Experiment #2 – Measurements, Accuracy, and Precision
Laboratory Overview
CHEM 1361
August 2012
Gary S. Buckley, Ph.D.
Department of Physical Sciences
Cameron University
PowerPoint Notes
Each lab will be accompanied by a short PowerPoint presentation showing
some of the basic ideas of the lab. Viewing is optional to you, but viewing
them may give you a better idea of what the key aspects of the
experiments are. It may also help with the prelabs.
This first one runs a little long – 17 slides. Most will be on the order of ten
slides.
If you decide you want to print these presentations, I suggest you use
either Black and White or Grayscale in the Print box. It will save
considerably on color ink without any adverse effect.
If you have problems with the slide show, please don’t hesitate to contact
me.
Dr. Buckley
gbuckley@cameron.edu
Phone: 580-581-2885
Learning Objectives
•Record length and volume measurements to the proper number of
significant figures
•Select the most appropriate piece of lab glassware to make volume
measurements to desired accuracy
•Use basic statistical concepts of mean and standard deviation to evaluate
precision of measurements
•Work with density to determine volume from mass
Table of Contents
(you may click on any of the topics below to go directly to that topic)
•Digital vs. Analog Devices
•Significant Figures
•Using the Balance
•Types of Glassware and its Uses
•Glassware Designations
•Measuring and Reading Liquid Volumes
•Density Background
•Accuracy and Precision
•Basic Statistics – Average and Standard Deviation
Digital vs. Analog Devices
The Definitions
Digital device – a device that indicates the measured
quantity directly in numbers. Examples: digital balance,
digital thermometer
Digital Balance
Analog device – a device that measures continuous
information. Examples: a ruler, a mercury-filled
thermometer, a bathroom scale with a needle
Ruler – example of an analog device
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Digital vs. Analog Devices
Reading the Devices
A digital device is simply read by recording the indicated digits in its
display. The reading on the balance to the right would be recorded
as 0.00 g.
An analog device is read by estimating the reading to one decimal
place BETWEEN the markings on the device. The reading of the
edge of the paper on the ruler below would be recorded as 94.05
cm, or 94.06 cm, or 94.07 cm. The last digit is an estimate and may
differ from one person to another.
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Significant Figures
Significant figures in a measurement indicate the precision to which the
measurement was made.
In the case of a digital device, all of the digits are considered to be significant
and are recorded even if there are trailing zeroes.
With an analog device, the number of significant figures is considered to be the
number of divisions on the device plus the one additional figure that is always
estimated. For example, on the ruler below the reading might be 94.06 cm,
which indicates four significant figures. If the paper had been right on the 94 cm
mark, the reading would have been recorded as 94.00 cm, still showing four
significant figures.
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Increasing the Number of Significant Figures
The only way to increase the number of significant figures in a
measurement is to increase the precision of the measuring device.
Consider the picture below with three different markings on the meter
sticks.
•Top stick. One estimates the reading for the edge of the paper as,
perhaps, 0.94 m. This gives two significant figures, one more decimal place
than the markings on the stick.
•Middle stick. The reading on this stick
appears to be 94.1 cm, giving three
significant figures.
•Bottom stick. The reading on this stick
appears to be 94.05 cm, giving four
significant figures.
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Using the Digital Balance
Using the digital balances is pretty straightforward :
•Bring your lab book with you to the balance.
•Push the On button to turn the balance on.
•Push the →O/T← button to set the balance reading to zero.
•Be sure the units on the balance show g, not N. If N shows
instead of g, hit the
button once to get g.
•Place your object on the balance.
•When the reading stabilizes, record all of the digits in the
balance window in your lab book immediately.
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Types of Glassware and its Use
Three basic functions of glassware:
•Holds liquids without measurement – e.g., beaker
•Holds a fixed volume of liquid, used for preparing solutions,
transferring a predetermined volume – e.g., volumetric flasks,
volumetric pipettes
•Graduated to allow the measurement of a range of volumes
that are contained or delivered – graduated cylinder, buret,
Mohr pipet
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Types of Glassware and its Use
•Hold liquid without measurement – the
markings on the sides are only very crude
measures
•Hold a fixed volume
Erlenmeyer
Flask
Beaker
Volumetric Flask
•Deliver or measure a range of volumes
Graduated Cylinder
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Glassware Designations
Often glassware will be marked with the
designation of either TC (To Contain) or TD
(To Deliver). There is sometimes a
statement indicating an uncertainty in the
volume of the vessel and the temperature of
the calibration .
Meaning of TC and TD:
•TC (To Contain): Accurate delivery from this
sort of vessel requires draining all of the
liquid out of the vessel. An example is a
volumetric flask.
•TD (To Deliver): These vessels are designed
so that the calibrated volume is delivered if
no special action is taken to remove
remaining liquid. Examples are burets,
volumetric pipets, graduated cylinders
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Measuring and Reading Liquid Volumes
Measuring liquid volumes requires observance of the
meniscus. The meniscus is the result of the adhesive
forces of the liquid for the glass compared to the
cohesive forces between molecules in the liquid. Some
liquids will have a meniscus that curves upward, some
downward. The figure to the right illustrates the
appearance of the meniscus for water. Volume readings
are taken at the bottom of the meniscus.
Meniscus
Reading: 1.40 mL
(Notice the buret has increasing volumes as you go
down so the reading is between 1 and 2 mL.)
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Density
Density is defined to be the mass of a sample of a substance
divided by its volume. In mathematical terms,
mass
density 
volume
If one knows the mass and density of a substance, the volume
may be determined by rearranging the above expression to:
volume 
mass
density
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Accuracy and Precision
Measurements in the laboratory are an attempt to find the “real” value
of a physical quantity. Two terms used in relation to measurement are:
•Accuracy – the nearness of the measured value to the “real” value
•Precision – the nearness of repeated measurements to each other
Note that a measured result may be accurate, but not precise; not
accurate, but precise; both accurate and precise; or neither accurate nor
precise.
The next couple of slides give one method for considering accuracy and
precision.
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Measures of Accuracy and Precision
Average or mean – the average, sometimes called the mean,
is simply the sum of repeated attempts to measure the same
quantity divided by the total number of attempts.
Standard deviation – the standard deviation is an indication
of the precision of repeated measurements. If one takes N
measurements of the same physical quantity , the standard
deviation, s, is given by:
N
s
 ( x  x)
i 1
2
i
N 1
where xi represents the ith measurement and x represents
the average of all of the measurements.
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Accuracy and Precision – An Example
Suppose you had measured the molarity of a solution (doesn’t
matter if you know what molarity is yet or not) and determined the
three values of 0.1042 M, 0.1004 M, and 0.1033 M. The average is
given by:
x
0.1042M  0.1004M  0.1033M
 0.1026M
3
The standard deviation would be calculated as:
s
(0.1042  0.1026)2  (0.1004  0.1026)2  (0.1033  0.1026)2
 0.0020M
3 1
The result would be reported as 0.1026 ± 0.0020 M, or more
properly as 0.103 ± 0.002 M as we try to keep one significant figure
in the standard deviation and round the average to match that
number of decimal places.
(If you are on your toes, you may find your calculator is capable of
doing these calculations if you can figure out how to make it work!)
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End of Slide Show