Chemistry is a quantitative science,
which means that in many cases we can measure a property of a substance and
compare it with a standard having a known value of the property. We express the
measurement as the product of a number and a unit. The unit indicates the
standard against which the measured quantity is being compared. When we say
that the length of the playing field in football is 100 yd., we mean that the
field is 100 times longer than a standard of length called the yard (yd.). In
this topic, we will introduce some basic units of measurement that are
important to chemists.
The scientific system of measurement is
called the Système Internationale d Unités (International System of
Units) and is abbreviated SI. It is a modern version of the metric system,
a system based on the unit of length called a meter (m). The meter was
originally defined as of the distance from the equator to the North Pole and
translated into the length of a metal bar kept in Paris. Unfortunately, this
length is subject to change with temperature, and it cannot be exactly
reproduced. The SI system substitutes for the standard meter bar an unchanging,
reproducible quantity: 1 meter is the distance traveled by light in a vacuum in
1/299,792,458 of a second. Length is one of the seven fundamental quantities in
the SI system (see Table). All other physical quantities have units that can be
derived from these seven. SI is a decimal system. Quantities differing from the
base unit by powers of ten are noted by the use of prefixes. For example, the
prefix kilo means one thousand times the base unit; it is abbreviated as ‘k’.
Thus or The SI prefixes are listed in Table below.
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| SI Base Quantities |
Mass
Mass describes the quantity of matter in
an object. In SI the standard of mass is 1 kilogram (kg), which is a fairly
large unit for most applications in chemistry. More commonly we use the unit
gram (g) (about the mass of three aspirin tablets). Weight is the force of
gravity on an object. It is directly proportional to mass, as shown in the
following mathematical expressions.
An object has a fixed mass (m), which is
independent of where or how the mass is measured. Its weight (W), however, may
vary because the acceleration due to gravity (g) varies slightly from one point
on Earth to another. Thus, an object that weighs 100.0 kg in St. Petersburg,
Russia, weighs only 99.6 kg in Panama (about 0.4% less). The same object would
weigh only about 17 kg on the moon. Although the weight of an object varies
from place to place, its mass is the same in all locations. The terms weight and
mass are often used interchangeably, but only mass is a measure of the quantity
of matter. A common laboratory device for measuring mass is called a balance. A
balance is often called, incorrectly, a scale.
The principle used in a balance is that
of counteracting the force of gravity on an unknown mass with a force of equal
magnitude that can be precisely measured. In older two-pan beam balances, the
object whose mass is being determined is placed on one pan and counterbalancing
is achieved through the force of gravity acting on weights, objects of
precisely known mass, placed on the other pan. In the type of balance most
commonly seen in laboratories today the electronic balance the counterbalancing
force is a magnetic force produced by passing an electric current through an
electromagnet. First, an initial balance condition is achieved when no object
is present on the balance pan. When the object to be weighed is placed on the
pan, the initial balance condition is upset. To restore the balance condition,
additional electric current must be passed through the electromagnet. The
magnitude of this additional current is proportional to the mass of the object
being weighed and is translated into a mass reading that is displayed on the
balance. An electronic balance is shown in the margin.
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| An electronic balance |
Time
In daily use we measure time in seconds,
minutes, hours, and years, depending on whether we are dealing with short
intervals (such as the time for a 100 m race) or long ones (such as the time
before the next appearance of Halley’s comet in 2062). We can use all these
units in scientific work also, although in SI the standard of time is the
second (s). A time interval of 1 second is not easily established. At one time
it was based on the length of a day, but this is not constant because the rate
of Earth’s rotation undergoes slight variations. In 1956, the second was
defined as of the length of the year 1900. With the advent of atomic clocks, a
more precise definition became possible. The second is now defined as the
duration of 9,192,631,770 cycles of a particular radiation emitted by certain
atoms of the element cesium (cesium-133).
Temperature
To establish a temperature scale, we
arbitrarily set certain fixed points and temperature increments called degrees.
Two commonly used fixed points are the temperature at which ice melts and the
temperature at which water boils, both at standard atmospheric pressure.*
On the Celsius scale, the melting point
of ice is 0 °C, the boiling point of water is 100 °C, and the interval between
is divided into 100 equal parts called Celsius degrees. On the Fahrenheit
temperature scale, the melting point of ice is 32 °F, the boiling point of
water is 212 °F, and the interval between is divided into 180 equal parts
called Fahrenheit degrees. Figure 1-8 compares the Fahrenheit and Celsius
temperature scales.
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| A comparison of temperature scales |
The SI temperature scale, called the
Kelvin scale, assigns a value of zero to the lowest possible temperature. The
zero on the Kelvin scale is denoted 0 K and it comes at 273.15 °C. We will
discuss the Kelvin temperature scale in detail in other posts. For now, it is
enough to know the following:
a. The interval on the Kelvin scale, called
a kelvin, is the same size as the Celsius degree.
b. When writing a Kelvin temperature, we do
not use a degree symbol. That is, we write 0 K or 300 K, not 0 °K or 300 °K.
c. The Kelvin scale is an absolute
temperature scale; there are no negative Kelvin temperatures.
In the laboratory, temperature is most
commonly measured in Celsius degrees; however, these temperatures must often be
converted to the Kelvin scale (in describing the behavior of gases, for
example). Occasionally, particularly in some engineering applications,
temperatures must be converted between the Celsius and Fahrenheit scales.
Temperature conversions can be made in a straightforward way by using the
algebraic equations shown below.
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| inter-conversion of temperature scales |
The factors 9/5 and 5/9 arise because the
Celsius scale uses 100 degrees between the two chosen references points and the
Fahrenheit scale uses 180 degrees: 180/100 = 9/5 and 100/180 = 5/9. The diagram
in figure illustrates the relationship among the three scales for several
temperatures.
Derived Units
The seven units listed in the table above
are the SI units for the fundamental quantities of length, mass, time and so
on. Many measured properties are expressed as combinations of these fundamental,
or base, quantities. We refer to the units of such properties as derived units.
For example, velocity is a distance divided by the time required to travel that
distance. The unit of velocity is length divided by the time, such as m/s or ms-1.
Some derived units have special names. For example the combination of kg
m-1 s-2 is called the Pascal and the combination kg m2
s-2 is called the joule.
An important measurement that uses
derived units is volume. Volume has the unit and the SI standard unit of volume
is the cubic meter (m3). More commonly used volume units are the
cubic centimeter and the liter (L). One liter is defined as a volume of which
means that one milliliter (1 mL) is equal to 1cm3. The liter is also
equal to one cubic decimeter (1 dm3). Several volume units are
depicted in Figure below.
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| Some Metric volume units compared |
Although its citizens are growing more
accustomed to expressing distances in kilometers and volumes in liters, the
United States is one of the few countries where most units used in everyday
life are still non-SI. Masses are given in pounds, room dimensions in feet, and
so on. In this book, we will not routinely use these non-SI units, but we will
occasionally introduce them in examples and blog posts in the end. In such
cases, any necessary relationships between non-SI and SI units will be given or
can be found by searching in the search box on the right top corner of this
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