Honors Chemistry
Chapter 3 Notes – Scientific Measurement
(Student’s edition)
Chapter 3 problem set: 57-61, 64, 65, 70, 71, 76, 84, 86, 89, 92, 101, 106
Useful diagrams: 3.5, 3.6, 3.9, 3.13
3.1 Measurements and Their Uncertainty
Measurement: a quantity that has both a and a .
Measurements are fundamental to the sciences. For that reason, it is
important to be able to make measurements and to decide whether a measurement is
correct.
Scientific Notation: a given number is written as the product of two numbers: a
coefficient and 10 raised to a power.
Accuracy: is a measure of how close a measurement comes to the or value of
whatever is measured.
Precision: is a measure of how close a series of measurements are to .
Percent Error:
Experiments don’t always give true results. Error is pretty much a given.
Observed Value (Experimental Value): the value in the lab.
True Value (Accepted Value, Theoretical Value): the value.
Absolute Error: the between the true and observed value.
Percent Error =
The order is important. It implies direction. + or - shows the direction of the
error. It indicates if values are either too or too .
However, some texts teach that percent error should be treated as absolute value. I say you should use + or – in order to show direction of error and better analyze your experiments.
Example: 65 oC is the answer in your experiment. 66 oC is the theoretical value.
Calculate the percent error.
NIB - Uncertainty in Measurement:
Two important points to remember regarding measurement:
1. Instruments can only measure so well.
2. We only need some measurements to be really exact.
A person has a height of 5’ 11” inches, not 5.916666667 feet.
When measuring, include all readable digits and one digit.
0 1 2
What value is the arrow measuring to?
1
1.3
1.35
1.351
1.4
The answer is .
If the measurement is exactly half way between lines record it as 0.5
If it is a little over, record .7 or .8
If it is a little under, record .2 or .3
Significant Figures (Digits) - “Sig Figs”:
Significant Figures: includes all of the digits that are , plus a last digit that
is .
Measurements must always be reported to the correct number of significant
figures because calculated answers often depend on the number of significant
figures in the values used in the calculation.
Example: say you collect a paycheck for a 40 hour week. How much difference is there between getting paid pi vs. 3.14 per hour?
40 x pi = $125.66 x 4 weeks = $502.65 x 12 = ______
40 x 3.14 = $125.6 x 4 weeks = $502.4 x 12 = ______
Rules for finding the # of sig figs:
1. All non-zeros are significant
Examples: 7 à __
77 à __
4568 à __
2. Zeros between non-zeros are significant
Examples: 707 à __
7007 à __
3. All other zeros are significant only if....
a) they are to the right or left of decimal point
and
b) they are to the right of a sig fig
- all other (not a and b) are simply place holders
Examples: 700 à __
700. à __
700.0 à __
0.5 à __
0.50 à __
0.050 à __
Alternate arrow technique: use the arrow method with the above numbers that have a
decimal written in the number. Draw an arrow from left to right starting at the first non-
zero digit. Draw another arrow from the decimal going in both directions. If a zero has
two arrows under it, then it is significant.
Sig figs apply to scientific notation as well:
Examples: 9.7 x 102 à __
970 à __
1.20 x 10-4 à __
0.00120 à __
Calculating with Measurements ( Sig Fig Math )
In general, a calculated answer cannot be more precise than the _____ precise
measurement from which it was calculated.
Rules of Rounding:
numbers greater than 5 (6-9) get rounded ______
numbers less than 5 (1-4) get rounded ______
for numbers ending on 5 (the “5” rule):
if the preceding digit is odd, round ____
if the preceding digit is even, round ______
Round the following examples to 3 sig figs:
35.27 à ____
87.24 à ____
35.25 à ____
95.15 à ____
* zero is even
95.05 à ____
* The “5” rule only applies to a “dead even” 5. If any digit other than 0 follows a 5 to be rounded, then the number gets rounded up without regard to the previous digit.
Round the following examples to 3 sig figs:
35.250000000000000000000000001 à _____
Rules for calculating with sig figs:
1. When multiplying or dividing, the answer should have the smaller # of
sig figs in the original problem.
Example: 2 x 4.001283 doesn’t equal 8.002566
2 x 4.001283 = ___
Example: 15 divided by 3.79 doesn’t equal 3.9577836 15 divided by 3.79 = ___
2. When adding or subtracting, round to the last common decimal place on the right.
Example: 21.52 + 3.1 doesn’t equal 24.62 21.52 + 3.1 = _____
* Exact conversion factors do not limit the # of sig figs. The final answer
should always end with the # of sig figs that the problem.
* If both of the above rules are applied in a problem (see percent
error problem on previous page), ….
NIB - Use of +/- notation:
Scientists sometimes use +/- notation to show how much uncertainty there is in a
measurement.
46.85 mm +/- .03 mm
This means that the answer could be as high as 46.88 mm or as low as 46.82 mm.
Of course, there is always implied uncertainty. If we say a building is 9 m high, we’re saying that it is between 8 and 10 m high. We say 9 because it’s closer to 9 than 8 and closer to 9 than 10. We report 9 +/- .5 m
Measurement / Implied Range900
90
9
9.0
9.00
900.
900.0
3.2 International System of Units
SI system: Le Systeme International d’Unites: 7 base units
Quantity / SI Base Unit / SymbolLength / Meter
Mass / Kilogram
Temperature / Kelvin
Time / Second
Amount of Substance / Mole / mol
Luminous Intensity / Candela / cd
Electric Current / Ampere / A
SI Advantages: easily convertible using decimals. English system uses fractions.
Prefixes to know:
Prefix / Symbol / Value / Base Unit ValueGiga / G / 0.000 000 001 / 1
Mega / M / 0.000 001 / 1
Kilo / K / 0.001 / 1
Deca / da / 0.1 / 1
Deci / d / 10 / 1
Centi / c / 100 / 1
Milli / m / 1000 / 1
Micro / µ / 1,000,000 / 1
Nano / n / 1,000,000,000 / 1
Pico / p / 1,000,000,000,000 / 1
Units of Volume:
Volume = length x width x height
1 cm3 = ______
1 m3 = ______
Volume is a derived unit.
Derived Units: ______.
Other derived units: area à ______
Density à ______
Speed à m/s
Units of Temperature:
Temperature: a measure of an object is. It is used to determine the
of heat transfer.
K =
oC =
Units of Energy:
Energy: The capacity to do or to produce .
1 Joule = 0.2390 calories
1 cal = ______
3.3 Conversion Problems
General Rules for Problem Solving:
1. Read the problem - make a list of knowns and unknowns
2. Look up any needed information (conversion factors, etc.)
3. Work out a plan.
4. Do the math.
5. Check your work. Does the answer seem right? Did you record the correct number of sig figs? Does your answer have the proper unit?
Conversion Factor: a ratio of equivalent measurements.
Dimensional Analysis (Factor Label Method): a method of problem solving that treats
units like algebraic factors.
Basic Rules:
1. Put the known quantity over the number 1.
2. On the bottom of the next term, put the unit on top of the previous term.
3. On top of the current term put a unit that you are trying to get to.
4. On the top and bottom of the current term, put in numbers in order to create an equality.
5. If the unit on top is the unit of your final answer, multiply/divide and cancel units. If not, return to step # 2.
6. As far as sig figs are concerned, end with what you start with!
Example: convert 3.0 ft to inches
Example: convert 1.8 years to seconds
Example: convert 2.50 ft to cm if 1 inch = 2.54 cm
Example: convert 75 cm to m
Example: convert 150 g to kg
Example: convert 0.75 L to cm3
Example: convert 1,500,000,000 mm3 to m3
Example: convert 22 cm to dm
3.4 Density
Density: the ratio of the of an object to its .
D =
Density is an intensive property that depends only on the of a substance, not on the of the sample.
The density of a substance generally as its temperature increases.
Careers in Chemistry:
Analytical chemists focus on making quantitative measurements. They can work for a pharmaceutical company investigating the composition of medicines in drugs. They are creative thinkers and find solutions to problems. They can also be hired by biomedicine companies, biochemistry companies, and industrial manufacturers. Many of these jobs require a master’s degree or Ph. D.