Page 206 - Modern Analytical Chemistry

1400-CH07 9/8/99 4:03 PM Page 189

Chapter 7 Obtaining and Preparing Samples for Analysis 189

ated by determining R using several samples of similar mass. Once K s is known, the
mass of sample needed to achieve a desired relative standard deviation for sampling
can be calculated.

7
EXAMPLE .6
The following data were obtained in a preliminary determination of the
amount of inorganic ash in a breakfast cereal.

Mass of Cereal Percentage Ash
(g) (w/w)
0.9956 1.34
0.9981 1.29
1.0036 1.32
0.9994 1.26
1.0067 1.28

Determine K s and the amount of sample needed to give a relative standard
deviation for sampling of ±2.0%. Predict the percent relative standard
deviation and the absolute standard deviation if samples of 5 g are collected.
SOLUTION
To determine K s we need to know the average mass of the cereal samples and
the relative standard deviation for the %(w/w) ash. The average mass of the five
cereal samples is 1.0007 g. The average %(w/w) ash and the absolute standard
deviation are, respectively, 1.298% and 0.03194. The percent relative standard
deviation, therefore, is

0 03194
.
s s
2
R = ´100 = ´100 =46.%
.
X 1 298
Thus
2
2
K s = mR = (1.0007 g)(2.46) = 6.06 g
The amount of sample needed to give a relative standard deviation of ±2%,
therefore, is
.
606 g
K s
m = 2 = 2 =15 . g
20)
R (.
If we use 5.00-g samples, then the expected percent relative standard deviation is
.
606 g
K s
R = = =110.%
.
m 500 g
and the expected absolute standard deviation is
s s
R = ´100
X
RX (. ) ( .
1 10 1 298)
s s = = =0 0143
.
100 100