Practice Quiz Put the following in order from smallest to largest. l 1.8x10 -5 l 8.7x10 24 l 0.7x10...
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Transcript of Practice Quiz Put the following in order from smallest to largest. l 1.8x10 -5 l 8.7x10 24 l 0.7x10...
Practice Quiz Put the following in order from smallest to
largest. 1.8x10-5
8.7x1024
0.7x10-3
1.4x1040
Answers
Smallest Largest
1.8x10-5 0.7x10-3 8.7x1024 1.4x1040
Scientists (and those studying science) frequently must
deal with numbers that are very large or very small.
Instead of wasting time by writing many zeros before and after numbers, a method of writing
very large and very small numbers was invented. It is called scientific notation.
Rules
1) The first figure is a number from 1 to 9.
2) The first figure is followed by a decimal point and then the rest of the figures.
3) Then multiply by the appropriate power of 10.
Examples425=4.25x102 (102 is the same
as 100, so you are really multiplying 4.25 by 100)
0.00098=9.8x10-4 (10-4 is the same as 1/1000, so you are really multiplying 9.8 by 1/1000)
Practice
Write the following in scientific notation:
36000
0.0135
Try TheseTry to guess the answer without using
your calculator. 4.2x104kg + 7.9x103kg= 5.23x106mm x 7.1x10-2mm= 5.44x107g/8.1x104mol=
4.99x104kg3.7x105mm2
6.72x102g/mol
Metric System
Metric System Every measurement has two parts Number Scale (unit) SI system (le Systeme International) based
on the metric system Prefix + base unit Prefix tells you the power of 10 to multiply
by - decimal system -easy conversions
Copyright © Houghton Mifflin Company. All rights reserved.1–12
The Fundamental SI Units
Prefixes giga- G 1,000,000,000 109
mega - M 1,000,000106
kilo - k 1,000 103
deci-d 0.1 10-1
centi- c 0.01 10-2
milli- m 0.001 10-3
micro- m 0.000001 10-6
nano- n 0.000000001 10-9
Copyright © Houghton Mifflin Company. All rights reserved.1–14
The Prefixes Used in the SI System
Copyright © Houghton Mifflin Company. All rights reserved.1–15
Some Examples of Commonly Used Units
Deriving the Liter Liter is defined as the volume of 1 dm3 gram is the mass of 1 cm3
Copyright © Houghton Mifflin Company. All rights reserved.1–17
Measurement of Volume
Copyright © Houghton Mifflin Company. All rights reserved.1–18
Soda is Sold in 2-Liter Bottles- an Example of SI
Units in Everyday Life
Copyright © Houghton Mifflin Company. All rights reserved.1–19
Figure 1.7 Common Types of Laboratory Equipment Used to Measure Liquid
Volume
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Measurement of Volume Using a Buret
Mass and Weight Mass is measure of resistance to
change in motion Weight is force of gravity. Sometimes used interchangeably Mass can’t change, weight can
Copyright © Houghton Mifflin Company. All rights reserved.1–22
Figure 1.8 An Electronic Analytic Balance
Significant Figures
Uncertainty Basis for significant figures All measurements are uncertain to
some degree Precision- how repeatable Accuracy- how correct - closeness to
true value. Random error - equal chance of being
high or low- addressed by averaging measurements - expected
Copyright © Houghton Mifflin Company. All rights reserved.1–25
Figure 1.10 The Results of Several Dart Throws Show the Difference Between
Precise and Accurate
Neither accurate nor precise Precise but not accurate Both precise and accurate(large random error) (small random error, (small random error, large systematic error) no systematic error)
Uncertainty
Systematic error- same direction each time
Want to avoid this Better precision implies better accuracy you can have precision without accuracy You can’t have accuracy without
precision
Significant figures Meaningful digits in a MEASUREMENT Exact numbers are counted, have
unlimited significant figures If it is measured or estimated, it has sig
figs. If not it is exact. All numbers except zero are significant. Some zeros are, some aren’t
Rules
All non zero digits are significant
Ex: 127 Zeros between significant digits are always significant
Ex: 106 Leading zeros are never significant
Ex: 0.005 Trailing zeros are significant only if there is a decimal
Ex: 25.30
Copy the examples below and write the number of significant
figures1. 76231425162. 70843. 0.007614. 421.005. 0.5386. 50007. 5x103
8. 5.0 x103
9. 5000.10. 5120
Copy the examples below and write the number of significant
figures1. 7623142516 102. 7084 43. 0.00761 34. 421.00 55. 0.538 36. 5000 17. 5x103 18. 5.0 x103 29. 5000. 410. 5120 3
Which zeroes count? In between other sig figs does Before the first number doesn’t After the last number counts iff it is after the decimal point the decimal point is written in 3200 2 sig figs
3200. 4 sig figs
Multiplication and Division The final answer should have the same
number of sig figs as the measurement having the smallest number of sig figs
Ex: 10.305g x 0.00320g=
Ex: 3.64928g/5.2mL=
Addition and Subtraction Line the numbers up in column form
Ex: 3.461728+14.91+0.98001+5.2631=
Ex: 467.384-2.384=
Ex: 564321-264321=
Doing the math Multiplication and division, same
number of sig figs in answer as the least in the problem
Addition and subtraction, same number of decimal places in answer as least in problem.
Copyright © Houghton Mifflin Company. All rights reserved.1–35
Rounding Numbers
Significant Figures Song
To the tune of Three Blind Mice
Verse 1 Addition and Subtraction line numbers
up in columns (Repeat) Make sure the decimals are aligned
right,
Take off the numbers that are on the right
To get the sig figs (Repeat)
Verse 2 Multiplication and division count the
numbers (Repeat) Find the one that is the least
That’s the number, the rest will cease To get the sig figs (Repeat)
Temperature
Temperature A measure of the average kinetic
energy Different temperature scales, all are
talking about the same height of mercury.
Derive a equation for converting ºF toºC
0ºC 32ºF
0ºC = 32ºF
ºC
ºF
(0,32)= (C1,F1)
100ºC 212ºF
100ºC = 212ºF
0ºC 32ºF
0ºC = 32ºF
ºC
ºF
(0,32) = (C1,F1)
(120,212) = (C2,F2)
100ºC 212ºF0ºC 32ºF
100ºC = 212ºF0ºC = 32ºF
100ºC = 180ºF
100ºC 212ºF0ºC 32ºF
100ºC = 212ºF0ºC = 32ºF
100ºC = 180ºF1ºC =
(180/100)ºF1ºC = 9/5ºF
Copyright © Houghton Mifflin Company. All rights reserved.1–47
Figure 1.11 The Three Major Temperature Scales
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Figure 1.12 Normal Body Temperature
Equations
F=1.80(C)+32
C=(F-32)/1.80
Dimensional Analysis
Using the units to solve problems
Dimensional Analysis Use conversion factors to change the units Conversion factors = 1 1 foot = 12 inches (equivalence statement) 12 in = 1 = 1 ft.
1 ft. 12 in
2 conversion factors multiply by the one that will give you the
correct units in your answer.
Examples #1,2 11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mile The Kentucky Derby race is 1.25 miles.
How long is the race in rods, furlongs, meters, and kilometers?
A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?
Example #3 Science fiction often uses nautical
analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor 1.71, what is its speed in knots?
Warp 1.71 = 5.00 times the speed of light speed of light = 3.00 x 108 m/s 1 knot = 2000 yd/h exactly
Apothecaries (druggists) use the following set of measures in the English system:
20 grains ap = 1 scruple (exact) 3 scruples = 1 dram ap (exact) 8 dram ap = 1 oz. ap (exact) 1 dram ap = 3.888 g 1 oz. ap = ? oz. troy What is the mass of 1 scruple in grams?
Example #4
Example #5
The speed of light is 3.00 x 108 m/s. How far will a beam of light travel in 1.00 ns?
Group Practice
Group Practice-no flashcards1) Convert 0.049kg of sulfur to grams.
2) Convert 3µL of saline solution to liters.
3) Convert 150mg of aspirin to grams.
4) Convert 1.18dm3 to mL.
5) Convert 5230000nL of water to grams.
6) Convert 4.19L to cubic centimeters
7) Convert 310000cm3 of concrete to cubic meters
Complex Conversion Problems
#1
A heater gives off heat at a rate of 330kJ/min. What is the rate of heat output in kilocalories per hour? (1 cal=4.184J)
#1 Answer
4.7x103 kcal/h
#3
At the equator, Earth rotates with a velocity of about 465 m/s. What is the velocity in kilometers per hour? What is the velocity in kilometers per day?
#3 Answer
1670km/hr
4.02x104 km/d
#2
A water tank leaks water at the rate of 3.9mL/h. If the tank is not repaired, what volume of water in liters will it leak in a year?
#2 Answer
34L/yr
Density
Density Ratio of mass to volume D = m/V Useful for identifying a compound Useful for predicting weight An intrinsic property- does not depend
on what the material is
Formula Density=Mass/Volume D=m/V If you know the density triangle, you can
get the formulas for m and V. The units of density are always going to
have a division sign in them. Ex: g/mL
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Densities of Various Common Substances* at 20°
C
Example #1 An empty container weighs 121.3 g. Filled
with carbon tetrachloride (density 1.53
g/cm3 ) the container weighs 283.2 g. What is the volume of the container?
Example #2 A 55.0 gal drum weighs 75.0 lbs. when
empty. What will the total mass be when filled with ethanol?
density 0.789 g/cm3 1 gal = 3.78 L 1 lb = 454 g
Examples #3, 4, and 5(on your own)
3) Mercury has a density of 13.6g/mL. What volume of mercury must be taken to obtain 225g of the metal?
4) Isopropyl alcohol has a density of 0.785g/mL. What volume should be measured to obtain 20.0g of the liquid?
5) A beaker contains 725mL of water. The density of water is 1.00g/mL. Calculate the volume and mass of the water.
Answers
3) 16.5mL
4) 31.8mL
5) 0.725L, 0.725g