Accelerated Chemistry
Chapter 2 Notes – Measurement and Calculations
(Student edition)
Chapter 2 problem set: # 7, 9, 16, 18, 19, 22, 25, 29, 35, 38, 43, 44, 48, 52, 53
Useful diagrams:
2.1 Scientific Method (see text)
2.3 Using Scientific Measurements
Measurement: a quantity that has both a and a .
Measurements are fundamental to the experimental sciences. For that reason, it is
important to be able to make measurements and to decide whether a measurement is correct.
Accuracy: is a measure of how close a measurement comes to the actual or true value of whatever is measured.
Precision: is a measure of how close a series of measurements are to .
Observed Value (Experimental Value): the value in the lab.
True Value (Accepted Value, Theoretical Value): the value – typically found in a resource.
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 high or too low.
Example: 65 oC is the answer in your experiment. 66 oC is the theoretical value. Calculate the percent error.
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 cm 1 2
If the measurement is exactly half way between lines record it as
If it is a little over, record
If it is a little under, record
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 = $
40 x 3.14 = $
Rules for finding the # of sig figs:
1. All non-zeros are significant
Examples:
2. Zeros between non-zeros are significant
Examples:
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:
Let’s sing the sig fig song!!!!
Sig figs apply to scientific notation as well:
Examples:
Calculating with Measurements ( Sig Fig Math )
In general, a calculated answer cannot be more accurate than the least accurate 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
* 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: 35.25000000000000000000001 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
2 x 4.001283 =
Example: 15 divided by 3.79 doesn’t equal 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 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.
· Let’s refer back to sig figs and percent error now…
2.2 Units of Measurement
Measurement: ______
The problem is: what do you use as a standard?
Standard should be: ______.
The SI System: Le Systeme International d’Unites (The International System)
SI Advantages: easily convertible using decimals. English system uses fractions.
Important base units to know:
Quantity / Unit / AbbreviationMass / kilogram
Length / meter
Time / second
Temperature / kelvin
Amount of substance / mole
Electric current / ampere
Luminou Intensity / Candela
Important prefixes(multiples of base units) to know:
Prefix / Abbreviation / Meaning / Examplemega- / M / 106
kilo- / k / 103
deci- / d / 10-1
centi- / c / 10-2
milli- / m / 10-3
micro- / u / 10-6
nano- / n / 10-9
pico- / p / 10-12
Factor Label Method (Dimensional Analysis)
A method of problem solving that treats units like algebraic factors
Rules
Put the known quantity over the number 1.
On the bottom of the next term, put the unit on top of the previous term.
On top of the current term put a unit that you are trying to get to.
On the top and bottom of the current term, put in numbers in order to create equality.
If the unit on top is the unit of your final answer, multiply/divide and cancel units. If not, return to step # 2.
As far as sig figs are concerned, end with what you start with!
Example: convert 3.00 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 75.0 cm to m
Example: convert 150 g to kg
Example: convert 0.75 L to cm3
.
Example: convert 22 cm to dm
Density – ratio of mass to volume
Formula is:
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.
The common density units are:
Units of Volume:
Volume =
1 cm3 = 1 mL
1 dm3 = 1 L
Volume is a derived unit.
Derived Units: a combination of units.
Other derived units: area à cm2
Speed à m/s
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 305.0 g. What is the density of lead?
First, calculate it’s volume:
Next, calculate the density:
Back to Section 2.3…..Solving Quantitative Problems
1. Analyze – read carefully, list data with units, draw a picture
2. Plan – list conversion factors, show that units will work
3. Compute – use a calculator and use significant figures
4. Evaluate – does the answer “seem right?”
Proportional relationships
Directly proportional – examples – density (mass of water vs. volume), grades vs. freedom, etc.
In this example, we would say that, “volume of water is to mass of water.” We can write it as
Inversely proportional – examples – speed vs. time, more accidents = less driving
Another chemistry example, as the volume of a gas increases, the pressure decreases:
When two variables are related this way, they are said to be .
We can write it as
7