Chemistry 103 Lecture 2. Outline I. Sig Figs – Identification – Rounding – Math Operations II....
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Transcript of Chemistry 103 Lecture 2. Outline I. Sig Figs – Identification – Rounding – Math Operations II....
Chemistry 103
Lecture 2
Outline
• I. Sig Figs – Identification– Rounding– Math Operations
• II. Mathematics of Chemistry– Scientific Notation– Dimensional Analysis
Periodic Table - Elements to Memorize
Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings
Significant FiguresAre the digits in any measurement known with certainty, plus one digit that is uncertain.
Measured numbers convey
*Magnitude*Units
*Precision
The Calculator Problem
7.83.8
The Calculator Problem
7.83.8
Calculator Answer: 2.05263……
Rules for Significant Figures
It’s ALL about the ZEROs
Rules for Sig Figs
• All non-zero numbers in a measurement are significant.
4573
4573 has 4 sig figs
Rules for Sig Figs
• All zeros between sig figs are significant.
23007
23007 has 5 sig figs
Rules for Sig Figs
• In a number less than 1, zeros used to fix the position of the decimal are not significant.
0.000210.00021 has 2 sig figs
Rules for Sig Figs
• When a number has a decimal point, zeros to the right of the last nonzero digit are significant
0.00021000.0002100 has 4 sig figs
Rules for Sig Figs
• When a number has a decimal point, zeros to the right of the last nonzero digit are significant
3400.3400. has 4 sig figs
Rules for Sig Figs
• When a number without a decimal point explicitly shown ends in one or more zeros, we consider these zeros not to be significant. If some of the zeros are significant, bar notation is used.
_
820000 meters 3 sig figs 820000
Practice Identifying Sig Figs
Significant FiguresHow many assuming all numbers are measured?
a). 75924
b). 30.002
c). 0.004320
d). 0.000002
e). 46,000
Significant FiguresHow many assuming all numbers are measured?
a). 75924 (5 sig figs)
b). 30.002 (5 sig figs)
c). 0.004320 (4 sig figs)
d). 0.000002 (1 sig fig)
e). 46,000 (2 sig figs)
Rounding off Numbers
• The number of significant figures in measurements affects any calculations done with these measurements– Your calculated answer can only be as certain
as the numbers used in the calculation
Calculator: Friend or Foe?
• Sometimes, the calculator will show more (or fewer) significant digits than it should– If the first digit to be deleted is 4 or
less, simply drop it and all the following digits
– If the first digit to be deleted is 5 or greater, that digit and all that follow are dropped and the last retained digit is increased by one
Sig Fig Rounding Example:
• Round the following measured number to
4 sig figs:
• 82.56702
Sig Fig Rounding Example
• Round the following measured number to
4 sig figs:
• 82.56702
Sig Fig Rounding Example
• Round the following measured number to
4 sig figs:
• 82.56702 ANSWER: 82.57
Adding Significant Zeros• Sometimes a calculated answer requires more significant
digits. Then one or more zeros are added.
Calculated Answer Zeros Added to Give 3 Significant Figures
4 4.001.5 1.500.2 0.200
12 12.0
Practice Rounding Numbers
Significant FiguresRound each to 3 sig figs
a). 28.394
b). 0.000230600
c). 2568
d). 2562
e). 8
Significant FiguresRound each to 3 sig figs
a). 28.394 ANSWER: 28.4
b). 0.000230600 ANSWER: 0.000231
c). 2568 ANSWER: 2570
d). 2562 ANSWER: 2560
e). 8 ANSWER: 8.00
Math Operations & Sig Figs
When multiplying or dividing, use
• The same number of significant figures in your final answer as the measurement with the fewest significant figures.
• Rounding rules to obtain the correct number of significant figures.
Example:
110.5 x 0.048 = 5.304 = 5.3 (rounded)
4 SF 2 SF calculator 2 SF
Multiplication and Division
When adding or subtracting, use
• The same number of decimal places in your final answer as the measurement with the fewest decimal places (least precise measurement).
• Use rounding rules to adjust the number of digits in the answer.
25.2 one decimal place
+ 1.34 two decimal places
26.54 calculated answer
26.5 answer with one decimal place
Addition and Subtraction
Report Answer with Correct Number of Sig Figs
A). 124.54 x 2.2 =
B). 3420. + 2400. + 1095 =
C). 98.5564 = 45.68
When Math Operations Are Mixed
If you have both addition/subtraction and multiplication/division in a formula,
-carry out the operations in parenthesis first, and round according to the rules for that type of operation.
-complete the calculation by rounding according to the rules for the final type of operation.
When Math Operations Are Mixed
_____5.681g_____ =(52.15ml - 32.4ml)
When Math Operations Are Mixed
_____5.681g_____ =(52.15ml - 32.4ml)
-carry out the operations in parenthesis first, and round according to the rules for that type of operation.
When Math Operations Are Mixed
_____5.681g_____ = 5.681g(52.15ml - 32.4ml) 19.8ml
When Math Operations Are Mixed
_____5.681g_____ = 5.681g (4 sig figs)(52.15ml - 32.4ml) 19.8ml (3 sig figs)
-complete the calculation by rounding according to the rules for the final type of operation.
When Math Operations Are Mixed
_____5.681g_____ = 5.681g (4 sig figs)(52.15ml - 32.4ml) 19.8ml (3 sig figs)
ANSWER: 0.287g/ml
-complete the calculation by rounding according to the rules for the final type of operation.
Mixed Operations and Significant Figures
• What is the result (to the correct number of significant figures) of the following calculations? Assume all numbers are measured.
(179.8) x (24.4 - 23.1)
Scientific Notation
Scientific notation • Is used to write very large or very
small numbers• For the width of a human hair of
0.000 008 m is written as:
8 x 10-6 m• Of a large number such as
2 500 000 s is written as:
2.5 x 106 s
Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings
2.2 Scientific Notation• A number in scientific notation contains a coefficient (1 or greater, less than 10) and a power of 10.
150 0.000735 coefficient power of ten coefficient power of ten 1.5 x 102 7.35 x 10-4
• To write a number in scientific notation, the decimal point is moved after the first digit.
• The spaces moved are shown as a power of ten.
52 000 = 5.2 x 104 0.00378 = 3.78 x 10-3
Comparing Numbers in Standard and Scientific Notation
Standard Format Scientific NotationDiameter of Earth
12 800 000 m 1.28 x 107 mMass of a human
68 kg 6.8 x 101 kgLength of a pox virus
0.000 03 cm 3 x 10-5 cm
Comparing Numbers in Standard and Scientific Notation
Standard Format Scientific NotationDiameter of Earth
12 800 000 m 1.28 x 107 m (3 sig figs)Mass of a human
68 kg 6.8 x 101 kg (2 sig figs)Length of a pox virus
0.000 03 cm 3 x 10-5 cm (1 sig fig)
NOTE: The Coefficient is used to identify the number of significant figures in the measurement.
Dimensional Analysis
Defining Conversion Factors
Conversion Factors• Conversion factors
– A ratio that specifies how one unit of measurement is related to another
• Creating conversion factors from equalities– 12 in.= 1 ft
– I L = 1000 mL
1 = in 12
ft 1or 1
ft 1
in 12
1 = L 1
mL 1000or 1
mL 1000
L 1
Dimensional Analysis
How many seconds are in 2 minutes?
2 minutes x 60 seconds =
1 minute
120 seconds (exactly)
Dimensional Analysis
If we assume there are exactly 365 days in a year, how many seconds are in one year?
Dimensional Analysis
• A problem solving method in which the units (associated with numbers) are used as a guide in setting up the calculations.
unitsdesiredinAnswerunitgiven
unitdesiredxunitgivenintMeasuremen
Conversion Factor
Exact vs Measured Relationships
• Metric to Metric – exact
• English to English – exact
• Metric to English – typically measured
(must consider sig figs)
English to Metric Conversion Factors
Dimensional Analysis
What is 165 lb in kg?
STEP 1 Given: 165 lb Need: kg
STEP 2 Plan
STEP 3 Equalities/Factors
1 kg = 2.205 lb
2.205 lb and 1 kg
1 kg 2.205 lb
STEP 4 Set Up Problem
Practice Problem
• On a recent trip to Ireland, my average cost per day was 250. Euro. What was my average cost in U.S. Dollars?
(1 Euro = 1.36 U.S. Dollars)
50
A rattlesnake is 2.44 m long. How many centimeters long is the snake?
A) 2440 cm
B) 244 cm
C) 24.4 cm
Learning Check
Learning Check
• If a ski pole is 3.0 feet in length, how long is the ski pole in mm?
(1000mm = 1m, 12 inches=1ft, 1m=39.37inches)
A. 0.910 mm
B. 91 mm
C. 910 mm