chapter 1: scientists’ tools. chemistry is an experimental science this chapter will introduce the...
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Section 1.1—Observations & MeasurementsTRANSCRIPT
Chapter 1: Scientists’ Tools
Chemistry is an Experimental Science
This chapter will introduce the following tools that scientists use to “do chemistry”Section 1.1: Observations & MeasurementsSection 1.2: Converting UnitsSection 1.3: Significant DigitsSection 1.4: Scientific Notation
Section 1.1—Observations & Measurements
Collecting Data by Making Observations
Qualitative Data: Common Mistake: Clear vs Colorless
Clear
See-through
Cloudy
Parts are see-through with solid
“cloud” in it
Opaque
Cannot be seen through at all
Colorless does not describe transparencyWords to describe transparency
You can be clear & coloredYou can be cloudy & colored
Clear versus Colorless
Cherry Kool-adeExample:
Describe the following in
terms of transparency
words & colors
Whole Milk
Water
Clear versus Colorless
Cherry Kool-ade Clear & red
Example:Describe using the terms of
transparency & color
Whole Milk
Water
Opaque & white
Clear & Colorless
Types of Quantitative Data
Quantity
Mass (how much stuff is there)
Common Unit
gram (g)
Instrument used
Balance
Volume (how much space it takes up) milliLiters (mL) Graduated cylinder
Temperature (how fast the particles are moving) Celsius (°C) Thermometer
Length Meters (m) Meter stick
Time Seconds (sec) stopwatch
Energy Joules (J) (Measured indirectlycalorimeter)
Measuring VolumeEach instrument has different calibrations.
Beaker A: 10 ml calibrationsVolume = 28 mL
Graduated Cylinder B: 1 ml calibrationsVolume = 28.3 mL
Buret C: 0.1 calibrationsVolume = 28.32 mL
The more lines, the more precise the instrument.
Always record the numbers you definitely can read off the instrument, plus an estimated digit.
Use the bottom of the meniscus to record the volume of the liquid.
36.5 ml
Uncertainty in Measurement
Every measurement has a degree of uncertaintyThe last decimal you write down is an estimate
Write down a “5” if it’s in-between linesWrite down a “0” if it’s on the line
5 mL
10
15
20
25 mL
5 mL
10
15
20
25 mLRemember:Always read liquid levels from the bottom of the meniscus
Example:Read the
measurements
Uncertainty in Measurement
Every measurement has a degree of uncertaintyThe last decimal you write down is an estimate
Write down a “5” if it’s in-between linesWrite down a “0” if it’s on the line
5 mL
10
15
20
25 mL
5 mL
10
15
20
25 mL
Example:Read the
measurements
It’s in-between the 10 & 11 line
10.5 mL
It’s on the 12 line
12.0 mL
Measuring Length
Measurement Tool for Length
1.5 cm
1.95 cm
Uncertainty in Measurement
Example:Read the
measurements
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Uncertainty in Measurement
Example:Read the
measurements
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
It’s right on the 6.9 line6.90
It’s between the 3.8 & 3.9 line3.85
Measurement Tool for Temperature
What is the measurement of thermometer B seen to the right?
Measurement Tool for Mass
Always read exactly what the balance saysDo not add any additional numbers!
HINT:Uncertainty in Measurement
Choose the right instrument If you need to measure out 5 mL, don’t choose the
graduated cylinder that can hold 100 mL. Use the 10 or 25 mL cylinder
The smaller the measurement, the more an error matters—use extra caution with small quantities If you’re measuring 5 mL & you’re off by 1 mL, that’s a
20% error If you’re measuring 100 mL & you’re off by 1 mL, that’s
only a 1% error
Section 1.2—Accuracy, Precision & Significant Digits
Gathering Data
Multiple trials help ensure that you’re results weren’t a one-time fluke!
Precise—getting consistent data (close to one another)
Accurate—getting the “correct” or “accepted” answer consistently
Example:Describe
each group’s data as not
precise, precise or accurate
Correct value
Correct value
Correct value
Precise & Accurate Data
Example:Describe
each group’s data as not
precise, precise or accurate
Correct value
Correct value
Correct value
Precise, but not accurate
Precise & Accurate
Not precise
Can you be accurate without precise?
Correct value
This group had one value that was almost right on…but can we say they were
accurate?
No…they weren’t consistently correct. It was by random chance that they had a result
close to the correct answer.
Can you be accurate without precise?
Correct value
This group had one value that was almost right on…but can we say they were
accurate?
You Try! Accepted Value = bulls-eye
*not accurate but precise *accurate & precise *not precise nor accurate
Example: Below is a data table produced by three groups of students who were measuring the mass of a paper clip which had a known mass of 1.0004g.
Group 1 Group 2 Group 3 Group 4
1.01 g 2.863287 g 10.13251 g 2.05 g
1.03 g 2.754158 g 10.13258 g 0.23 g
0.99 g 2.186357 g 10.13255 g 0.75 g
Average 1.01 g 2.601267 g 10.13255 g 1.01 g
Group 1 has the most precise (all 3 measurements are consistent with each other) & accurate (the average value of the 3 trialsare closest to the accepted value of 1.0004g) data.
Percent Error
You Try!
A student measured an unknown metal to be 1.50 grams. The accepted value is 1.87 grams. What is the percent error?
% Error = |1.87 –1.50|x 100
1.87
= 20% error
Significant Digits
A significant digit is anything that you measured in the lab—it has physical meaning
The real purpose of “significant digits” is to know how many places to record in an answer from a calculation
But before we can do this, we need to learn how to count significant digits in a measurement
Taking & Using Measurements
You learned in Section 1.2 how to take careful measurements
Most of the time, you will need to complete calculations with those measurements to understand your results
1.00 g 3.0 mL
= 0.3333333333333333333 g/mL
If the actual measurements were only taken to 2 or 3 decimal places…
how can the answer be known to and infinite number of decimal places?
It can’t!
Significant Digit Rules
1 All measured numbers are significant
2 All non-zero numbers are significant
3 Middle zeros are always significant
4 Trailing zeros are significant if there’s a decimal place
5 Leading zeros are never significant
All the fuss about zeros
102.5 g Middle zeros are important…we know that’s a zero (as opposed to being 112.5)…it was measured to be a zero
125.0 mL The convention is that if there are ending zeros with a decimal place, the zeros were measured and it’s indicating how precise the measurement was.
125.0 is between 124.9 and 125.1
125 is between 124 and 126
0.0127 m The leading zeros will dissapear if the units are changed without affecting the physical meaning or precision…therefore they are not significant
0.0127 m is the same as 127 mm
Sum it up into 2 Rules: Oversimplification Rule
1If there is no decimal point in the number, count from the first non-zero number to the last non-zero number
2If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end
The 4 earlier rules can be summed up into 2 general rules
Examples of Summary Rule 1
Example:Count the number of significant figures in
each number
124
20570
200
150
1If there is no decimal point in the number, count from the first non-zero number to the last non-zero number
Examples of Summary Rule 1
Example:Count the number of significant figures in
each number
124
20570
200
150
1If there is no decimal point in the number, count from the first non-zero number to the last non-zero number
3 significant digits
4 significant digits
1 significant digit
2 significant digits
Examples of Summary Rule 2
Example:Count the number of significant figures in
each number
0.00240
240.
370.0
0.02020
2If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end
Examples of Summary Rule 2
Example:Count the number of significant figures in
each number
0.00240
240.
370.0
0.02020
3 significant digits
3 significant digits
4 significant digits
4 significant digits
2If there is a decimal point (anywhere in the number), count from the first non-zero number to the very end
Importance of Trailing Zeros
Just because the zero isn’t “significant” doesn’t mean it’s not important and you don’t have to write it!
“250 m” is not the same thing as “25 m” just because the zero isn’t significant
The zero not being significant just tells us that it’s a broader range…the real value of “250 m” is between 240 m & 260 m.
“250. m” with the zero being significant tells us the range is from 249 m to 251 m
Let’s Practice
Example:Count the number of significant figures in
each number
1020 m
0.00205 g
100.0 m
10240 mL
10.320 g
Let’s Practice
Example:Count the number of significant figures in
each number
1020 m
0.00205 g
100.0 m
10240 mL
10.320 g
3 significant digits
3 significant digits
4 significant digits
4 significant digits
5 significant digits
Rounding
Example:Round each number to
number of sig figs in the
parentheses
1320 m (2)
0.00205 g (2)
752.4 m (3)
7.007 mL (3)
10.350 g (3)
1. Go to the digit you want to round to2. Look to the right.
If the number is less than 5, the digit you want to round to stays the same. Drop the rest of the digitsIf the number is greater than 5, the digit you want to round to moves up by one. Drop the rest of the digits.
Rounding
Example:Round each number to
number of sig figs in the
parentheses
1320 m
0.00205 g
752.4 m
7.007 mL
10.350 g
1300
.0021
752
7.01
10.4
1. Go to the digit you want to round to2. Look to the right.
If the number is less than 5, the digit you want to round to stays the same. Drop the rest of the digitsIf the number is greater than 5, the digit you want to round to moves up by one. Drop the rest of the digits.
Performing Calculations with Sig Figs
1Addition & Subtraction: Answer has least number of decimal places as appears in the problem
2Multiplication & Division: Answer has least number of significant figures as appears in the problem
When recording a calculated answer, you can only be as precise as your least precise measurement
Always complete the calculations first, and then round at the end!
Always complete the calculations first, and then round at the end! EXCEPTION: When adding/subtracting
and then multiplying/dividing, follow the rules for addition/subtraction first and then apply that number of sig figs to the multiplication/division rules.
(6.350- 6.010) / 2.0 = _______ .340 / 2.0 = 3 s.f. / 2 s.f. = .17
Addition & Subtraction Example #1
Example:Compute &
write the answer with the correct number of
sig digs
15.502 g+ 1.25 g
This answer assumes the missing digit in the problem is a zero…but we really don’t have any idea what it is
1Addition & Subtraction: Answer has least number of decimal places as appears in the problem
16.752 g
Addition & Subtraction Example #1
Example:Compute &
write the answer with the correct number of
sig digs
15.502 g+ 1.25 g
1Addition & Subtraction: Answer has least number of decimal places as appears in the problem
16.752 g
16.75 g
3 decimal places
2 decimal placesLowest is “2”
Answer is rounded to 2
decimal places
Addition & Subtraction Example #2
Example:Compute &
write the answer with the correct number of
sig digs
10.25 mL- 2.242 mL
This answer assumes the missing digit in the problem is a zero…but we really don’t have any idea what it is
1Addition & Subtraction: Answer has least number of decimal places as appears in the problem
8.008 mL
Addition & Subtraction Example #2
Example:Compute &
write the answer with the correct number of
sig digs
10.25 mL- 2.242 mL
1Addition & Subtraction: Answer has least number of decimal places as appears in the problem
8.01 mL
2 decimal places
3 decimal placesLowest is “2”
Answer is rounded to 2
decimal places
8.008 mL
Multiplication & Division Example #1
Example:Compute &
write the answer with the correct number of
sig digs
10.25 g2.7 mL = 3.796296296 g/mL
2Multiplication & Division: Answer has least number of significant figures as appears in the problem
Multiplication & Division Example #1
Example:Compute &
write the answer with the correct number of
sig digs
3.8 g/mL
4 significant digits
2 significant digits
Lowest is “2”
Answer is rounded to 2
sig digs
10.25 g2.7 mL = 3.796296296 g/mL
2Multiplication & Division: Answer has least number of significant figures as appears in the problem
Multiplication & Division Example #2
Example:Compute &
write the answer with the correct number of
sig digs
1.704 g/mL 2.75 mL
4.686 g
2Multiplication & Division: Answer has least number of significant figures as appears in the problem
Multiplication & Division Example #2
Example:Compute &
write the answer with the correct number of
sig digs
4.69 g
4 significant dig
3 significant digLowest is “3”
Answer is rounded to 3
significant digits
2Multiplication & Division: Answer has least number of significant figures as appears in the problem
1.704 g/mL 2.75 mL
4.686 g
Let’s Practice #1
Example:Compute &
write the answer with the correct number of
sig digs
0.045 g+ 1.2 g
Let’s Practice #1
Example:Compute &
write the answer with the correct number of
sig digs
1.2 g
3 decimal places
1 decimal placeLowest is “1”
Answer is rounded to 1
decimal place
1.245 g
Addition & Subtraction use number of decimal places!
0.045 g+ 1.2 g
Let’s Practice #2
Example:Compute &
write the answer with the correct number of
sig digs
2.5 g/mL 23.5 mL
Let’s Practice #2
Example:Compute &
write the answer with the correct number of
sig digs
59 g
2 significant dig
3 significant digLowest is “2”
Answer is rounded to 2
significant digits
2.5 g/mL 23.5 mL
58.75 g
Multiplication & Division use number of significant digits!
Let’s Practice #3
Example:Compute &
write the answer with the correct number of
sig digs
1.000 g2.34 mL
Let’s Practice #3
Example:Compute &
write the answer with the correct number of
sig digs
0.427 g/mL
4 significant digits
3 significant digits
Lowest is “3”
Answer is rounded to 3
sig digs
1.000 g2.34 mL = 0.42735 g/mL
Multiplication & Division use number of significant digits!
Let’s Practice #4
Example:Compute &
write the answer with the correct number of
sig digs
1.704 m 2.75 m
Let’s Practice #4
Example:Compute &
write the answer with the correct number of
sig digs
4.69 m2
4 significant dig
3 significant digLowest is “3”
Answer is rounded to 3
significant digits
1.704 m 2.75 m
4.686 g
Multiplication & Division use number of significant digits!
Multi Step Calculations
Section 1.3—Metric System & Dimensional Analysis
The Metric System
Universal system of measurementsBased on the powers of tenOnly the US and Myanmar do not use this
system
Metric Prefixes Used in the metric system to describe
smaller or larger amounts of base unitsThe Great Magistrate King Henry Died by drinking chocolate milk Monday near paris T • • G • • M • • K H D b d c m • • μ • • n • • p
1 x 1012 1 x 109 1 x 106 1000 100 10 1 .1 .01 .001 1 x 10 -6 1 x 10-9 1 x 10-12
Base Units have a value of 1Examples are: Liters (L) meters (m) grams (g) seconds (s) Place a prefix in front of a base unit to make a larger or smaller number Example: ks = kilosecond
mm = millimeter cg = centigram m = meter
Converting with the Metric System Using the Ladder Method
1. Determine the starting point.2. Count the jumps to your endpoint.3. Move the decimal the same number of jumps in the
same direction4. If using the other prefixes, remember that there is a
difference of 1000 or 3 places between each. T • • G • • M • • K H D b d c m • • μ • • n • • p
EXAMPLE: 4 km = ______ m4000
ExamplesT • • G • • M • • K H D b d c m • • μ • • n • • p
Convert 15 cl into ml
Convert 6000 mm into Km
Convert 1.6 Dag into dg
Convert 3.4 nm into m
150 ml
.006 Km
160 dg
.0000000034 m
A Different Way to Convert between UnitsDimensional Analysis is another
methodIt uses equivalents called conversion
factors to make the exchange
Conversion Factors
Change the Equivalents to Conversion Factors
1 foot = 12 inches or 4 quarters = 1 dollar
What happens if you put one on top of the other? You create a ratio equal to 1
1 foot 12 inches
4 quarters 1 dollar
Common Equivalents
1 ft 12 in
1 in 2.54 cm
1 min 60 s
1 hr 3600 s
1 quart (qt) 0.946 L
4 pints 1 quart
1 pound (lb) 454 g
=======
Steps for using Dimensional Analysis
1 Write down your given information
2 Determine what you want.
3 Use or create a conversion factor to compare what you have to what you want
4 Set up the math so that the given unit is on the bottom of the conversion factor…Calculate the answer. Multiply across the top. Multiply across the bottom of the expression. Divide the bottom by the top
5
Example #1
Example:How many yards are in
52 feet?
52 ft
1 Write down your given information
Example #1
Example:How many yards are in
52 feet?
52 ft
2Determine what you want.
= ________ yds
Example #1
Example:How many yards are in
52 feet?
52 ft = ________ yds
3 &4 Use or create a conversion factor to compare what you have to what you want
The equivalent with these 2 units is: 3 ft = 1 ydA tip is to arrange the units first and then fill in numbers later!
ft
yd
Put the unit on bottom that you want to cancel out!
3
1
Example #1
Example:How many yards are in
52 feet?
52 ft = ________ ydft
yd
3
1
5Calculate the answer. Multiply across the top. Multiply across the bottom of the expression. Divide the bottom by the top
Enter into the calculator: 52 1 3
17.33
Example #2
Example:How many grams are equal to
127.0 mg?
127.0 mg
1 Write down your given information
Example #1
Example:How many grams are equal to
127.0 mg?
127.0 mg
2Write down an answer blank and the desired unit on the right side of the problem space
= ________ g
Example #1
Example:How many grams are equal to
127.0 mg?
127.0mg = ________ g
3 &4 Use or create a conversion factor to compare what you have to what you want
The equivalent with these 2 units is: 1 g = 1000 mgA tip is to arrange the units first and then fill in numbers later!
mg
g
Put the unit on bottom that you want to cancel out!
1000
1
Example #1
Example:How many grams are equal to
127.0 mg?
127.0 mg = ________ gmg
g
1000
1
5Calculate the answer. Multiply across the top. Multiply across the bottom of the expression. Divide the bottom by the top
Enter into the calculator: 127 1 1000
.127
Metric Conversion Factors
Many students get confused where to put the number shown in the previous chart…1.Select which unit is greater. 2.Make that unit 1 and then determine how many smaller units are in the bigger unit.
1 kg = 1000 g my way OR.001Kg = 1 g the other way
Example:Write a correct
equivalent between
“kg” and “g”
Try More Metric Equivalents
There are two options:1 L = 1000 ml my way0.001 L = 1 mL the other way
Example:Write a correct
equivalent between “mL” and
“L”
There are two options: 1 cm = 10 mm my way .1cm = 1mm the other way
Example:Write a correct
equivalent between “cm” and
“mm”
Multi-step problems
There isn’t always an equivalent that goes directly from where you are to where you want to go!
With multi-step problems, it’s often best to plug in units first, then go back and do numbers.
Example #3
Example:How many kilograms
are equal to 345 cg?
345 cg = _______ kg
There is no direct equivalent between cg & kgWith metric units, you can always get to the base unit from any prefix!And you can always get to any prefix from the base unit!
You can go from “cg” to “g”Then you can go from “g” to “kg”
345 cg = _______ kg
Example #3
Example:How many kilograms
are equal to 345 cg?
cg
g
Go to the base unit
g
kg
Go from the base unit
= _______ kg
Example #3
Example:How many kilograms
are equal to 345 cg?
cg
g
100
1345 cg
g
kg
1000
1
100 cg = 1 g1000 g = 1 kg
Remember—the # goes with the base unit & the “1” with the prefix!
= _______ kg
Example #3
Example:How many kilograms
are equal to 345 cg?
cg
g
100
1
Enter into the calculator: (345 1 x 1) (100 x 1000)
0.00345345 cg g
kg
1000
1
You Try! #1
Example:0.250 kg is
equal to how many
grams?
10000.250 kg
You Try! #1
Example:0.250 kg is
equal to how many
grams?
= ______ gkg
g
1
1 kg = 1000 g
Enter into the calculator: 0.250 1000 1
250.
Last One! NOT in YOUR NOTES
Example:How many mL is equal to 2.78 L?
10002.78 L
Example:How many mL is equal to 2.78 L?
= ______ mLL
mL
1
1 mL = 0.001 L
Enter into the calculator: 2.78 1000 1
2780
Metric Volume Units
To find the volume of a cube, measure each side and calculate: length width height
length
heig
ht
width
But most chemicals aren’t nice, neat cubes!Therefore, they defined 1 milliliter as equal to
1 cm3 (the volume of a cube with 1 cm as each side measurement)
1 cm3 1 mL=
You Try! #3
Example:147 cm3 is equal to
how many liters?
You Try! #3
Example:147 cm3 is equal to
how many liters?
Remember—cm3 is a volume unit, not a length like meters!
= _______ Lcm3
mL
1
1147 cm3
mL
L
1000
1
There isn’t one direct equivalent1 cm3 = 1 mL1 L = 1000 mL or .001L = 1mL
Enter into the calculator: 147 1 0.001 1 1
0.147
Section 1.4—Scientific Notation
Scientific Notation
Scientific Notation is a form of writing very large or very small numbers that you’ve probably used in science or math class before
Scientific notation uses powers of 10 to shorten the writing of a number.
Writing in Scientific Notation
The decimal point is put behind the first non-zero number
The power of 10 is the number of times it moved to get there
A number that began large (>1) has a positive exponent & a number that began small (<1) has a negative exponent
Example #1
Example:Write the following
numbers in scientific notation.
240,000 m
0.0000048 g
Example #1
Example:Write the following
numbers in scientific notation.
240,000 m
0.0000048
2.4 10 m5
6.5423 10 g-6
The decimal is moved to follow the first non-zero number
The power of 10 is the number of times it’s moved
Reading Scientific Notation
A positive power of ten means you need to make the number bigger and a negative power of ten means you need to make the number smaller
Move the decimal place to make the number bigger or smaller the number of times of the power of ten
Example #2
Example:Write out
the following numbers.
5.3 107 m
53000000 m
Example #3
Example:Write out
the following
numbers in scientific notation.
123000000
0.000987
0.000000045
480000000000
0.00000612
1.23 x 108
9.87 x 10-4
4.5 x 10-8
4.8 x 1011
6.12 x 10-6
Example #3
Example:Write out
the following
numbers in ordinary notation.
3.4 10-9 m
1.12 105 m
2.347 107 g
8.9 10-3 g
7.23 10-12 m
.0000000034
112000
23470000
.0089
.00000000000723
HONORS ONLY: Scientific Notation & Significant DigitsScientific Notation is more than just a
short hand.Sometimes there isn’t a way to write a
number with the needed number of significant digits
…unless you use scientific notation!
How to enter scientific notation numbers into the calculator1. Punch the digit number into your
calculator.2. Push EE or EXP button. (Do not use
the x(times) button.3. Enter the exponent number. Use the
+/- button to change its sign.Example: Multiply 6.0 x105 times 4.0 x103 on your calculator. Your answer is:
240000000 or 2.4 x 109