Download Chapter 5 - Scarsdale Public Schools

Chapter 5: Measurements and Calculations... Brought to you by Eli Nobler.
A quantitative observation is called a measurement.
5.1: Scientific Notation
Objective: To show how very large or very small numbers can be expressed as the product of a number
between 1 and 10 and a power of 10.
Key Concepts:
● Scientific notation is a method for making very large or very small numbers more compact and
easier to write.
○ 125 = 1.25 X 100 is the same as 125 = 1.25 X 102
○ This simply expresses a number as a product of a number between 1 and 10 and the
appropriate power of 10.
93,000,000 = 9.3 X 10,000,000 = 9.3 X 107
○ Whenever the decimal point is moved to the left, the exponent of 10 is positive
○ Whenever the decimal point is moved to the right, the exponent of 10 is negative
5.2: Units
Objective: To learn the English, metric, and SI systems of measurement.
Key Concepts:
The units part of a measurement tells us what scale or standard is being used to represent the
results of the measurement.
○ English system- used in United States
○ Metric system- used practically internationally
○ The International System was eventually set up due to its effectiveness, aka SI.
Some Fundamental SI Units
Physical Quantity
Name of Unit
Abbreviation
mass
Kilogram
kg
length
Meter
m
time
Second
s
temperature
Kelvin
K
The Commonly Used Prefixes in the Metric System
Prefix
Symbol
Meaning
mega
kilo
deci
centi
milli
micro
nano
M
k
d
c
m
µ
n
1,000,000
1000
0.1
0.01
0.001
0.000001
0.000000001
Power of 10 for Scientific
Notation
106
103
10-1
10-2
10-3
10-6
10-9
5.3: Measurements of Length, Volume, and Mass
Objective: To use the metric system to measure length, volume, and mass.
Key Concepts:
The fundamental SI unit of length is the meter, which is a little longer than a yard (1 meter =
39.37 inches)
The Metric System for Measuring Length
Symbol
Meter Equivalent
km
1000m or 103m
m
1m or 1m
dm
0.1m or 10-1m
cm
0.01m or 10-2m
mm
0.001m or 10-3m
µ
0.000001m or 10-6m
nm
0.000000001m or 10-9m
Unit
kilometer
meter
decimeter
centimeter
millimeter
micrometer
nanometer
Volume is the amount of three-dimensional space occupied by a substance
Liter is a unit measurement for volume, abbreviated as L
One cubic centimeter is called a milliliter (abbreviated mL), a unit of volume used very
commonly in chemistry
The Relationship Between the Liter and Milliliter
Unit
Symbol
Equivalence
liter
L
1L = 1000mL
milliliter
mL
1/1000L = 10-3L = 1mL
Mass is the quantity of matter present in an object
The fundamental unit, and prefix variations, are based on the gram
Unit
kilogram
gram
milligram
The Most commonly Used Metric Units for Mass
Symbol
Gram Equivalent
kg
1000g = 103 = 1kg
m
1g
mg
0.001g = 10-3g = 1mg
5.4: Uncertainty in Measurement
Objective: To learn how uncertainty in a measurement arises. To learn to indicate a measurement’s
uncertainty by using significant figures.
Key Concepts:
Whenever a measurement is made with a device such as a ruler or a graduated cylinder, an
estimate is required.
Because the last number is a precise measurement is based on a visual estimate, it may be
different when other people make the same measurement.
The digits that are constant in a collective group of measurements are called the certain numbers
of the measurement.
The last digit that varies among the group of measurements is called the uncertain number of the
measurement.
A measurement always has some degree of uncertainty.
The numbers recorded in a measurement (all the certain numbers plus the first uncertain number)
are called significant figures.
○ Determined by the inherent uncertainty of the measuring device
5.5: Significant Figures
Objective: To learn to determine the number of significant figures in a calculated result.
Key Concepts:
●
●
●
●
Rules for counting Significant Figures
○ 1. Nonzero integers. Nonzero integers always count as significant figures.
○ 2. Zeros. There are three classes of zeros:
■ A. Leading zeros are zeros that precede all of the nonzero digits. They never
count as significant figures
■ B. Captive zeros are zeros that fall between nonzero digits. They always count as
significant figures.
■ C. Trailing zeros are zeros at the right end of the number. They are significant
only if the number is written with a decimal point.
○ 3. Exact numbers. Often calculations involve numbers that were not obtained using
measuring devices but were determined by counting.
Rules for counting significant figures also apply to numbers written in scientific notation.
○ Two advantages to using scientific notation
■ number of sig figs can be indicated easily
■ fewer zeros are need to write a very large or a very small number
Occasionally, rounding off is needed in order to convert a number you get on your calculator
into sig figs
○ Rules for rounding off
■ if the digit to be removed
● is less than 5, the preceding digit stays the same
● is equal to or greater than 5, the preceding digit is increased by 1
■ in a series of calculations, carry the extra digits through to the final result and
then round off
Rules for Using Significant Figures in Calculations
○ for multiplication and division, the number of sig figs in the result is the same as that in
the measurement with the smallest number of sig figs
○ for addition or subtraction, the limiting term is the one with the smallest number of
decimal places
5.6: Problem Solving and Dimensional Analysis
Objective: To learn how dimensional analysis can be used to solve various types of problems.
Key Concepts:
● The conversion factor is the ratio of the two parts of the statement that relates the two units.
● An equivalence statement is a statement that indicates two values that are equal, yet with
different units
● Conversion factors are rations of the two parts of the equivalence statement that relates the two
units.
● We choose a conversion factor that cancels the units we want to discard and leave the units we
want in the result.
● Changing from one unit to another via conversion factors (based on the equivalence statements
between the units) is often called dimensional analysis.
● General steps of dimensional analysis
○ To convert from one unit to another, use the equivalence statement that relates the
two units. The conversion factor needed is a ratio of the two parts of the equivalence
statement.
○ Choose the appropriate conversion factor by looking at the direction of the required
change (make sure the unwanted units cancel).
○ Multiply the quantity to be converted by the conversion factor to give the quantity with
the desired units.
○ Check that you have the correct number of sig figs.
○ Ask whether your answer makes sense.
5.7: Temperature Conversion: An Approach to Problem Solving
Objective: To learn the three temperature scales. To learn to convert from one scale to another. To
continue to develop problem-solving skills.
Key Concepts:
● Fahrenheit scale is when water boils at 212ºF and freezes at 32ºF, normal body temperature is
98.6ºF, and it is used widely in the United States and Great Britain.
● Celsius scale is used in Canada and Europe and in sciences in most countries. It is based off the
metric system in where it is based off the powers of 10. Its freezing point is 0ºC and its boiling
point is 100ºC.
● Another scale used in sciences is the absolute or Kelvin scale, the freezing point is 273K and the
boiling point is 373K.
● Key points in comparing the three scales:
○ The size of each unit (degree) is the same in C and K. The difference between the
freezing and boiling points are both 100.
○ F degrees are smaller than C and K. There are 180 degrees between freezing and boiling
in F, as opposed to 100.
○ The zero points are different on all three scales.
● In converting Kelvin to Celsius you simply add 273 to the Celsius value to achieve the Kelvin
value.
● There are two adjustments in converting Fahrenheit and Celsius
○ For the different size units
212 - 32 = 180 (F) and 100 - 0 = 100 ©
180 F = 100 C
Divide both by 100.
1.80 F = 1.00 C
○ For the different zero points
Temperature in F = (1.80) X (Temperature in C) + (32)
Temperature Conversion Formules
Celsius to Kelvin
TK = T⁰C + 273
Kelvin to Celsius
T⁰C = TK - 273
Celsius to Fahrenheit
T⁰F = 1.80(T⁰C) + 32
Fahrenheit to Celsius
T⁰C = (T⁰F - 32) ÷ (1.80)
5.8: Density
Objective: To define density and its units.
Key Concepts:
● Density can be defined as the amount of matter present in a given volume of substance.
○ Density = mass ÷ volume
○ the unit for density is generally g/mL
○ This formula can easily be manipulated to solve for any of the three values.
● Specific gravity is defined as the ratio of the density of a given liquid to the density of water at
4oC
○ specific gravity has no units
References:
Zumdahl, S, et. al.; World of Chemistry; Houghton Mifflin Co. © 2002