measurements and calculations
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Measurements and Calculations. Chapter 2. Scientific Method. A logical approach to solving problems by: Observing and collecting data Formulating hypotheses Testing hypotheses, and Formulating theories that are supported by data. Observing. Using the five senses to gather information - PowerPoint PPT PresentationTRANSCRIPT
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Chemistry Chapter 2 1
Measurements and Calculations
Chapter 2
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Chemistry Chapter 2 2
Scientific Method
A logical approach to solving problems by:Observing and collecting dataFormulating hypothesesTesting hypotheses, andFormulating theories that are supported by data
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Chemistry Chapter 2 3
Observing
Using the five senses to gather information
Often involves making measurements and collecting data
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Chemistry Chapter 2 4
Qualitative data
DescriptiveNot numericalExample – the sky is blue
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Chemistry Chapter 2 5
Quantitative data
NumericalMeasurable or countableExample – the temperature of the water
went up 1 °C
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Chemistry Chapter 2 6
System
A specific portion of matter in a given region of spaceHas been selected for study during an
experiment or observation
Must be defined by the experimenter
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Chemistry Chapter 2 7
Formulating hypotheses
Hypothesis – testable statementGeneralizations about dataBasis for making predictions and
designing experimentsUsually if-then statements
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Chemistry Chapter 2 8
Testing hypotheses
Doing experimentsYou must be ready to reject a hypothesis
that is proven wrong
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Chemistry Chapter 2 9
Theorizing
Model – an explanation of how phenomena occur and how data or events are relatedMay include a physical object or drawingMay be visual, verbal, or mathematical
Theory – a broad generalization that explains a body of facts or phenomenaMust predict to be successful
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Chemistry Chapter 2 10
Discuss
Section ReviewPage 31
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Chemistry Chapter 2 11
Quantity
Something that has magnitude, size, or amount.
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Chemistry Chapter 2 12
SI Measurement
Le Système International d’UnitésMetric systemSeven base units – the rest are derived
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Chemistry Chapter 2 13
Standards of measurement
Objects or phenomena that are of constant value, easy to preserve and reproduce, and practical in size.
Note – ten thousand is written 10 000, not 10,000. Some countries use the comma as a decimal point.
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Chemistry Chapter 2 14
Mass
Measure of the quantity of matterKilogram is base unitkgYour textbook has a mass of about 1 kgA paper clip has a mass of about 1 g, or
1/1000 of a kg
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Chemistry Chapter 2 15
Mass vs. weight
Weight is the measure of the gravitational pull on matter.
The weight of an object on the moon is 1/6 its weight on earth, but its mass is the same.
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Chemistry Chapter 2 16
Length
MetermAbout 39 inches – width of a doorway1 km = 1000 m1 m = 100 cm
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Chemistry Chapter 2 17
Other base units
Time – seconds – sTemperature – kelvin – KAmount of substance – mole – molElectric current – ampere – ALuminous intensity – candela – cd
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Chemistry Chapter 2 18
Prefixes
Used to indicate multiples of 10See table 2-2 on page 35
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Chemistry Chapter 2 19
Derived SI units
Combinations of base unitsCan also use prefixes
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Chemistry Chapter 2 20
Volume
Amount of space occupied by an object.SI unit is cubic meters, or m3
We often use cubic centimeters, or cm3
Important – 1 cm3 = 1 mL1 m3 = 1 000 000 cm3
We also use the liter, or LEqual to 1 cubic dm, or dm3
There are 1000 mL in 1 L
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Chemistry Chapter 2 21
Density
The ratio of mass to volume
volume
massdensity
V
mD
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Chemistry Chapter 2 22
Density
SI unit is kg/m3
We often use g/mL or g/cm3 in Chemistryg/L or kg/m3 might be used for gases
massdensity
volume
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Chemistry Chapter 2 23
Conversion factors
Used to convert from one unit to anotherA ratio derived from equality
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Chemistry Chapter 2 24
Example
How many seconds are in 1 day?
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Chemistry Chapter 2 25
Example
How many centigrams are there in 6.25 kg?
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Chemistry Chapter 2 26
Units
When doing conversions, keep track of your units.
They should cancel out to get units you want at the end.
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Chemistry Chapter 2 27
Examples using table
Convert 10 cm to m.Convert 25 mL to L.Convert 50 mg to kg.Convert 33 cm3 to mm3.
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Chemistry Chapter 2 28
Discuss
Section ReviewPage 42
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Chemistry Chapter 2 29
Accuracy vs. Precision
Accuracy – closeness to correct or accepted value
Precision – closeness of a set of measurements of the same quantity made the same way
See page 44, figure 2-3
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Chemistry Chapter 2 30
Percent error
Finds accuracy of a single value or an average value.
See sample problem 2-3 on page 45
100
accepted
alexperimentacceptederrorpercent
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Chemistry Chapter 2 31
Reading instruments
Estimate the last digit.Example – a ruler is marked to a tenth of
a centimeter.Your measurement should be to the nearest
hundredth of a centimeter.Example – a thermometer is marked to
the nearest degree.Your measurement should be to the nearest
tenth of a degree
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Chemistry Chapter 2 32
Significant Figures
All the digits known in a measurement, plus one that is somewhat uncertain.
All nonzero digits are significant Zeros are governed by four rules
1. Zeros between nonzero digits are significant
203 has 3 sig figs 5.0279 has 5 sig figs
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Chemistry Chapter 2 33
Significant Figures
2. Zeros in front of all nonzero digits are not significant
0.0035 has 2 sig figs 0.0008 has 1 sig fig
3. Zeros at the end of a number and after the decimal point are significant.
75.000 has 5 sig figs 0.000800 has 3 sig figs
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Chemistry Chapter 2 34
Significant Figures
4. Zeros at the end of a number but before the decimal point may or may not be significant.
If a zero is just a placeholder, it is not significant. If it has been measured, it is significant. To show all
zeros are significant, use a decimal point. To show some are, use scientific notation (tomorrow) 2000 has 1 sig fig 2000. has 4 sig figs
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Chemistry Chapter 2 35
How many sig figs?
2.52 sig figs
2.503 sig figs
2502 sig figs
2.50 x 102
3 sig figs
250.04 sig figs
0.00252 sig figs
0.002503 sig figs
0.0025014 sig figs
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Chemistry Chapter 2 36
Rounding
If the next digit is less than five, round down.3.044 → 3.04
If the next digit is more than five, round up.3.046 → 3.05
If the next digit is a five and there are nonzero digits after it, round up3.0452 → 3.05
If the next digit is a five and not followed by nonzero digits round to the even number3.045 → 3.043.035 → 3.04
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Chemistry Chapter 2 37
Adding or subtracting with sig figs
The answer must have the same number of digits after the decimal point as there are in the measurement with the fewest digits after the decimal point.
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Chemistry Chapter 2 38
Example
Since 1.040 only has 3 sig figs after the decimal, the answer can only have 3 sig figs after the decimal. Round the answer to 1.253
25342.1
21342.0
040.1
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Chemistry Chapter 2 39
Multiplication and Division
The result should have the same number of significant figures as the least number of significant figures in any factor.
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Chemistry Chapter 2 40
Example
Since 1.2 only has 2 sig figs, our answer can only have 2 sig figs. We would round our answer to 1.6
608.12.134.1
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Chemistry Chapter 2 41
Conversion factors
Are not considered when finding the number of significant figures.
Are exact
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Chemistry Chapter 2 42
Discuss
How do you round a number that ends in a five if you are rounding to the place before the five?
What is the difference between accuracy and precision?
How many significant figures are in the answer when you multiply? When you subtract?
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Chemistry Chapter 2 43
Scientific Notation
Useful when writing very small or very large numbers
696 000 000 m = 6.96 x 108 m4 000 000 km = 4 x 106 km0.012 kg = 1.2 x 10-2 kg0.000 000 000 567 s = 5.67 x 10-10 s
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Chemistry Chapter 2 44
Scientific notation
The mantissa (number in front) is greater than or equal to 1 but less than 10.
Only significant figures are shown.All digits shown are significant figures.
2000 has 1 sig fig2000. has 4 sig figs2.0 x 103 has 2 sig figs2.00 x 103 has 3 sig figs
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Chemistry Chapter 2 45
Multiplying in Scientific Notation
Multiply the mantissas.Multiply the units.Add the exponents.
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Chemistry Chapter 2 46
Example
m 100.6m 100.2m 100.3 999
327 m 1036
326 m 106.3
3999 m 100.60.20.3
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Chemistry Chapter 2 47
Dividing in scientific notation
Divide the mantissas.Divide the unitsSubtract the exponents.
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Chemistry Chapter 2 48
Example
31
3
m 1050.1
kg 10635.7
313
m
kg10
50.1
635.7
32
m
kg1009.5
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Chemistry Chapter 2 49
Addition and subtraction
If the exponents (and units) are the same, you can simply add or subtract the mantissas and keep the exponents and units the same.
If the exponents are different, do it on your calculator.Your book shows you how, but most people don’t like to
do it that way.
If the units are different, you can’t add or subtract.
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Chemistry Chapter 2 50
Direct proportions
Two quantities are directly proportional if dividing one by the other gives a constant.
Graph is a straight line that passes through the origin
General forms of the equation:
kx
y
kxy
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Chemistry Chapter 2 51
Inverse proportions
Two quantities are inversely proportional if their product is constant.
Graph is a hyperbola (see page 57)General forms of the equation:
kxy
x
ky