Download 2.8 x 10 -2

Pure substances have unique and consistent physical and chemical
properties.
Physical Properties:
•Melting Temperature
•Boiling Temperature
•Color
•Density
Measurement and the Metric System
A measurement is always expressed as a number (containing a certain
number of significant digits) accompanied by a unit (such as inches).
The set of units used in making scientific measurements is called the
Système International d’Unités, or simply, SI units.
All other units are derived from these units:
In the metric system of expressing numbers, all units can be prefixed
by a multiple of 10. These multiples are written as prefixes
immediately before the unit itself.
The following are the same number: 1.0 x 10-3 m = 1.0 mm.
Measurement, Uncertainty, and Significant Figures
Unless a measurement is made by counting a small number of objects, a
measurement will always contain some uncertainty, or error.
This error is expressed by the number of significant digits reported for
the measured number.
The number of significant digits in a number can be determined by the
following rules:
•A trailing zero, as in 4.130, is significant.
•A zero within a number, as in 35.06 cm, is significant.
•A zero before a digit, as in 0.082, is not significant.
•A number ending in zero with no decimal point, as in 20, is
ambiguous.
Ambiguities of this last type can be prevented by the use of scientific or
exponential notation.
Numbers obtained by counting, or exact definitions such as 12 inches =
1 foot, or 2.54 cm = 1 inch, have an infinite number of significant digits.
Scientific Notation
To write a number in scientific notation we write it as a number
between 1 and 10 multiplied by 10 raised to a whole-number power:
2.33 x 102.
The coefficient is the number between 1 and 10 (2.33) and the
exponential factor is the whole number exponent of 10 (2).
Any number raised to the 0 power is 1.
3 is written:
3 x 10o
24 is written: 2.4 x 101
346 is written: 3.46 x 102
2,537 is written: 2.537 x 103
Numbers less than 1 are written in a similar way:
0.0003 is written:
3 x 10-4
0.0346 is written:
3.46 x 10-2
0.0024 is written: 2.4 x 10-3
0.2537 is written:
2.537 x 10-1
In this case, the exponent represents the number of places to the left to
move the decimal place to convert from scientific notation back into
decimal notation.
Adding and subtracting numbers expressed in scientific notation:
(3.63 x 10-2) + (4.85 x 10-3) = (3.63 x 10-2) + (.485 x 10-2)
= (3.63 + .485) x 10-2
= 4.115 x 10-2
= 4.12 x 10-2
Multiplying numbers expressed in scientific notation:
(3.4 x 103) x (2.8 x 10-2) = (3.4 x 2.8) x (103 x 10-2)
= 9.52 x 103-2
= 9.52 x 101
Dividing numbers expressed in scientific notation:
(2.8 x 105) / (4.0 x 102) = (2.8 / 4.0) x (105 / 102)
= 0.70 x 105-2
= 0.70 x 103
= 7.0 x 102
When multiplying or dividing two numbers, the product or quotient generally
contains more significant digits than either of the two numbers entering into
the calculation.
8.5 in. x 8.5 in. = 72.25 in.
In this case, the product or quotient should be rounded to contain the same
number of significant digits as the lesser of the two numbers.
8.5 in. x 8.5 in. = 72.25 in. = 72 in.
The process of rounding involves discarding digits to the right of the
position we are rounding to.
If the next digit to the right of the rounding position is 5 or greater,
we round to the next higher digit. If the next digit is less than 5, we
round down:
1.5546 = 1.555
To 4 significant digits
1.5546 = 1.55
To 3 significant digits
1.5546 = 1.6
To 2 significant digits
1.5545 = 2
To 1 significant digit
(74 in. x 173 in.)
= 12802 in2
Too many significant digits.
= 1.2802 x 104 in2
Convert to scientific notation.
= 1.3 x 104 in2
Round to 2 significant digits.
The process for determining the correct number of significant digits for
the sum or difference of two numbers is somewhat different.
First express the two numbers to the same power of ten.
(9.3835 x 101) + (3.7 x 100) = (9.3835 x 101) + (0.37 x 101)
The sum or difference cannot have more digits to the right of the
decimal point than either of the two numbers being added or
subtracted.
(9.3835 x 101) + (0.37 x 101) = 9.7535 x 101
= 9.75 x 101
When adding two numbers, the number of significant digits may
increase:
9.9 + 9.9 = 19.8
When subtracting two numbers, the number of significant digits may
decrease:
19.8 – 18.9 = 0.9
A method commonly used to solve problems involving numbers having
units is the unit conversion method or factor analysis.
In this method, a number and its unit is converted to the corresponding
new number and unit by means of a conversion factor.
N1 unit1 = (N2 unit2) x (factor)
= (2 feet) x (12 inches / 1 foot)
= (2 x 12 / 1) x (feet x inches / foot)
24 inches = 24 inches
(feet/foot) = 1 with no units
Conversion factors are generally expressed as definitions or equalities:
1 mile = 5280 feet
From a definition two conversion factors may be derived:
(1 mile / 5280 feet) and (5280 feet / 1 mile)
The first factor can be used to convert feet into miles and the second to
convert miles into feet.
1760 feet x (1 mile / 5280 feet) = 1/3 mile
1/3 mile x (5280 feet / 1 mile ) = 1760 feet
If a conversion factor is correctly applied, a unit will always cancel.
1760 feet x (5280 feet / 1 mile) = (1760 x 5280) x (feet2/mile)
Incorrect!!
Several conversion steps may be necessary to solve a problem:
How many mm are there in 2.5 km?
(2.5 km) x (103 m / 1 km) x (1 mm / 10-3 m)
= (2.5 x 103 m) x (1 mm / 10-3 m)
= 2.5 x 106 mm
How many seconds are there in 7 days?
(7 days) x (24 hr. / 1 day) x (60 min. / 1 hr.) x (60 sec. / 1 min.)
= 6.04800 x 105 sec. (if 7 days means exactly 7 days)
= 6 x 105 sec.
(if 7 days means 7 days  1 day)
Mass is a measure of the quantity of matter and is independent of the
temperature, pressure, or location of the measurement.
The mass of an object is usually measured as its weight, however, the
weight of an object may change, depending upon location.
The weight of an object at the top of Mt. Everest is about 0.2% less
than at sea level.
The weight of an object in a satellite, orbiting the Earth, is zero.
The mass of an object can be accurately measured by comparing its
mass to that of a known standard mass by means of a balance.
The SI unit of mass is the kg. This is the only SI base unit that involves a
metric prefix.
The volume of a sample is the amount of space that it occupies.
Devices commonly used to measure liquid volume:
A graduated cylinder has an error of
about 1% ( 0.1 mL in 10 mL).
Volumetric flasks and pipettes
(fixed volume) and burets (variable
volume) have an error of about 0.1%
( 0.01 mL in 10 mL).
Hypodermic syringes have an error
of about 5–6% ( 0.5-0.6 mL in 10
mL).
All volumetric containers are calibrated in milliliters (mL).
One mL is exactly equal to 1 cm3.
1000 mL = 1 Liter = 1000 cm3
1 Liter = 1000 cm3 x (10-2 m / 1 cm)3
= 103 cm3 x (10-6 m3 / 1 cm3)
1 Liter = 10-3 m3
or
103
Liter = 1
m3
0.1 m3 = 1 L
Density
The density of an object is the ratio of its mass to its volume:
The density of an object varies slightly with temperature because the
volume of most substances increases with increasing temperature.
To measure the density of an object one must first measure its mass and
its volume.
The mass of an object is generally measured using a laboratory balance. In
the case of a gas or liquid, the sample and its container is weighed and the
mass of the empty container is subtracted.
The volume of a liquid or gas can be obtained from the volume of its
container.
The volume of a regular solid can be calculated from its dimensions.
Alternatively, and for an irregular solid, the volume can be obtained from the
volume of liquid displaced when the solid is placed in a partially filled
graduated cylinder.
An alternative way to measure the density of a liquid is to compare its
density to that of a series of objects of known density.
A solid whose density is greater than that of the liquid will sink in the
liquid.
A solid whose density is less than that of the liquid will float on the
liquid.
A solid whose density is equal to that of the liquid will remain
wherever placed in the liquid and will neither sink nor float.
A hydrometer is a device based on the above principles that can be used
to easily measure the density of a liquid.
Most hydrometers are calibrated to read the ratio of the unknown liquid
to that of a reference liquid, usually water. This ratio is known as the
specific gravity of the liquid.
Specific gravity has no
units, since it is the ratio of
two densities.
Temperature
Heat will always flow from a hot object to a cold object if they are placed
in contact.
The property that is measured to express the “hotness” of an object is
called the temperature of the object and is measured using a
thermometer.
Most common thermometers are based on the fact that liquids expand
upon heating. If a tube is connected to a reservoir filled with a liquid, the
liquid will be forced to rise up in the tube upon heating.
A thermometer can be calibrated by placing it in freezing water and
marking the liquid level, and then placing it in boiling water and marking
the new liquid level.
If 99 divisions are inscribed between the
two marks (making 100 equally spaced
intervals) and the freezing temperature is
specified as 0, the thermometer will
indicate temperature on the Celsius scale.
If 179 division are inscribed between the
two marks (making 180 equally spaced
divisions) and the freezing point is specified
as 32, the thermometer will indicate
temperature on the Fahrenheit scale.
Another temperature scale, the Kelvin scale, is almost always used when
making scientific temperature measurements. On this scale, the freezing
point of water is 273.15 K and the boiling point of water is 373.15 K.
There is a simple relationship between the Kelvin scale and the Celsius
scale:
The relationship between the Fahrenheit and Celsius scales is slightly
more complicated: