chapter 1: scientists’ tools. chemistry is an experimental science this chapter will introduce the...

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

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

Clear versus Colorless

Cherry Kool-ade Clear & red

Example:Describe using the terms of

transparency & color

Whole Milk

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

25 mLRemember:Always read liquid levels from the bottom of the meniscus

Example:Read the

measurements

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

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

Example:Read the

measurements

1 2 3 4 5 6 7 8

Example:Read the

measurements

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

Precise & Accurate Data

Example:Describe

each group’s data as not

precise, precise or accurate

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

= 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

3 significant digits

1 significant digit

each number

0.00240

0.02020

each number

0.00240

0.02020

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

each number

1020 m

0.00205 g

100.0 m

10240 mL

10.320 g

Let’s Practice

each number

1020 m

0.00205 g

100.0 m

10240 mL

10.320 g

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

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

16.752 g

Example:Compute &

sig digs

15.502 g+ 1.25 g

16.752 g

16.75 g

3 decimal places

2 decimal placesLowest is “2”

Answer is rounded to 2

decimal places

Example:Compute &

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

8.008 mL

Example:Compute &

sig digs

10.25 mL- 2.242 mL

8.01 mL

2 decimal places

3 decimal placesLowest is “2”

decimal places

8.008 mL

Multiplication & Division Example #1

Example:Compute &

sig digs

10.25 g2.7 mL = 3.796296296 g/mL

Example:Compute &

sig digs

3.8 g/mL

Lowest is “2”

sig digs

10.25 g2.7 mL = 3.796296296 g/mL

Example:Compute &

sig digs

1.704 g/mL 2.75 mL

4.686 g

Example:Compute &

sig digs

4.69 g

4 significant dig

3 significant digLowest is “3”

significant digits

1.704 g/mL 2.75 mL

4.686 g

Let’s Practice #1

Example:Compute &

sig digs

0.045 g+ 1.2 g

Let’s Practice #1

Example:Compute &

sig digs

3 decimal places

1 decimal placeLowest is “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 &

sig digs

2.5 g/mL 23.5 mL

Let’s Practice #2

Example:Compute &

sig digs

2 significant dig

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 &

sig digs

1.000 g2.34 mL

Let’s Practice #3

Example:Compute &

sig digs

0.427 g/mL

Lowest is “3”

sig digs

1.000 g2.34 mL = 0.42735 g/mL

Let’s Practice #4

Example:Compute &

sig digs

1.704 m 2.75 m

Let’s Practice #4

Example:Compute &

sig digs

4.69 m2

4 significant dig

significant digits

1.704 m 2.75 m

4.686 g

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

Example #1

Example:How many yards are in

52 feet?

Example #1

52 feet?

2Determine what you want.

= ________ yds

Example #1

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!

Put the unit on bottom that you want to cancel out!

Example #1

52 feet?

52 ft = ________ ydft

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

Example #2

Example:How many grams are equal to

127.0 mg?

127.0 mg

Example #1

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

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!

Put the unit on bottom that you want to cancel out!

Example #1

127.0 mg?

127.0 mg = ________ gmg

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

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

equivalent between “mL” and

“L”

There are two options: 1 cm = 10 mm my way .1cm = 1mm the other way

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

Go to the base unit

Go from the base unit

= _______ kg

Example #3

1345 cg

100 cg = 1 g1000 g = 1 kg

Remember—the # goes with the base unit & the “1” with the prefix!

= _______ kg

Example #3

Enter into the calculator: (345 1 x 1) (100 x 1000)

0.00345345 cg g

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

1 kg = 1000 g

Enter into the calculator: 0.250 1000 1

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

1 mL = 0.001 L

Enter into the calculator: 2.78 1000 1

Metric Volume Units

To find the volume of a cube, measure each side and calculate: length width height

length

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

1147 cm3

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

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

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

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

.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

chapter 1: scientists’ tools. chemistry is an experimental science this chapter will introduce the...

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