SCIENTIFIC MEASUREMENTS

© 2019, 2004, 1990 by David A. Katz. All rights reserved.

A BRIEF HISTORY OF MEASUREMENT

Measurement was among one of the first intellectual achievements of early humans. People
learned to measure centuries before they learned how to write and it was through measurement
that people learned to count.

People of the Peking and Neanderthal periods had

implements constructed from materials individually
determined to be the right length or weight for a
particular purpose. A tool that worked well became
the model and standard for another. (See Figure 1)
To measure distance, they used their fingers, hands,
arms, legs, etc... Measurement of weights were
based on use of certain containers or what a person
or beast could haul. Each unit was separate and
unrelated since their ability to count was not
developed. Figure 1. A stone ax and stones cut to
the same size by comparison
Since humans have ten fingers, we learned to count measurements from the Hittite
by tens, and ways were soon found to relate units to Museum in Cappadocia, Turkey.
each other. Some of the most well known of the
early units of measurement were:

inch - the width of the thumb.

digit - the width of the middle finger (about 3/4 inch)
palm - the width of four fingers (about 3 inches)
span - the distance covered by the spread hand (about 9 inches)
foot - the length of the foot. Later expressed as the length of 36 -barleycorns
taken from the middle of the ear (about 12 inches).
cubit - distance from the elbow to the tip of the middle finger (about 18 inches).
yard - distance from the center of the body to the fingertips of the outstretched
arm (about 36 inches).
fathom - distance spanned by the outstretched arms (about 72 inches).

Of course, these units varied from person to person, creating many difficulties. When
individuals worked together, the leader would use his body as the sole authority. Measurements
would be matched to samples made by him. As measurement and tools became more
sophisticated, measuring sticks were made.

Many early civilizations tried to set up systems of weights and measures:

Shih Huang-Ti, a founder of the Chinese Empire has the Great Wall built during his rule.
His design for Chinese unity was: one law, one weight, one measure. Only the Great
Wall continues to stand.
 The Egyptians had a strong system of measurement. The royal cubit was 524 millimeters
(20.62 inches) in the Great Pyramid at Giza. Variations, however, have been found in the
Egyptian empire.

The Greeks and Romans had strong systems of measurements, but these disintegrated
with the empires.

Through the medieval period, people used measurements which became accepted in particular
trades, but no standards existed. Generally, measurements standards for a region would be
embedded in the wall of the city hall or in the central square of a town. (See Figure 2.) Finally, in
an effort to introduce a standard into the measuring system, in the eleventh century, King Henry
I, of England, defined the standard yard from the tip of his nose to the end of his thumb on his
outstretched arm. In 1490, King Henry VII adopted an octagonal yard bar which was distributed
as the national standard. Although the yard was changed about 100 years later, by Elizabeth I,
the idea of a standard yard remained.

Figure 2. Above: Measurement standards

embedded in the wall of the city hall in Assisi,
Italy. The measurements are the foot, the cubit,
and the yard. Right: Measurements in the wall of
the city hall in Regensburg, Germany. The
measurements are the foot, the yard, and the
fathom.

A parliamentary Committee undertook the job of clearing away the medieval weights and
measures, setting up a standard system of weights and measures in 1824. The Americans,
already accustomed to the English system of weights and measures, set up their system which
became standardized in the mid-1900’s.
While the British and Americans were trying to standardize their weights and measures, the
National Assembly of France called upon the French Academy of Science, on May 8, 1790, to
“deduce an invariable standard for all of the measures and all weights”.

In 1791, the French National Assembly approved the report of the French Academy of Sciences
outlining the metric system. On June 19, 1791, a committee of 12 mathematicians, geodesists,
and physicists met with Louis XVI and received his formal approval, one day before he tried to
escape from France and was arrested.

The metric system was adopted by France in 1795, but it existed along with use of the old
medieval units until 1840 when it proclaimed as the exclusive system of weights and measures.

In 1875, the metric system was universally accepted at the International Metric Convention in
France and provisions were made to set up an International Bureau of Weights and Measures in
Paris.

At the 11th General Conference on Weights and Measures, in Paris in October 1960, the
definitions of the original metric standards were redefined to 20th-century standards of
measurement and a new International System of Units was formulated.
THE INTERNATIONAL SYSTEM OF UNITS (SI)

The International System of Units, as amended in 1971, consists of seven base units as listed in
Table 1.

Table 1. SI Base Units

Quantity Measured Unit Symbol

Length meter m
Mass kilogram kg
Time second s
Thermodynamic kelvin K
temperature
Amount of substance mole mol
Electric current ampere A
Luminous intensity candela Cd

The five base units that are useful in general chemistry are defined below:

1. The meter (m) was originally measured to be one ten-

millionth of the distance from the north pole to the
equator along the meridian running near Dunkirk,
Paris, and Barcelona. It was redefined in 1971 as the
length of path traveled by light in a vacuum during the
time interval of 1/299 792 458 second.

2. The kilogram (kg) is the mass of a particular cylinder of

platinum-iridium alloy, called the International Prototype
Kilogram, kept at the International Bureau of Weights
and Measures in Serves, France. The kilogram, the only
unit defined by an artifact, was derived from the mass of
a cubic decimeter of water.

In 2018, the kilogram was defined by taking the fixed

numerical value of the Planck constant h to
be 6.62607015×10−34 when expressed in the unit J⋅s
 (Jouleꞏsecond), which is equal to kg⋅m2⋅s−1, where the meter and the second are
defined in terms of c (the speed of light) and ΔνCs (a specific atomic transition
frequency). This is almost exactly the same as the mass of one liter of water.

3. The second (s) was originally defined as 1/86,400th of a mean solar day. It was
redefined in 1967 as the duration of 9,192,631,770 periods of the radiation
corresponding to the transition between two hyperfine levels of the fundamental state
of a cesium-133 atom.

4. The kelvin (K) is 1/273.16 of the temperature interval between absolute zero and the
triple point of water (the temperature at which ice, liquid water, and water vapor are
in equilibrium). The Celsius scale is derived from the Kelvin scale. An interval of 1
K is equal to 1°C.

5. The mole (mol) is the amount of substance which contains as many entities as there
are atoms in exactly 0.012 kg of carbon-12. This number is known as Avogadro’s
Number which has a value of 6.0220943 x 1023 per mole *6.3 x 1017 (determined
by U.S. National Bureau of Standards in 1974).

Instead of having a large number of units of different sizes, such as inches, feet, years, fathoms,
furlongs, and miles in the English system, it was decided to use prefixes which would multiply
base units by multiples of tens for larger measurements and decimal fractions for smaller
measurements. The prefixes used for multiples and submultiples of SI units are listed in Table 2.
The prefixes commonly used in chemistry are printed in bold print.

Table 2. The SI prefixes

These prefixes multiply base units These prefixes are decimal

for larger measurements fractions that multiply base
units for smaller measurements
Prefix Symbol Multiple Prefix Symbol Submultiple
18
exa E 10 deci d 10-1
peta P 1015 centi c 10-2
tera T 1012 milli m 10-3
giga G 109 micro  10-6
mega M 106 nano n 10-9
kilo k 103 pico p 10-12
2
hecto h 10 femto f 10-15
deka da 10 atto a 10-18

Prefix symbols are printed in Roman type with no space between the prefix symbol and the
base unit symbol.

Examples: millimeter is mm
microsecond is µs
It should be noted that the first letter of the SI abbreviation represents the prefix and the
second letter represents the base unit.

Among the base units, the kilogram has a prefix built into its name. The names of the decimal
fractions and multiples of the kilogram are constructed using the appropriate prefix with the stem
word “gram” (symbol: g).

Examples: megagram is Mg
centigram is cg

When a prefix is affixed to an SI unit, it multiplies the base unit by the appropriate factor listed
in Table 2.

Examples: millimeter: 1 mm = 10-3 m

microsecond: 1 µs = 10-6 s
megagram: 1 Mg = 106 g
centigram: 1 cg = 10-2 g
kilometer: 1 km = 103 m

Since the SI system is based on factors of ten, there are relationships between the metric prefixes
that should be noted. Each of the first three prefixes above or below the base unit either multiply
or divide the base unit by ten. After that, each prefix represents a multiplication or division by
1,000. The factors that relate the more commonly used SI prefixes are shown in Table 3.

Examples: Using m as the base unit:

1,000 pm = 1 nm
1,000 nm = 1 µm
1,000 µm = 1 mm
10 mm = 1 cm
10 cm = 1 dm

To convert between units with difference prefixes, multiply by the factors that occur between
them. Some examples, using m as the base unit, are shown below.

To convert from nm to mm, we first note that there are 1,000 nm in 1 µm and 1,000 µm in
1 mm, then, to convert, multiply the two factors of 1,000 together to get:

1,000,000 nm = 1 mm

To convert from µm to cm, multiply the factors of 1,000 µm in 1 mm and 10 mm in 1 cm

together to get:

10,000 µm = 1 cm
To convert from cm to km, multiply the factors of 100 cm in 1 m and 1000 m in 1 km to
get:

100,000 cm = 1 km

Table 3. Relationship between SI prefixes

Prefix Symbol Multiple

mega M 106
1000 {
kilo k 103
Base unit
to mega:
Base
unit to
10 {
hecto h 102
1 000 000
units
kilo:
1000
10 { deka da 10
units 10 { [base unit]
milli 10 { deci d 10-1
micro to to base
base unit: unit: 10 { centi c 10-2
1 000 000 1000
units units 10 { milli m 10-3
1000 { micro  10-6
1000 { nano n 10-9
1000 { pico p 10-12
Table 4 lists SI-derived units with special names. The most commonly used units in general
chemistry are listed in bold print. A number of these units are named in honor of individuals
who did significant work in the area where the unit is often used.

Table 4. SI-Derived units with special names

_________________________________________________________
Physical Quantity Unit Symbol Formula
_________________________________________________________
Frequency hertz Hz (cycles) s-1
Force newton N kg ꞏ m s-2
Pressure pascal Pa N ꞏ m-2
Energy joule J Nꞏm
Power watt W J ꞏ s-1
Electric potential
difference volt V W ꞏ A-1
Electric charge coulomb C Aꞏs
Electric resistance ohm  V ꞏ A-1
Electric capacitance farad F C ꞏ V-1
Electric conductance siemens S A ꞏ V-1
Magnetic flux weber Wb Vꞏs
Magnetic flux density tesla T Wb ꞏ m-2
Inductance henry H Wb ꞏ A-1
Luminous flux lumen lm cd ꞏ sr(a)
Illuminance lux lx lm ꞏ m-2
Activity
(radionuclide) becquerel Bq (disintegration) s-1
Absorbed dose
(radiation) gray Gy m2 ꞏ s-2
_________________________________________________________
(a) sr = steradian
Table 5 lists units that are derived from either SI base units or from the SI derived units with
special names. The units from which each is derived are shown in the column labeled “Symbol”

Table 5. Other SI-Derived Units

_________________________________________________________
Physical Quantity Unit Symbol
_________________________________________________________
Area square meter m2
Volume cubic meter m3
Velocity meter per second m ꞏ s-1
Acceleration meter per second squared m ꞏ s-2
Wave number 1 (Wave) per meter m-1
Density kilogram per cubic meter kg ꞏ m-3
Concentration mole per cubic meter mol ꞏ m-3
Molar mass kilogram per mole kg ꞏ mol-1
Molar volume cubic meter per mole m3 ꞏ mol-1
Heat capacity joule per kelvin J ꞏ K-1
Molar energy joule per mole J ꞏ mol-1
Electric field
strength volt per meter V ꞏ m-1
Electric dipole
moment coulomb meter Cꞏm
_________________________________________________________

In general chemistry, there are certain non-SI units which may be retained due to widespread
use. The definitions of some of these units are given below:

The calorie (cal) is the amount of heat needed to raise the temperature of 1.0 gram of
water by 1°C at 15°C.

The erg is the energy involved when a force of one dyne acts through a distance of one
centimeter.

A dyne (dyn), is the force required to produce an acceleration of one centimeter per
second squared on a mass of one gram.

The Angstrom (Å) is a unit of length that was commonly used in describing sizes of
atoms. One Angstrom is equal to one-tenth of a nanometer.

The tonne or metric ton (t) is equal to 1000 kg. It is an established commercial unit of
volume.

The atmosphere (atm) is the unit of pressure based on the Earth’s standard air pressure
at sea level. One atmosphere pressure is equal to a barometric pressure of 760 mm Hg.

The liter (L) is an established unit of volume in nations using the metric system. It is
equal to one cubic decimeter. (Formerly defined as one kilogram of water.)
 Two units of energy that are used with SI whose values are obtained by experiment are:

The electronvolt (eV) is the kinetic energy acquired by an electron passing through a
potential difference of 1 volt in vacuum.

The unified atomic mass unit (u) is equal to the fraction 1/12 of the mass of an atom of
the nuclide 12C

Table 6 lists these non-SI units with conversion factors to SI.

Table 6. Non-SI units used in chemistry with conversion factors to SI

______________________________________________________________________________
Physical SI Unit Non-SI Unit Symbol Conversion Factor
Quantity
______________________________________________________________________________
Energy joule calorie cal 1 cal = 4.184 J
erg erg 1 erg = 10-7 J
electronvolt eV 1 eV = 1.60219 x 10-19 J
Force newton dyne dyn 1 dyn = 10-5 N
Length meter Angstrom Å 1 Å = 10-10 m
= 10-1 nm
Mass kilogram tonne t 1 t = 103 kg
atomic mass unit amu 1 amu = 1.66057 x 10-27 kg
Pressure pascal atmosphere atm 1 atm = 1.013 x 105 Pa
torr or mm Hg 1 torr = 1 mm Hg = 133 Pa
Temperature kelvin K
Celsius °C 1°C = 1 K
Volume cubic meter liter L 1 L = 1 dm3 = 10-3 m3
Time second minute min 1 min = 60 s
hour hr 1 hr = 3600 s
day d 1 d = 86 400 s
______________________________________________________________________________

Two conversion factors which will be extremely useful, especially in laboratory work are:

The relationship between volume in cubic centimeters and the non-SI unit of liters:

1 cm3 = 1 mL

Note: A cubic centimeter is sometimes called a cc in the medical field

The relationship between volume and mass of water is:

1 mL H2O = 1 g H2O
SOME ENGLISH-SI CONVERSION FACTORS

Although modern chemistry uses only SI units, it may be useful to know some English-SI
conversion factors in the event it may be necessary to convert between the English system and
the SI system. There are a great number of conversion factors that apply to the large number of
English units. The ones that will be most useful in everyday encounters are:

Length: 1 in = 2.54 cm

Volume: 1.057 qt = 1 L

Mass: 1 lb = 453.6 g

Since length has many English units with different names, some other useful conversion factors
for length are:

39.37 in = 1 m

1 mi = 1.609 km

Another useful conversion factor for mass is:

2.2 lb = 1 kg