Chapter 2a Measurements and Calculations Chapter 2 Table of Contents 2.1 2.2 2.3 2.4 2.5 Scientific Notation Units Measurements of Length, Volume, and Mass Uncertainty in Measurement Significant Figures Return to TOC.
Download ReportTranscript Chapter 2a Measurements and Calculations Chapter 2 Table of Contents 2.1 2.2 2.3 2.4 2.5 Scientific Notation Units Measurements of Length, Volume, and Mass Uncertainty in Measurement Significant Figures Return to TOC.
Chapter 2a
Measurements and Calculations
Chapter 2 Table of Contents
Measurements of Length, Volume, and Mass
Section 2.1
Scientific Notation Measurement
• Quantitative observation.
• Has 2 parts – number and unit.
Number tells comparison.
Unit tells scale.
Section 2.1
Scientific Notation
• Technique used to express very large or very small numbers.
• Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.
Section 2.1
Scientific Notation Using Scientific Notation
• Any number can be represented as the product of a number between 1 and 10 and a power of 10 (either positive or negative).
• The power of 10 depends on the number of places the decimal point is moved and in which direction.
Section 2.1
Scientific Notation Using Scientific Notation
• The
number of places
the decimal point is moved determines the power of 10. The
direction
of the move determines whether the power of 10 is positive or negative.
Section 2.1
Scientific Notation Using Scientific Notation
• If the decimal point is moved to the left, the power of 10 is positive.
345 = 3.45 × 10 2 very large number • If the decimal point is moved to the right, the power of 10 is negative.
0.0671 = 6.71 × 10 –2 very small number In Webassign homework use format: 345 = 3.45e02
0.0671 = 6.71e-02
Section 2.1
Scientific Notation Concept Check
Which of the following correctly expresses 7,882 in scientific notation ?
a) 7.882 × 10 4 b) 788.2 × 10 3 c) 7.882 × 10 3 d) 7.882 × 10 –3
Section 2.1
Scientific Notation Concept Check
Which of the following correctly expresses 0.0000496 in scientific notation ?
a) 4.96 × 10 –5 b) 4.96 × 10 –6 c) 4.96 × 10 –7 d) 496 × 10 7
Section 2.1
Scientific Notation
Precision vs. Accuracy
good precision poor accuracy poor precision good accuracy good precision good accuracy
Section 2.1
Scientific Notation Measurement Accuracy
How long is this line?
There is no such thing as a totally accurate measurement!
Section 2.2
Units Nature of Measurement
• •
Measurement
Quantitative observation consisting of two parts.
number scale (unit) Examples 20 grams 6.63 × 10 –34 joule·seconds If a CHP asks you what do you have and you answer I have 3 kilos, you may go to jail. You should have said I have 3 kg of doughnuts for my chemistry instructor.
Section 2.1
Measurement in Chemistry
Length Mass Volume Time meter gram Liter second Km=1000m Kg=1000g 100cm=1m KL=1000L 1min=60sec 1000mg=1 g 1000mL=1L 60min=1hr 1000mm=1m
http://www.kickstarter.com/projects/52746223/the state-of-the-unit-the-kilogram-documentary-fil
Foot 12in=1ft 3ft=1yd 5280ft=1mile pound 16oz=1 lb gallon 4qt=1gal 2000 lb=1 ton 2pts=1qt second (same)
Section 2.1
Scientific Notation Conversion between British and SI Units
2.54 cm = 1 in 454 g = 1 lb 1 (cm)
3
= 1 cc = 1 ml = 1 g
water
1.06 qt = 1 L
Section 2.2
Units Prefixes Used in the SI System
• Prefixes are used to change the size of the unit.
Section 2.3
Measurements of Length, Volume, and Mass Length
• Fundamental SI unit of length is the meter.
Section 2.3
Measurements of Length, Volume, and Mass
• • • • •
Volume
Measure of the amount of 3-D space occupied by a substance.
SI unit = cubic meter (m 3 ) Commonly measure solid volume in cm 3 .
1 mL = 1 cm 3 1 L = 1 dm 3
Section 2.3
Measurements of Length, Volume, and Mass
• • • •
Mass
Measure of the amount of matter present in an object.
SI unit = kilogram (kg) 1 kg = 2.2046 lbs 1 lb = 453.59 g
Section 2.3
Measurements of Length, Volume, and Mass Concept Check
Choose the statement(s) that contain improper use(s) of commonly used units (doesn’t make sense)?
A gallon of milk is equal to about 4 L of milk.
A 200-lb man has a mass of about 90 kg.
A basketball player has a height of 7 m tall.
A nickel is 6.5 cm thick.
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Section 2.4
Uncertainty in Measurement
• • • A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
Record the certain digits and the first uncertain digit (the estimated number).
Section 2.4
Uncertainty in Measurement Measurement of Length Using a Ruler
• The length of the pin occurs at about 2.85 cm.
Certain digits: 2.85
Uncertain digit: 2.85
Estimate between smallest division!
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Section 2.4
Uncertainty in Measurement Significant Figures
• Numbers that measure or contribute to our accuracy.
• The more significant figures we have the more accurate our measurement.
• Significant figures are determined by our measurement device or technique.
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Section 2.4
Uncertainty in Measurement Rules of Determining the Number of Significant Figures
1. All non-zero digits are significant.
234 = 3 sig figs 1.333 = 4 sig figs 1,234.2 = 5 sig figs 2. All zeros between non-zero digits are significant.
203 = 3 sig figs 1.003 = 4 sig figs 1,030.2 = 5 sig figs
Section 2.4
Uncertainty in Measurement Rules of Determining the Number of Significant Figures
3. All zeros to the right of the decimal and to the right of the last non-zero digit are significant .
2.30 = 3 sig figs 1.000 = 4 sig figs 3.4500 = 5 sig figs 4. All zeros to the left of the first non-zero digit are
NOT
significant.
0.0200 = 3 sig figs 0.1220 = 4 sig figs 0.000000012210 = 5 sig figs
Section 2.4
Uncertainty in Measurement Rules of Determining the Number of Significant Figures
5.
Zeros to the right of the first non-zero digit and to the left of the decimal may or may not be significant. They must be written in scientific notation.
2300 = 2.3 x 10 3 or 2.30 x 10 3 or 2.300 x 10 3 2 sig figs 3 sig figs 4 sig figs
Section 2.4
Uncertainty in Measurement Rules of Determining the Number of Significant Figures
6. Some numbers have infinite significant figures or are exact numbers.
233 people 14 cats (unless in biology lab) 7 cars on the highway 36 schools in town
Section 2.4
Uncertainty in Measurement How many significant figures are in each of the following?
1) 23.34
4 significant figures 2) 21.003
3) .0003030
4) 210 5) 200 students 6) 3000 5 significant figures 4 significant figures 2 or 3 significant figures infinite significant figures 1, 2, 3, or 4 significant figures
Section 2.4
Uncertainty in Measurement Chapter 2b
Measurements and Calculations
Section 2.4
Uncertainty in Measurement
Problem Solving and Dimensional Analysis
Temperature Conversions: An Approach to Problem Solving
Section 2.4
Uncertainty in Measurement Using Significant Figures in Calculations
1.
2.
3.
Addition and Subtraction Line up the decimals.
Add or subtract.
Round off to first full column. 23.345 +14.5 + 0.523 = ?
23.345
14.5
+ 0.523
38.368
= 38.4 or three significant figures
Section 2.4
Uncertainty in Measurement Using Significant Figures in Calculations
1.
2.
Multiplication and Division Do the multiplication or division.
Round answer off to the same number of significant figures as the least number in the data.
(23.345)(14.5)(0.523) = ? = 177 or three significant figures 177.0368075
Section 2.5
Significant Figures Rules for Rounding Off
1. If the digit to be removed is less than 5, the preceding digit stays the same.
5.64 rounds to 5.6 (if final result to 2 sig figs)
Section 2.5
Significant Figures Rules for Rounding Off
1. If the digit to be removed is equal to or greater than 5, the preceding digit is increased by 1.
5.64 rounds to 5.6 (if final result to 2 sig figs) 3.861 rounds to 3.9 (if final result to 2 sig figs)
Section 2.5
Significant Figures Rules for Rounding Off
2. In a series of calculations, do within the parenthesis first and determine the significant figures and use that answer to calculate and find the significant figures after the multiplication and/or division.
Section 2.5
Significant Figures Concept Check
You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred). How would you write the number describing the total volume? 3.08 mL What limits the precision of the total volume? 2.80
1 st graduated cylinder
+ .280
2 nd graduated cylinder
3.080 or 3.08 ml
•
Section 2.6
Problem Solving and Dimensional Analysis Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?
To convert from one unit to another, use the equivalence statement that relates the two units.
1 ft = 12 in The two unit factors are: 1 ft 12 in and 12 in 1 ft
Section 2.6
Problem Solving and Dimensional Analysis
•
Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?
Choose the appropriate conversion factor by looking at the direction of the required change (make sure the unwanted units cancel).
6.8 ft 12 in 1 ft in
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Section 2.6
Problem Solving and Dimensional Analysis
•
Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?
Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units.
6.8 ft 12 in 1 ft 82 in • Correct sig figs? Does my answer make sense?
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Section 2.6
Problem Solving and Dimensional Analysis Example #2 An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams?
(1 kg = 2.2046 lbs; 1 kg = 1000 g) 4.50 lbs 1 kg 2.2046 lbs 1000 g 1 kg 454 g OR 4.50 lbs x ------------- = 2043g = 2.04x10
3 1 lb g
Section 2.6
Problem Solving and Dimensional Analysis Concept Check
What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation .
Sample Answer: Distance between New York and Los Angeles: 2500 miles Average gas mileage: 25 miles per gallon Average cost of gasoline: $3.25 per gallon 1 gal 25 mi $3.25
= $325 1 gal = $(3.3x10
2 )
Section 2.7
Temperature Conversions: An Approach to Problem Solving
• • •
Three Systems for Measuring Temperature
Fahrenheit Celsius Kelvin Gabriel Fahrenheit Lord Kelvin
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Section 2.7
Temperature Conversions: An Approach to Problem Solving The Three Major Temperature Scales
F = 1.8C + 32 C = (F-32)/1.8
K = C + 273 What is 35 o C in o F? 95 o F What is 90 o F in o C?
32 o C What is 100K in o C? -173 o C
Section 2.7
Temperature Conversions: An Approach to Problem Solving Exercise
The normal body temperature for a dog is approximately 102 o F. What is this equivalent to on the Kelvin temperature scale?
a) 373 K b) 312 K c) 289 K d) 202 K C = (F-32)/1.8 = (102-32)/1.80 = 38.9
o C K = C + 273 = 38.9 + 273 = 312 K
Section 2.7
Temperature Conversions: An Approach to Problem Solving Exercise
At what temperature does C = F?
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Section 2.7
Temperature Conversions: An Approach to Problem Solving Solution
• • • Since ° C equals ° F, they both should be the same value (designated as variable
x
). Use one of the conversion equations such as:
T
C
T
F 1.80
32 Substitute in the value of
x
for both
T °
C for
x
.
and
T °
F . Solve
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Section 2.7
Temperature Conversions: An Approach to Problem Solving Solution
T
C
T
F 1.80
32
x
x
32 1.80
1.80x = x -32 x = -32/0.80 0.80x = -32
x
40 So –40°C = –40°F
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Section 2.8
Density
• • Mass of substance per unit volume of the substance.
Common units are g/cm 3 or g/mL.
mass Density = volume Copyright © Cengage Learning. All rights reserved
Section 2.8
Density Measuring the Volume of a Solid Object by Water Displacement
Section 2.8
Density Example #1
A certain mineral has a mass of 17.8 g and a volume of 2.35 cm 3 . What is the density of this mineral?
mass Density = volume 17.8 g Density = 2.35 cm 3 Density = 7.57 g/cm 3
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Section 2.8
Density Example #2
What is the mass of a 49.6 mL sample of a liquid, which has a density of 0.85 g/mL?
mass Density = volume
x
0.85 g/mL = 49.6 mL OR
Section 2.8
Density Exercise
If an object has a mass of 243.8 g and occupies a volume of 0.125 L, what is the density of this object in g/cm 3 ? a) 0.513
b) 1.95
c) 30.5
d) 1950
243.8 g 0.125 L 1L 1000mL 1mL 1
cm 3
= 1.95g/
cm 3
Section 2.8
Density Using Density as a Conversion Factor
How many lbs of sugar is in 945 gallons of 60.0 Brix (% sugar) orange concentrate if the density of the concentrate is 1.2854 g/mL?
945 gal 4 qt 1 gal 1 L 1000 mL 1.06qt
1 L 1.2854 g T 1 mL 60.0 g S 100 g T 1 lb s 454g S = 6057.865514lbs
= 6.06 x 10 3 lbs sugar lbs of what? Coffee? Cocaine?
Section 2.8
Density Using Density as a Conversion Factor Using the Formula
How many lbs of sugar is in 256 L of 60.0 Brix (% sugar) orange concentrate if the density of the concentrate is 1.2854 g/mL?
M D = Solve for Mass DV = M V (1.2854 g/mL)(256,000 mL) = 329062.4 g T = 3.29 x 10 5 g T 3.29 x 10 5 g T 1 lb T 454 g T 60.0 lbs S 100 lbs T = 434.8017621 lbs = 4.35 x 10 = 435 lbs S 2 lbs S S
Section 2.8
Density Concept Check
Copper has a density of 8.96 g/cm 3 . If 75.0 g of copper is added to 50.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise?
a) 8.4 mL b) 41.6 mL 75.0g
1 cm 3 8.96g
1mL 1 cm 3 = 8.37mL Cu c) 58.4 mL d) 83.7 mL 8.37 mL Cu + 50.0 mL water = 58.4 mL