CH7_LabExperiments_2017.doc - Whitman College

CHAPTER 7 Laboratory Experiments 7.1 Introduction
This chapter contains several useful laboratory experiments for an
instrumental methods of analysis class. These start with a statistics
assignment and then go on to more complicated lab experiments. Sample
student results are provided for most experiments. 7.2 Computer Laboratory I: Linear Least Squares Analysis
Computer Laboratory II: Student's t test Equipment needed: A lab-top computer equipped with Excel®
A basic knowledge of spreadsheets Purpose of this Exercise:
One of the first lessons that you need to learn in Instrumental
Analysis is that few, if any, instruments report direct measurement of
concentration or activity without calibration. Even our balances need
periodic calibration. More complicated instruments need even more involved
calibration. Instruments respond to calibration standards in either a
linear or exponential manner, and exponential responses can easily be
converted to a linear plot by the log or natural log transformation. The
goals of the first computer exercise is to create a linear least squares
(LLS) spreadsheet for analyzing calibration data and learn to interpret the
results of your spreadsheet. The goal of the second computer exercise is
to create a spreadsheet for conducting the student's t test for (1)
comparing your analysis results to a known reference standard, and (2)
comparing two group's results to each other. The student's t test allows
you to tell if the results are within an acceptable range and if the
results are acceptable. Programming Hints:
First, here are a few hints on using Microsoft Excel®:
-calculations must start with a "="
-the "$" locks a cell address, you can lock rows, columns, or
both
-mathematical symbols are as you expect except "^" is used to
raise a
number to a power
-text is normally entered as text, but sometimes you may have
to start the
line with a single quote symbol, ' Introduction:
Linear Least Squares Equations:
The first step in analyzing unknown samples is to have something to
reference the instrument signal to (instrument do not directly read
concentration). To do this we create a standard curve (line) relating
signal response to concentration. All of our calibration curves will be some form of linear relationship
(line) of the form y = mx + b. Sensitivity refers to the equation S = mc + S
where S is the signal (abs, pk ht) response,
m is the slope of the straight line,
c is the concentration of the analyte, and
Sblank is the instrumental signal (abs, etc.) for the blank. This is the calibration equation for a plot of S on the y-axis and C on the
x-axis. The slope is m and the y-intercept is Sblank. The detection limit
will be Sm = Sblank + kstandard deviation blank (where k = 3). We will usually collect a set of data correlating S to c. Examples of S
include light absorbance in spectroscopy,
peak height in chromatography, or
peak area in chromatography. We will plot our data set on linear graph paper and develop an equation for
the line connecting the data points. We will define the difference between
the point on the line and the measured data point as the residual (in the x
and y direction). For calculation purposes we will use the following equations (S's are sum
of squared error or residuals) where xi and yi are individual observations, N is the number of data pairs,
and x-bar and y-bar are the average values of the observations. Six useful
quantities can be computed from these. The slope of the line (m) is m = Sxy/Sxx The y-intercept (b) is b = y-bar - (m) (x-bar) The standard deviation sy of the residuals, which is given by
The standard deviation of the slope sm:
The standard deviation sb of the intercept:
The standard deviation sc for analytical results obtained with the
calibration curve: where yc-bar is the mean signal value for the unknown sample, L is the
number of times the sample is analyzed, N is the number of standards in
your calibration curve, and y-bar is the mean signal value of the y
calibration observations (from standards). So, you will have a reported
value of plus or minus a value. It is important to note what sc refers to-it is the error of your sample
concentration results from the linear least squares analysis. Since the
equation for sc (above) does not account for any error or deviation in your
sample replicates (due to either sample preparation error such as pipeting
or concentration variations in your sampling technique), sc does not
account for all sources of error in precision. To account for these latter
errors you will need to make a standard deviation calculation on your
sample replicates.
Most of your calculators have an r or r2 key and you probably know
that the closer this value is to 1.00 the better. Where does this number
comes from
r (and r2) are called the coefficient of regression or regression
coefficient. Student's t Test Equations After you obtain a mean value for a sample, you will want to know if this
is in an acceptable range of the true value, or you may want to compare
mean values obtained from two different techniques. We can do this with a
statistical technique called the student's t test. To perform this test,
we simply rearrange the equation for the confidence limits to
where x-bar is the mean of your measurements,
? is the known or true value of the sample,
t is the value from the t table,
s.d. is the standard deviation, and
N is the number of replicates that you analyzed. Basically, we are looking at the acceptable difference between the measured
value and the true value. The basis for comparison is dependent on a t
value, the standard deviation, and the number of observations. "t" values
are taken from tables such as the one given out in your quantitative
analysis or instrumental analysis textbook and you must pick a confidence
interval and the degrees of freedom (this will be N-1 for this test). If
the experimental value of (x-?) is larger than the value of (x-?)
calculated from the equation above, the presence of bias in the method is
suggested. If, on the other hand, the value calculated by the equation is
larger, no bias has been demonstrated. A more useful, but difficult procedure can be performed to compare the mean
results from two experiments or techniques. This uses the following
equation where s1 and s2 are the respective standard deviation of each mean, and n1
and n2 are the number of observations in each mean. In this case the degrees of freedom in the table "t" value will be (N-2) (2
because you are using two s-squared values). As in the procedure above, if
the experimental (observed) value of (x1-x2) is larger than the value of
(x1-x2) calculated from the equation above, there is a basis for saying
that the two techniques are different. If, on the other hand, the value
calculated by the equation is larger, no basis is present for saying that
the two techniques are different. (i.e. the value from the equation gives
your tolerance (or level of acceptable error). Also, note that by using
the 95% CI, you will be right 95 times out of 100 and wrong 5 times out of
100. Assignment:
Your task is to create a spreadsheet that looks identical to the ones
available from this chapter's web page. During the first laboratory period
you will create a linear least squares analysis sheet. For the second
laboratory period you will create a spreadsheet for conducting a student's
t test. The cells contains bold numbers are the only numbers that should
be entered when you actually use the spreadsheet for calibrating an
instrument. All other cells should contain equations that will not be
changed (and can be locked to insure that these cells do not change). What do you turn in?
A one-page print out (print to fit on one page) of each spreadsheet.
Before you turn in your spreadsheets, change the format of all column data
so that they only show 3 or 4 significant figures (which ever is correct).
Explain your LLS analysis and student's t test results (approximately 1
page each, typed). Here are some things to include in your write-up.
Give: the equation of the line,
the signal to noise ratios for your analysis, and
the minimum detection limit.
Was bias indicated in your analysis of the unknown (the 5 ppm
sample)
and the true value?
Were the results from the two groups comparable?
How do the numbers compare to the results from your calculator? What shortcomings does your calculator have (if any)?
The complete spreadsheet is available from this chapter's web page as a
downloadable file. 7.3 Solutions, Weights, and Lab Technique OBJECTIVES: Develop and refine student's calculation and laboratory skills
Introduce students to analytical equipment (and see what
you
learned in Quantitative Methods of Analysis) The scientific method requires the collection of experimental data
and the data must be collected in a manner that insures precision and
accuracy. No matter what field of science that you work in, you will
eventually have to make solutions of specified concentrations. There are
two main goals of this lab exercise: (1) to test your ability to determine
how to make a solution of specified concentration, and (2) to test your
accuracy and precision in making these solutions. You will complete this
experiment using gravimetric and volumetric techniques. EXPERIMENTAL / SOLUTIONS NEEDED:
An FAAS equipped with a Ca lamp
Each pair of students will be supplied with:
1 or 2, 5, 10, 25 mL Class A pipets,
25, 50, 100, 250, and 500 mL Class A volumetric flasks,
99.6 % pure CaCO3 (CAS number 471-34-1) (dried at 104 C overnight),
1% by volume nitric acid for dilution purposes,
and your knowledge of genera