in the formula weight
. . .u 0 0271 16 0 0 43g/mol g/molFW #= =
 he formula weight, therefore, is 16.0±0.4 g/mol.
 (b) To improve the uncertainty in the formula weight we need to 
identify the variables that have the greatest individual uncertainty. 
he relative uncertainties for the ive measurements are
80 90 100 110 120
% recovery
Figure SM4.3 Normal distribution curve 
for Problem 4.4 given a population with a 
mean of 99.5% and a standard deviation of 
6.3%; the area in blue is the probability that 
a spike recovery is between 85% and 115%.