Measurement
Measurements
• A measurement is not complete unless it has a
unit. A unit is the part of the measurement
that tells us what scale or standard is being
used to represent the results of the
measurement.
• The need for common units applies to
scientists, who measure quantities such as
mass, length, time, and temperature.
The Metric System
• There are two measurement systems that are
commonly used:
1. The English System (used in the United States)
2. The Metric System (used in most of the rest of
the world)
• In Chemistry, we will use
the metric system. This
system has long been
preferred for most
scientific work.
SI Units
• The International System (or le Systeme
Internationale in French) is the type of units
that are based on the metric system. These
units are also known as SI units. We will be
using SI units in Chemistry.
• SI Units
Property
Unit
Symbol
mass
kilogram
kg
length/distance
meter
m
time
second
s
temperature
Kelvin
K
amount of a
substance
mole
mol
Metric Prefixes
• The fundamental SI units are not always a
convenient size, so the SI system uses prefixes
to change the size of the unit.
Metric
prefixes
mega-
Symbol
Value
M
1,000,000
Scientific
Notation
106
kilo-
k
1,000
103
deci-
d
0.1
10-1
centi-
c
0.01
10-2
milli-
m
0.001
10-3
micro-
µ
0.000001
10-6
nano-
n
0.000000001
10-9
Measuring Length
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•
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Length is measured with a ruler or meter stick
On a 12” ruler, there are 30.5cm
On a meter stick, there are 100cm
The SI unit is the meter, abbreviated “m”
Measuring Volume
• Volume is the amount of three-dimensional
space occupied by a substance.
• The SI unit of volume is the cubic meter,
abbreviated “m3,” but in Chemistry
we will use liters, abbreviated “L”
or the milliliter, abbreviated “mL”
• Volume is measured with a
graduated cylinder
Volume and the meniscus…
• Measuring volume with a graduated cylinder is
complicated by a meniscus. A meniscus is the
curvature of the surface of the water. Water
“sticks” to the walls of the graduated cylinder, but
only on the sides and not the middle. When you
look at the surface, the water level is not straight.
Measurement should be at the lowest point. You
must read the meniscus at eye level in order to
get an accurate reading. You should
place the graduated cylinder on the
table and then lower your head to
be able to read the meniscus at
eye level.
Measuring Mass
• The SI unit is the kilogram, abbreviated “kg,”
but in Chemistry we will use grams,
abbreviated “g”
• Mass is measured with a balance
Measuring Temperature
• The SI unit is the Kelvin, but in Chemistry we
will use degrees Celsius, abbreviated, “°C”
• Temperature is measured with a thermometer
Uncertainty in Measurement
• A measurement always has some degree of
uncertainty.
• Whenever a measurement is made with a
ruler, graduated cylinder, or thermometer, an
estimate is required.
Uncertainty with a ruler
• On the ruler to the right, you can accurately measure
the pencil length to 8.2cm, but it is not exactly on the
line. So, an estimation of the next division is required.
This estimation is your degree of uncertainty.
• One student might say 8.24cm, another might say
8.25cm, a third might say 8.23cm.
• To account for the uncertainty, the measurement
usually is written 8.24 ± 0.01 cm.
The “± 0.01 cm” tells us that the
measurement is uncertain to 1/100
of a centimeter.
Uncertainty with a thermometer
• The same is true for thermometers:
• On the thermometer to the right, you can accurately
measure the temperature to be 23°C, but it is not
exactly on the line. So an estimation of the next
division is required. This estimation is your degree of
uncertainty.
• To account for the uncertainty,
the measurement should be
23.5 ± 0.1 °C. This tells us that
the thermometer is uncertain to
1/10 of a degree.
Uncertainty with a graduated cylinder
• The same is true for graduated cylinders:
• On the graduated cylinder to the right, you can
accurately measure the temperature to be 43mL,
but it is not exactly on the line. So an estimation
of the next division is required. This estimation is
your degree of uncertainty.
• To account for the uncertainty, the
measurement should be 43.1 ± 0.1 mL. This tells
This tells us that the graduated cylinder is
uncertain to 1/10 of a mL.
Experimental Error
Experimental Error
• In the laboratory, NO measurement is exact.
There are always errors that affect our results
– whether we are using a 10-cent ruler or an
$800 balance.
Accuracy & Precision
• Accuracy measures how close a measured value
is to the true value or accepted value.
• Precision measures how closely two or more
measurements agree with each other. Precision
is sometimes referred to as “repeatability”
or “reproducibility.” A
measurement which is
highly reproducible tends to
give values which are very
close to each other.
Sources of Experimental Error
• When conducting an experiment, there are
three types of errors that you will encounter:
“human” error, random error, and systematic
error.
Human Error
A human error is simply another word
for mistake, blunder, or screw-up. Examples
include:
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Not setting up an experiment correctly
Misreading an instrument
Using the wrong chemical(s)
Not following directions
Spilling or general sloppiness
Bad calculations, doing math incorrectly, using the wrong formula
Human errors are NOT a source of experimental
error, but rather they are “experimenter’s” error.
Random Error
Random errors are unavoidable variations that will either
increase or decrease a given measurement. Examples may
include:
• Fluctuations in the laboratory balance (your sample may weigh a few
hundredths of a gram higher or lower at any given time, depending on the
quality of the balance and the conditions in the room).
• Using a stopwatch to time a reaction (regardless of how careful you are you
will sometimes stop the watch too soon and sometimes too late).
To minimize random errors, try to use high-quality
laboratory equipment whenever possible and use
consistent techniques when performing an experiment.
Since random errors are equally likely to be high
as low, performing several trials (and averaging the
results) will also reduce their effect considerably.
Systematic Error
Systematic error is an error inherent in the
experimental setup which causes the results to be
skewed in the same direction every time.
For example:
• A mis-calibrated thermometer may increase all temperature readings by 0.5°C.
• A cloth tape measure used to measure the length of an object could be
stretched out from years of use (as a result, all of your length measurements
would be too small).
• Substituting 10.00 grams of rock salt for 10.00 grams of table salt in an
experiment will affect the rate at which the reaction takes place. In this case,
the reaction rate would decrease due to the decreased surface area.
Since systematic errors always skew data in one direction, they cannot
be eliminated by averaging. However, they can usually be avoided by
changing the way in which the experiment was carried out (using more
reliable equipment, modifying a procedure, changing laboratory
conditions, etc.).
Analyzing Experimental Error
• The most common way to analyze
experimental error is to compare your results
with a known value (if available) using the
percent error formula: