LECTURE 15: SAM PL ING
Marc Mate
 Sampling
 Solids
 Liquids
 Gases
 Statistics of Sampling
 The most important step in performing an analytical procedure
is the collection of the sample of the material to be analyzed
 The significance and accuracy of measurements can be limited
by the sampling process.
 Unless sampling is done properly, it becomes the weak link in
the chain of the analysis.
A life could sometimes depend on the proper handling of
a blood sample during and after sampling
Sampling: process by which a representative fraction is
acquired from a material of interest
Very often, the native form of a sample is unsuitable for analysis.
This could be due to
(i) the complex nature of the object, which could provide false
measurements due to interferences or masking agents;
(ii) the size of the object being too large to analyze in its entirety
(e.g., laboratory sample of contaminated soil);
(iii) the awkward shape of the object, preventing it from fitting
within the instrument in which the measurement is to be
made.
To overcome these problems, some sort of sample preparation
must be performed
- Sample should be representative of the material
- Sample should be properly taken to provide reliable
characterization of the material
- Sufficient amount must be taken for all analysis
Representative Sample
Reflects the true value and distribution of analyte in the
original material
Aliquot
Quantitative amount of a test portion of sample solution
 The items chosen for analysis are often
called sampling units or sampling
increments.
 The collection of sampling units or
increments is called the gross sample.
 For laboratory analysis, the gross sample is
usually reduced in size and homogenized to
create the laboratory sample.
 The composition of the gross sample and
the laboratory sample must closely resemble
the average composition of the total mass of
material to be analyzed.
Samples collected for analysis can generally be classified into three
categories based on their state:
(i) solids, (ii) liquids, and (iii) gases.
Samples are typically classified on the basis of their state as a
method of providing an initial means of handling/treating them.
 Once a representative sample has been obtained from the
object of interest, the next step is to prepare the sample for
analysis.
 Since sample preparation depends upon both the analyte
and the instrumentation used to perform the measurement,
details of the preparation process will vary from analysis to
analysis.
Samples can also be categorized based on the time period they
are collected or number of collection points
 Grab samples
Samples taken at a single point in time
 Composite Samples
Samples taken over a period of time or from different locations
 The most difficult to sample since least homogeneous compared
to gases and liquids
 Large amounts are difficult to stir
 Must undergo size reduction (milling, drilling, crushing, etc.) to
homogenize sample
 Adsorbed water is often removed by oven drying
Problems associated with obtaining solid gross samples;
 Inhomogeneity of the material
 variation in particle size
 variation within the particle
These materials tend to be homogeneous and are much easier to
sample
 May be collected as grab samples or composite samples
 Adequate stirring is necessary to obtain representative sample
 Stirring may not be desired under certain conditions (analysis of
oily layer on water)
 Undesired solid materials are removed by filtration or
centrifugation
 Layers of immiscible liquids may be separated with the separatory
funnel
 These procedures are performed either to remove any species that
may cause interferences in the particular analysis or
 To provide a means of concentrating the analyte prior to analysis
 Generally considered homogeneous
 Samples are stirred before portions are taken for analysis
 Gas samples may be filtered if solid materials are present
 The usual method of sampling gases involves displacement of a
liquid.
 The liquid must be one in which the sample has little solubility
and with which it does not react
Scrubbing: Trapping an analyte out of the gas phase
Examples
• Passing air through activated charcoal to adsorb organic vapors
• Bubbling gas samples through a solution to absorb the analyte
Sampling for a chemical analysis necessarily requires the use of
statistics because conclusions will be drawn about a much larger
amount of material from the analysis of a small laboratory sample.
Statistically, the goals of the sampling process are:
1. To obtain a mean analyte concentration that is an unbiased
estimate of the population mean. This goal can be realized only
if all members of the population have an equal probability of
being included in the sample.
2. To obtain a variance in the measured analyte concentration that
is an unbiased estimate of the population variance so that
valid confidence limits can be found for the mean. This goal can
be reached only if every possible sample is equally likely to be
drawn.
 The accuracy and precision of an analysis is limited by the
sampling rather than the measurement step.
 The overall variance of an analysis is the sum of the sampling
variance and the variance of the remaining analytical
operations, that is
You can improve the precision of sampling by increasing the number
of samples. The greater the sample size, the smaller the variance.
 The minimum size of individual increments for a well-mixed
population of different kinds of particles can be estimated from
Ingamell’s sampling constant;
Where;
 w is the weight of sample analyzed
 R is the percent relative standard (RSD)
deviation of the sample composition.
 Ks represents the weight of sample for 1%
sampling uncertainty at a 68% confidence
level
Ingamell’s sampling constant for the analysis of the
nitrogen content of wheat samples is 0.50 g. What
weight sample should be taken to obtain a sampling
precision of 0.2% rsd in the analysis?
 The number of individual sample increments needed to achieve
a given level of confidence in the analytical results is estimated
by;
Where;
 t is the Student t value for the confidence level
desired,
 SS2 is the sampling variance,
 SX2 is the results variance
𝑺𝑿 = 𝒓𝒙
r is the acceptable relative standard deviation
(RSD) of the average of the analytical results, 𝒙 ̅
It was found that an analysis for the inorganic ash content of a
breakfast cereal required a sample of 1.5 g to establish a
relative standard deviation for sampling of ±2.0%. How many
samples are needed to obtain a relative sampling error of no
more than 0.80% at the 95% confidence level?
The iron content in a blended lot of bulk ore material is about 5%
(wt/wt), and the relative standard deviation of sampling, s s , is
0.021 (2.1% rsd). How many samples should be taken in order to
obtain a relative standard deviation, r, of 0.016 (1.6% rsd) in the
results at the 95% confidence level [i.e., the standard deviation, s„
for the 5% iron content is 0.08% (wt/wt)]??
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