1. Chapter 2 Notes Measurements and Solving Problems
Problem Set: 14-19, 22-25, 29-31, 35-44
Crash Course Chemistry Video

2. Scientific Method 1. Problem state it clearly – usually as a question
2. Gather information
do some research on your problem
3. Hypothesis
a suggested solution
4. Procedure
experiment and examine the situation to check the hypothesis
5. Data
Note everything your senses can gather. Record the data and keep careful records.
6. Analysis
Put the data in order- charts/tables. Figure out the meaning of the data
7. Conclusion
Explain the data. State whether or not it supports the hypothesis.

3. Scientific Method Theory
A hypothesis that has been rigorously tested, and not found faulty, usually also having been found somewhat useful.
Law
A readily demonstrable fact, that cannot be disproven.

4. 2.1 Units of Measurement
Measurement – comparison of an object to a standard.
The problem is, what do you use as a standard?
Standard should be an object or natural phenomenon of constant value, easy to preserve and reproduce, and practical in size.

5. 2.1 Units of Measurement The SI System SI = Standard International
Important base units to know:
Quantity
SI Base Unit
Abbreviation
Mass
Kilogram
(Kg)
Length
Meter
(m)
Volume
Liter or cm3
L or cm3
Time
Second
(s)
Temperature
Kelvin
(K)
Amount of a substance
Mole

6. Meter, liter, gram, second
2.1 Units of Measurement
Important prefixes(multiples of base units) to know:
Prefix
Abbreviation
Meaning
Example
tera  T
1012
1 terameter = 1,000,000,000,000
giga G 
109
1 gigameter = 1,000,000,000
mega-  M
106
1 megameter = 1,000,000
kilo- k 
103
1 kilogram = 1000
hecto-  H
102
1 hectometer = 100
deka D 
101
1 dekameter = 10
BASE
Meter, liter, gram, second 1
deci- d 
10-1
1 deciliter =
centi-  c
10-2
1 centimeter =
milli- m 
10-3
1 millimeter= 1,
micro-  u
10-6
1 micrometer = 1,000,
nano- n 
10-9
1 nanometer = 1,000,000,
pico- p 
10-12
1 picometer = 1,000,000,000,

7. 2.3 Using Scientific Measurement
Significant Figures (Digits) - “Sig Figs”
Definition: digits in a measurement that are known + 1 estimated digit
1.15 ml implies ml
The more significant digits, the more reproducible the measurement is.
These are the numbers that “count!”
Ex1: π = 22/7 = what do math teachers let you use?
Ex2: You collect a paycheck for a 40 hour week – what’s the difference between getting paid pi vs ?

8. Rules for finding the # of sig figs
1. All non-zeros are significant ex. 7 [ ] 77 [ ] 4568 [ ] 2. Zeros between non-zeros are significant ex. 707 [ ] 7053 [ ] [ ] 3. Zeroes to the left of the first nonzero digit serve only to fix the position of the decimal point and are not significant ex: [ ] [ ] [ ] 4. In a number with digits to the right of a decimal point, zeroes to the right of the last nonzero digit are significant ex: 43 [ ] [ ] 43.0 [ ] [ ] [ ] 5. In a number that has no decimal point, and that ends in zeroes (ex. 3600), the zeroes at the end may or may not be significant (it is ambiguous). To avoid ambiguity, express in scientific notation and show in the coefficient the number of significant digits. ex = 3.6 x 103 [ ]

9. Scientific Notation A way to express very small or very large numbers
Example:
12345 = x 104
= 4.56 x 10-3
Exponent – the # of times the decimal was moved
(+) to the left
(-) to the right
Coefficient – must be between 1 and 9
Base

10. Scientific Notation 56934 = 0.0000037 = 2.347 x 10-3 = 8.98736 x 105 =
56934 = =
2.347 x 10-3 =
x 105 =
Reverse it!
(+) right
(-) left

11. Counting significant digits
1. Convert to scientific notation
2. Disappearing zeroes just hold the decimal point, they aren’t significant
Ex1:
700 [ ] - means “about 700 people at a football game”
700. [ ] - means “exactly ”
700.0 [ ] - means “teacher weighs exactly lbs”
Other examples
0.5 [ ] 0.50 [ ] [ ] 
Sig. figs apply to scientific notation as well 
9.7 x = [ ]
1.20 x = [ ]

12. Calculating with Measurements ( Sig Fig Math )
Rounding Rules
XY > Y
When Y > 5, increase X by 1
When Y < 5, don’t change X
When Y = 5,
If X is odd, increase X by 1
If X is even, then don’t change X
Ex1: round to 3 sig figs = = = =
Note - 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.
Ex2: round to 3 sig figs =

13. Calculating rules:
Multiplying or dividing – round results to the smaller # of sig. figs in the original problem. 
Ex1: cm Ex2: g
cm / m
x cm

14. Calculating rules:
2. Adding or subtracting - round to the last common decimal place on the right. 
Ex1: Ex2: g g

15. Partner Share Partner Share:
How do you determine the proper sig figs when adding and subtracting?
How do you determine the proper sig figs when multiplying or dividing?
What is the 5 rule?

16. 2.1 Units of Measurement Factor Label Method (Dimensional Analysis)
A method of problem solving that treats units like algebraic factors
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 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!

17. 2.1 Units of Measurement Factor Label Method (Dimensional Analysis)
Ex1 - convert 26 inches to feet
Ex2 - convert 1.8 years to seconds
Ex3 - convert 2.50 ft to cm if 1 inch = 2.54 cm

18. 2.1 Units of Measurement Factor Label Method (Dimensional Analysis)
Ex4 -   convert 150. g to ug
Ex5 -   convert 75 cm to Hm
Ex6 - convert 0.75 L to cm3 (1 cm3 = mL)

19. 2.1 Units of Measurement
Density – ratio of mass to volume
The common density units are:
g/cm3 for solids
g/ml for liquids
g/L for gases
Formula is D = m/v
Density is
a) a characteristic b) and intensive property c) temperature dependent
Two ways to find volume in density problems:
1. Water displacement 2. Volume formula
Note: the density is the same no matter what is the size or shape of the sample.

20. 2.1 Units of Measurement Ex1: Find the density of an object with
m= 10g and v=2 cm3
Ex2: A cube of lead 3.00 cm on a side has a mass of g. What is the density of lead?  
First, calculate it’s volume:
Next, calculate the density:
Density = mass/volume =

21. 2.1 Units of Measurement
Ex 3: A graduated cylinder contains 25 mL of water. When a 4.5 g paper clip is dropped into the water, the water level rises to 36 mL. What is the density of the paper clip?

22. 2.3 Using Scientific Measurement
Precision vs. Accuracy
Precision
Accuracy
Reproducibility
Check by repeating measurements
A function of the instrument
Poor precision results from poor technique
Correctness – closeness to the true value
Check by using a different method
A function of the user
Poor accuracy results from procedural or equipment flaws

23. 2.3 Using Scientific Measurement
Precision vs. Accuracy
good precision & good accuracy
poor accuracy but good precision
good accuracy but poor precision
poor precision & poor accuracy

24. 2.3 Using Scientific Measurement
Percent Error - experiments don’t always give true results - error is pretty much a given 
Actual (experimental value) - data found in an experiment
True value (theoretical value) - data that is generally accepted as true
Percent (%) error = (actual - theoretical) x 100
theoretical value
+/- shows the direction of the error - values are either too high or too low
Note: some texts teach that percent error should be treated as absolute value - I say you should use +/- in order to show direction of error and better analyze your experiments.
Ex1: 66 Co is the answer in your experiment 65 CO is the theoretical value

25. 2.3 Using Scientific Measurement
Two important points:
Uncertainty in Measurement
making a measurement usually involves comparison with a unit or a scale of units
When making a measurement, include all readable digits and 1 estimated digit
always read between the lines!
the digit read between the lines is always uncertain

26. 2.3 Using Scientific Measurement
Uncertainty in Measurement
when measuring, include all readable digits and 1 estimated digit
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
You would read this as 18.0 mL and not 18.5 mL.