Transcript Scientific Measurement

Chapter 3
3.1
3.
1
◦ Measurements are fundamental to the experimental
sciences. For that reason, it is important to be able
to make measurements, and to use them correctly
when calculating answers.
 A measurement is a quantity that has both a number
and a unit.
◦ Good measurements are accurate, precise, and
have low error.
3.
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◦ Accuracy is a measure of how close a measurement
comes to the actual or true value of whatever is
measured.
◦ Precision is a measure of how close a series of
measurements are to one another. The more
sensitive the instrument (smaller unit), the more
precise will be the measurements.
 Good measurements need to be BOTH accurate and
precise.
3.
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3.
1
◦ Error is the difference between the experimental
value and the accepted value.
 The accepted value is the correct value based on reliable
references (reference tables).
 The experimental value is the value measured in the lab.
3.
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 The percent error is the absolute value of the error
divided by the accepted value, multiplied by 100%.
 See reference table T.

What is a student’s percent error if she found
the boiling point of water to be 99.1°C at STP?


Numbers that are part of a measurement are
called significant figures.
Measurements should always be reported to
the correct number of significant figures.
 Suppose you estimate a weight between 2.4 lb and 2.5 lb
to be 2.46 lb. The last digit (6) is an estimate and involves
some uncertainty. However, all three digits convey useful
information and are called significant figures.
◦ The significant figures in a measurement include all
of the digits that are known, plus a last digit that is
estimated.
◦ Good measurements always estimate one decimal
place beyond the calibration of the instrument. In
other words, read between the lines!

Sometimes zeroes are just place holders and are used
to locate the decimal point. They are NOT a part of
the measurement, and are therefore insignificant.
◦ When doing calculations with measurements, it
becomes necessary to round off the answer. This
must be done correctly so as not to imply better
instrumentation than was actually used.
◦ To round off correctly, you must be able to
determine the precision (number of significant
figures) in a measurement.
◦ What if you can’t see the instrument used? How do
you determine the number of significant figures in a
measurement (its precision)?
1. Nonzero digits are always significant.
2. Leading zeros (occur before any nonzero digit)
are never significant.
3. Embedded zeros (between nonzero digits) are
always significant.
4. Trailing zeros (after the last nonzero digit) are
only significant if the measurement has a decimal
point.
5. Counted quantities, physical constants and
conversion factors have unlimited significant
figures.
◦ When calculating using measurements, the answer
should never be more precise than the least precise
measurement from which it was calculated.
◦ The calculated answer must be rounded to make it
consistent with the measurements from which it was
calculated.
◦ Rounding calculations depends upon (1) the
number of significant figures in the measurements
and (2) the mathematical process used to arrive at
the answer.
3.
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◦ Addition and Subtraction
 The answer to an addition or subtraction calculation
should be rounded to the same number of decimal
places (not digits) as the measurement with the least
number of decimal places.
3.
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◦ Multiplication and Division
 In calculations involving multiplication and division,
you need to round the answer to the same number of
significant figures as the measurement with the least
number of significant figures.
 The position of the decimal point has nothing to do with
the rounding process when multiplying and dividing
measurements.
3.2
3.
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◦ All measurements depend on units that serve as
reference standards. The standards of
measurement used in science are those of the
metric system.
◦ The International System of Units (abbreviated SI,
after the French name, Le Système International
d’Unités) is a revised version of the metric system.
3.
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◦ What SI units are commonly used in Chemistry?
◦ See reference table D
3.
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◦ Units of Length
 In SI, the basic unit of length, or linear measure, is the
meter (m). For very large or and very small lengths, it
is more convenient to use a unit of length that has a
prefix. See reference table C
3.
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 Common metric units of length include the centimeter,
meter, and kilometer.
3.
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◦ Units of Volume
 The SI unit of volume is the cubic meter (m)3. A more
convenient unit of volume for everyday use is the liter,
a non-SI unit.
 1 mL = 1 cm3
 There are 1000 mL in a liter
3.
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 The volume of 20 drops of liquid from a medicine
dropper is approximately 1 mL.
3.
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 A sugar cube has a volume of 1 cm3. 1 mL is the same
as 1 cm3.
3.
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 A gallon of milk has about twice the volume of a 2-L
bottle of soda.
3.
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◦ Units of Mass
 The mass of an object is measured in comparison to a
standard mass of 1 kilogram (kg), which is the basic SI
unit of mass.
 A gram (g) is 1/1000 of a kilogram. A penny has a
mass of around 5 grams.
3.
2
◦ Units of Temperature
 Temperature is a measure of how
hot or cold an object is.
 Thermometers are used to measure
temperature.
3.
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◦ Scientists commonly use two equivalent units of
temperature, the degree Celsius and the Kelvin.
3.
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 On the Celsius scale, the freezing point of water is 0°C
and the boiling point is 100°C.
 On the Kelvin scale, the freezing point of water is 273
Kelvin (K), and the boiling point is 373 K.
 The Kelvin scale starts at absolute zero.
 “Standard Temperature” equals the freezing point of
water, 0°C or 273K
 See reference table A
3.
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 Because one degree on the Celsius scale is equivalent
to one Kelvin on the Kelvin scale, converting from one
temperature to another is easy. You simply add or
subtract 273, as shown in the following equations.
3.
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◦ Units of Energy
 Energy is the capacity to do work or to produce heat.
 The joule and the calorie are common units of energy.
3.
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 The joule (J) is the SI unit of energy. We will use this
unit this year.
 It takes 4.18 joules of heat (or I calorie) to raise the
temperature of 1 g of pure water by 1°C.
 See reference table B
3.3
3.
33

Because each country’s currency
compares differently with the U.S.
dollar, knowing how to convert
currency units correctly is very
important. Conversion problems are
readily solved by a problem-solving
approach called dimensional
analysis.
◦ Chemists often need to convert from one unit of
measurement to another. To do this they use
conversion factors.
3.
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 A conversion factor is a ratio of equivalent
measurements.
 The ratios 100 cm/1 m and 1 m/100 cm are examples of
conversion factors.
3.
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◦ When a measurement is multiplied by a conversion
factor, the unit is changed so the numerical value is
different, but the actual size of the quantity
measured remains the same.
3.
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◦ Dimensional analysis is a way to analyze and solve
problems using the units, or dimensions, of the
measurements.
 Dimensional analysis uses conversion factors to solve
problems.
 Given quantities are multiplied by conversion factors so
that units cancel out until the desired unit remains.
◦ An exchange student lands on Mars and finds the
chemical stockroom. She needs 14 grams of silver
(Ag) for a research project. The attendant asks her
“How many zooms of silver do you need?” Whoops!
Different mass units! The student finds that on
Mars the following units are used: woofs, zings,
warps and zooms.
◦ It turns out 9 woofs = 1 gram. Also, 2 zings = 7
warps. 8 woofs = 3 warps and 4 zooms = 3 zings.
◦ How many zooms does the student need?
3.4

If you think that these lily
pads float because they are
lightweight, you are only
partially correct. The ratio
of the mass of an object to
its volume can be used to
determine whether an
object floats or sinks in
water.

Determining Density
◦ What determines the density of a substance?
 Density is the ratio of the mass of an object to its
volume.
 See reference table T
 Each of these 10-g samples has a different volume
because the densities vary.
 Density is an intensive property that depends only on the
composition of a substance, not on the size of the sample.
 The density of corn oil is
less than the density of
corn syrup. For that reason,
the oil floats on top of the
syrup.

Density and Temperature
◦ How does a change in temperature affect density?
◦ Experiments show that the volume of most
substances increases as the temperature
increases. Meanwhile, the mass remains the
same. Thus, the density must change.
 The density of a substance generally decreases as
its temperature increases.