ch. 2 “scientific measurement & problem solving”
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Ch. 2 “Scientific Measurement & Problem Solving”. SAVE PAPER AND INK!!! If you print out the notes on PowerPoint, print "Handouts" instead of "Slides“ in the print setup. Also, turn off the backgrounds (Tools>Options>Print>UNcheck "Background Printing")!. - PowerPoint PPT PresentationTRANSCRIPT
Ch. 2 “Scientific Measurement & Problem Solving”
SAVE PAPER AND INK!!! If you print out the notes
on PowerPoint, print "Handouts" instead
of "Slides“ in the print setup. Also, turn off the backgrounds
(Tools>Options>Print>UNchec
k "Background Printing")!
Types of Observations and Measurements
• We make QUALITATIVE observations of reactions — Describes using wordsEx. Odor, color, texture, and physical state.
• We also make QUANTITATIVE observations, using numbers- measurements
• Ex. 25.3 mL, 4.239 g
Standards of Measurement
When we measure, we use a measuring tool to compare some dimension of an object to a standard. For example, at one time the
standard for length was the king’s foot. What are some
problems with this standard?
Accuracy – how close a measurementcomes to the true value of what is measured
Precision – is concerned with the reproducibility of the measurement
Our measurements must be bothAccurate & precise!
Three targets with three arrows each to shoot.
Can you hit the bull's-eye?
Both accurate and precise
Precise but not accurate
Neither accurate nor precise
How do they compare?
Stating a Measurement
In every measurement there is a
¨Number followed by a
¨ Unit from a measuring device
The number should also be as precise as the
measurement!
SI Measurement• Le Systeme International d’Unites : SI
Metrics• System of measurement agreed on all over the
world in 1960• Contains 7 base units• units are defined in terms of standards of
measurement that are objects or natural occurrence that are of constant value or are easily reproducible
• We still use some non-SI units!
• SI units — based on the metric system
• The only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly
• Among countries with non-metric usage, the U.S. is the only country significantly holding out. The U.S. officially adopted SI in 1966.
Information from U.S. Metric Association
Le Système international d'unités
The 7 Base Units of SI
S.I. (the ones you’re responsible for knowing!)
Selected S.I. base (or standard) units
Mass kg
Length m
Time sec
Temperature KAmount of Substance mole mol
Derived Unitsmade by combining Base Units!
• Volume length cubed m3 cm3
• Density mass/volume g/mL kg/L g/ cm3
g/L
• Speed length /time mi/hr m/s km/hr
• Area length squared m2 cm2
We use prefixes to expand on the base units!
S.I. prefixes you must memorize!
Prefix Abbreviation Value
kilo k 103
deci d 10-1
centi c 10-2
milli m 10-3
micro m10-6
nano n 10-9
Metric System• These prefixes are based on powers of
10. • From each prefix every “step” is either:
• 10 times larger or
• 10 times smaller• For example
• Centimeters are 10 times larger than millimeters
• 1 centimeter = 10 millimeters kilo hecto deca
Base Unitsmetergramliter
deci centi milli
Metric System
• An easy way to move within the metric system is by moving the decimal point one place for each “step” desiredExample: change meters to centimeters1.00 meter = 10.0 decimeters = 100.
centimeters
kilo hecto decameterlitergram
deci centi milli
mass – measure of the quantity of matter
SI unit of mass is the kilogram (kg)
1 kg = 1000 g = 1 x 103 g
Not to be confused with -
weight – mass + gravity
force that gravity exerts on an object
Mass does not vary from place to place!
A 1 kg bar will weigh
1 kg on earth
0.1 kg on moon
A 1 kg bar has a mass of 1 kgon earth and on the moon
Volume – Amount of space occupied by matter
SI derived unit for volume is cubic meter (m3)
1 L = 1000 mL = 1000 cm3 = 1 dm3
1 mL = 1 cm3
1 dm3 = 1 L
We often use the Liter (L) when working with liquid volumes!
m3 = m x m x m
Temperature Scales• Fahrenheit• Celsius• Kelvin
Anders Celsius1701-1744
Lord Kelvin(William Thomson)1824-1907
TEMPERATURE SCALES
In Chemistry, the terms heat and temperature are often used to describe specific properties of a sample.
HEAT is the most common form of energy in nature and is directly related to the motion of particles of matter.
The faster the motion of particles in a sample the greater its heat content.
A forest fire and a lit match may both be at the same temperature, but there is a large difference in the amount of heat each possess.
TEMPERATURE is associated only with the intensity of heat and is not affected by the size of the sample.
Heat always spontaneously flows from a hotter system (higher temp.) to a colder system (lower temp.).
Temperature Scales
Notice that 1 Kelvin = 1 degree Celsius
Boiling point of water
Freezing point of water
Celsius
100 ˚C
0 ˚C
100˚C
Kelvin
373 K
273 K
100 K
Fahrenheit
32 ˚F
212 ˚F
180˚F
Temperature Scientists do not know of any limit on how high a temperature may be. The temperature at the center of the sun is about 15,000,000 °C. However, nothing can have a temperature lower than –273°C. This temperature is called absolute zero. It forms the basis of the Kelvin scale. Because the Kelvin scale begins at absolute zero, 0 K equals –273°C, and 273 K equals 0 °C.
Calculations Using Temperature
• Many chemistry equations require temp’s to be
in Kelvin
• K = ˚C + 273• Body temp = 37 ˚C + 273 = 310 K
• Liquid nitrogen = 273 -77 K = -196 ˚C
˚C = K - 273
DENSITY –
Density mass (g)volume (cm3)
Mercury
13.6 g/cm3 21.5 g/cm3
Aluminum
2.7 g/cm3
Platinummercuryplatinum
an important and useful physical property (Derived Unit)ratio of mass per unit of volume
DENSITY• Density is an
INTENSIVE property of matter.• Since it is a ratio
of mass to volume -does NOT depend on quantity of matter.
Styrofoam Brick
The density of 1 g of gold =The density of 5 kg of gold!
Problem A piece of copper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.095 cm thick. Calculate density (g/cm3).
Get out those calculators!
Copper orePure copper metal
SOLUTION1. Make sure dimensions are in common
units. (all are in cm’s)2. Calculate volume in cubic centimeters. L x W x H = volume
3. Calculate the density.57.54 g6.4 cm3 = 9.0 g / cm3
(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm3
Learning Check
Which diagram represents the liquid layers in the cylinder?(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)
1) 2) 3)
K
K
W
W
W
V
V
V
K
Solution
(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)
1)
KW
V
Denser materials ‘sink’ inless dense materials!
Most solids sink in their liquid form.Can you think of an exception to this?!
WATER!!
Finding Volume of an IrregularSolid byWater Displacement
A solid displaces a matching volume of water when the solid is placed in water.
25 mL33 mL
Volume of solidis 8 mL
Calculator Time! What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? a) 0.2 g/ cm3 b) 6.0 g/cm3 c) 252 g/cm3
33 mL 25 mL
Percent Error• Percent Error:
• Measures the inaccuracy of experimental data
• Can have + or – value• Accepted value : correct value based on reliable
references• Experimental value: value you measured in the lab
%100accepted
alexperimentaccepted
Scientific NotationThe number of atoms in 12 g of carbon:
602,200,000,000,000,000,000,000
6.022 x 1023
The mass of a single carbon atom in grams:
0.0000000000000000000000199
1.99 x 10-23
N x 10n
N is a number between 1 and 10(1 non-zero digit to left of dec. pt.)
n is a positive or negative integer
To change standard form to scientific notation…
• Place the decimal point so that there is one non-zero digit to the left of the decimal point.
• Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.
• If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.
Examples• Given: 289,800,000• Use: 2.898 (moved 8 places)• Answer: 2.898 x 108
• Given: 0.000567• Use: 5.67 (moved 4 places)• Answer: 5.67 x 10-4
To change scientific notation to standard
form…• Simply move the decimal point to
the right for positive exponent 10. • Move the decimal point to the left
for negative exponent 10.
(Use zeros to fill in places.)
Example• Given: 5.093 x 106
• Answer: 5,093,000 (moved 6 places to the right)
• Given: 1.976 x 10-4
• Answer: 0.0001976 (moved 4 places to the left)
Learning Check• Express these numbers in
Scientific Notation:
1) 4057892) 0.0038723) 30000000004) 25) 0.478260
Scientific Notation568.762
n > 0568.762 = 5.68762 x 102
move decimal left0.00000772
n < 00.00000772 = 7.72 x 10-6
move decimal right
Addition or Subtraction
1. Write each quantity with the same exponent n
2. Combine N1 and N2 3. The exponent, n, remains
the same
4.31 x 104 + 3.9 x 103 =
4.31 x 104 + 0.39 x 104 =
4.70 x 104
Scientific NotationCalculations
Multiplication1. Multiply N1 and N2
2. Add exponents n1 and n2
3. Put in proper format, if necessary
(4.0 x 10-5) x (7.0 x 103) =(4.0 x 7.0) x (10-5+3) =
28 x 10-2 =2.8 x 10-1
Division1. Divide N1 and N2
2. Subtract exponents n1 and n2
3. Put in proper format, if necessary
8.5 x 104 ÷ 5.0 x 109 =(8.5 ÷ 5.0) x 104-9 =
1.7 x 10-5
Significant FiguresThe numbers reported in a
measurement are limited by the measuring tool
Significant Figures in a measurement include all certain digits plus one estimated digit
•7.50 cm
•19.5 mL
Significant Figures• All certain digits plus one
estimated digit (used when recording measurements)
Known + Estimated DigitsIn 2.85 cm…
• Known digits 2 and 8 are 100% certain(there are lines on the ruler for these!)
• The third digit, 5, is estimated (uncertain)
• In the reported length, all three digits (2.76 cm) are significant including the estimated one
Figure 5.5: Measuring a pin.There are not really lines on the scale here – just estimates!
Reading a Meterstick. l2. . . . I . . . . I3 . . . .I . . . . I4. . cm
First digit (known) = 2 2.?? cmSecond digit (known)= 0.8 2.8? cmThird digit (estimated) between 0.03- 0.05Length reported = 2.83 cm
or 2.84 cm
or 2.85 cm
Learning Check
. l8. . . . I . . . . I9. . . . I . . . . I10. . cm
What is the length of the line?
1) 9.3 cm
2) 9.40 cm
3) 9.30 cm
How does your answer compare with your neighbor’s answer?
Rules for Counting Significant Figures
RULE 1. All non-zero digits in a measured number are significant.
Number of Significant Figures?
38.15 cm5.6 mL65.6 kg122.55 m
42
35
Sandwiched ZerosRULE 2. Zeros between nonzero numbers are
significant. Number of Significant Figures?
50.8 mm
2001 min
.702 mg
400005 m
34
3
6
Leading Zeros (in front)
RULE 3. Leading zeros in decimal numbers are NOT significant. Number of Significant Figures?
0.008 mm
0.0156 g
0.0042 cm
0.0002602 mL
1
3
2
4
Trailing Zeros (at end)RULE 4. Trailing zeros in numbers
without decimals are NOT significant. They are only serving as place holders.
Number of Significant
Figures?
25,000 m
200 L
48,600 mg
25,005,000 kg
2
1
35
Trailing Zeros, cont.
RULE 5. Trailing zeros in numbers with decimals ARE significant.
Number of Significant
Figures?
35,000.0 m
700. s
48.600 L
25,005.000 g
6
3
5
8
How many significant figures are in each of the following measurements?
24 mL 2 significant figures
3001 g 4 significant figures
0.0320 m3 3 significant figures
6.4 x 104 molecules 2 significant figures
560 kg 2 significant figures
Significant Numbers in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from 1) adding or subtracting
2) multiplying or dividing
Rounding• Need to use rounding to write a calculation
involving measurements correctly.• Calculator gives you lots of insignificant
numbers so you must round to the correct decimal place
• When rounding, look at the digit after the one you can keep• Greater than or equal to 5, round
up• Less than 5, keep the same
ExamplesRound each of the following measurements
so they have 3 sig figs: 761.50 14.334 10.44 10789 8024.50 203.514
76214.3
10.4108008020204
Series of operations: keep all non-significant digits during the intermediate calculations, and round to the correct number of SF only when reporting an answer.
Ex: (4.5 + 3.50001) x 2.00 =
(8.00001) x 2.00 = 16.0002 → 16
Adding and SubtractingThe answer has the same number of decimal places as the measurement with the fewest decimal places.
25.2 one decimal place (to right of decimal pt.)
+ 1.34 two decimal places (to right of decimal pt.)
26.54Answer: 26.5 (one decimal place)
Using Sig Figs in Calculations• Adding/Subtracting:
• end with the least number of decimal places
Using Sig Figs in Calculations• Adding/Subtracting:
• end with the least number of decimal places
Significant Figures
Addition or Subtraction (con’t,)
89.3321.1+
90.432 round off to 90.4one significant figure after decimal point
3.70-2.91330.7867
two significant figures after decimal point
round off to 0.79
Learning Check
In each calculation, round the answer to the correct number of significant figures.A. 235.05 + 19.6 + 2.1 =
1) 256.75 2) 256.8 3) 257
B. 58.925 - 18.2 =1) 40.725 2) 40.73 3) 40.7
Multiplying and Dividing
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.(Sometimes you’ll need to put the answer into Sci. Notation to get correct # of sig figs!)
Using Sig Figs in Calculations
• Multiplying/Dividing:• end with the least number of sig figs
(Counting sig figs from left)
Using Sig Figs in Calculations• Multiplying/Dividing:
• end with the least number of sig figs
Significant Figures
Multiplication or DivisionThe number of significant figures in the result is set by the original number that has the smallest number of significant figures
4.51 x 3.6666 = 16.536366 = 16.5
3 sig figs round to3 sig figs
6.8 ÷ 112.04 = 0.0606926
2 sig figs round to2 sig figs
= 0.061
Learning Check A. 2.19 X 4.2 =
1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60
C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 3) 0.041
For exact numbers (e.g. 4 beakers) and those used in conversion factors (e.g. 1 inch = 2.54 cm), there is no uncertainty in their measurement. Therefore, IGNORE exact numbers when finalizing your answer with the correct number of significant figures.
(Numbers from definitions or numbers of objects are consideredto have an infinite number of significant figures)
The average of three measured lengths, 6.64, 6.68 and 6.70 is:
6.64 + 6.68 + 6.70
3= 6.67333 = 6.67
Because 3 is an exact number
= 7
Chemistry In ActionOn 9/23/99, $125,000,000 Mars Climate Orbiter entered Mar’s atmosphere 100 km lower than planned and was destroyed by heat.
1 lb = 1 N
1 lb = 4.45 N
“This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”
Conversion Factors• Ratio that comes from a statement of
equality between 2 different units• every conversion factor is equal to 1
dollarquarters 14
Example:
statement of equality
conversion factor 141
quartersdollar 4 quarters
1 dollar=
Conversion Factors (con’t.)
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: 1 in. = 2.54 cm
Factors: 1 in. and 2.54 cm 2.54 cm 1 in.
Learning Check
Write conversion factors that relate each of the following pairs of units:1. Liters and mL
2. Hours and minutes
3. Meters and kilometers
1 L. and 1000 mL 1000 mL 1 L
1 hr. and 60 mins. 60 mins. 1 hr
1000 m and 1 km__ 1 km 1000 m .
Conversion Factors
• can be multiplied by other numbers without changing the value of the number (since you are just multiplying by 1)
quartersdollar
quartersdollars 121
43
1.9
Dimensional Analysis Method of Solving Problems
1. Start with the given
2. Determine what unit label is needed on the answer
3. Add conversion factor(s) & cancel units until you are left with the desired unit label!
1 L = 1000 mL
How many mL are in 1.63 L?
1L1000 mL
1.63 L x = 1630 mL
1L1000 mL
1.63 L x = 0.001630 L2
mL
Sample Problem• You have $7.25 in your pocket in
quarters. How many quarters do you have?
7.25 dollars 4 quarters 1 dollar
X = 29 quarters
Learning Check
How many seconds are in 1.4 days?
Unit plan: days hr min seconds
1.4 days x
Solution
Unit plan: days hr min seconds
1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min
= 1.2 x 105 sec
Example Convert 5.2 cm to mm
• Known: 100 cm = 1 m1000 mm = 1 m
• MUST use m as an intermediate
mmmmm
cmmcm 52
11000
10012.5
Example
Convert 0.020 kg to mg
• Known: 1 kg = 1000 g1000 mg = 1 g
• Must use g as an intermediate
mggmg
kggkg 000,20
11000
11000020.0
Advanced Conversions
• A more difficult type of conversion deals w/units that are fractions themselves
• Be sure convert one unit at a time; don’t try to do both at once
• Setup your work the exact same way
When unit labels are fractions (or ratios), unzip them!
11.3 g/mL can be written as 11.3 g 1 mL
OR 1 mL 11.3 g
Ex. Convert 11.3 g/mL to g/L
11.3 g 1 mL = 1.13 x 104 g/L
1000 mL
1 L
PROBLEM: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 cm3 of Hg in grams?
Solve the problem using DIMENSIONAL ANALYSIS.
95 cm3 • 13.6 gcm3 = 1.3 x 103 g
The speed of sound in air is about 343 m/s. What is this speed in miles per hour?
What is the given? What do you have to convert?
1 mi = 1609 m 1 min = 60 s 1 hour = 60 min
343 ms x 1 mi
1609 m 60 s
1 minx 60 min
1 hourx = 767 mi
hour
meters to miles seconds to hours
1.9
Advanced Conversions
• Another difficult type of conversion deals with squared or cubed units
• Be sure to square or cube the conversion factor you are using to cancel all the units
• If you tend to forget to square or cube the number in the conversion factor, try rewriting the conversion factor instead of just using the exponent
Square and Cubic units• Use the conversion factors you already
know, but when you square or cube the unit, don’t forget to cube the number also!
• Best way: Square or cube the ENTIRE conversion factor
• Example: Convert 4.3 cm3 to mm3
4.3 cm3 10 mm 3 1 cm ( ) =
4.3 cm3 103 mm3
13 cm3
= 4300 mm3
Example
• Convert: 2000 cm3 to m3
• No intermediate needed
OR
Known:100 cm = 1 m cm3 = cm x cm x cmm3 = m x m x m
3002.0100
1100
1100
12000 mcm
mcm
mcm
mcmcmcm
33
3 002.0100
12000 mcm
mcm