S

Making Measurements

Day 1- Tuesday

Measurements in Life

What are some examples of situations in your life that require making measurements? Amount of time it takes to do

something Body temperature when you’re sick Speed of a thrown baseball Distance between the line of

scrimmage and the goal

2 Types of Measurements

There are 2 types of measurements that can be made: Qualitative Quantitative

Qualitative: measurements that do NOT involve the use of numbers and are concerned with characteristics of an object.

Quantitative: measurements that involve numbers and must be determined with an apparatus of some sort.

Qualitative or Quantitative?

It is hot outside. Yesterday I ran 3 miles. It was 102° outside this afternoon. The balloon was big and blue. The paper felt soft on my skin. I need 3.25mm of string for my

project. I am 3 foot 4 inches tall. Wow you’re short!!

Qualitative

Quantitative

Quantitative

Quantitative

Quantitative

Qualitative

Qualitative

Qualitative

Don’t Forget…

Why are units just as important in communicating a quantitative measurement as the number is? A number without a unit is meaningless Ex: 35 °F is cold and 35 °C is hot

Accuracy vs Precision

Accuracy: refers to how close a measured value is to an accepted value

Precision: refers to how close a series of measurements are to one another

Accuracy vs Precision

Ken Sue Jon

Trial 1(g/cm3)

1.54 1.40 1.70

Trial 2(g/cm3)

1.60 1.68 1.69

Trial 3(g/cm3)

1.57 1.45 1.71

Average

(g/cm3)

1.57 1.51 1.70

Who collected the most accurate data?

Who collected the most precise data?

Accepted Value = 1.59 g/cm3

Ken, because his average is closest to the accepted value.

Jon, because his values varied by the smallest amount (0.02 g/cm3.

Scientific Notation Rules

1. The first figure is a number from 1-9.

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.

Scientific Notation

Given: 289,800,000Use: 2.898 (moved 8 places)Answer: 2.898 x 108

Given: 0.000567Use: 5.67 (moved 4 places)Answer: 5.67 x 10-4

Learning Check Express these numbers in Scientific

Notation:1) 405789 2) 0.003 872 3) 3,000,000,0004) 0.000 000 02 5) 0.478260

4.05789 x 105

3.872 x 10-3

3 x 109

2 x 10-8

4.7826 x 10-1

Tuesday – Exit Ticket Convert the following number to

scientific notation 1.) 0.000 000 000 276 2.) 150, 000, 000 3.) Determine if the following set of

data is accurate, precise or both.The bug is 2.59 cm long

3.58 cm3.59 cm3.57 cm

Day 2- WednesdaySignificant Figures

What is the difference between

75.00 mL

75.0 mL

75 mL

Are they all the same number or are they different?

Rounding rules Look at the number

behind the one you’re rounding.

If it is 0 to 4 don’t change it

If it is 5 to 9 make it one bigger

5.87192 Round 2 digits Round 3 digits Round 4 digits

7.9237439 Round 1 digits Round 2 digits Round 4 digits Round 5 digits

Rounding

5.9

5.87

5.872

8

7.9

7.924 7.923

7

How many sig figs are in the following measurements?

458 g

4085 g

4850 g

0.0485 g

0.004085 g

40.004085 g

Learning Check

3

4

3

3

4

8

Significant Figures How do we read the ruler? 4.5515 cm? 4.551 cm? 4.55 cm? 4.5 cm? 4 cm? We needed a set of rules to decide

21 3 4 5

Significant Figure Rules

Rule #1: All real numbers (1, 2, 3, 4, etc.) count as significant figures.

Therefore, you only have to be concerned with the 0

Whether a 0 is significant or not depends on the location of that 0 in the number

Which zeros count?

Rule #2: Zeros at the end of a number without a decimal point don’t count

12400 g (3 sig figs)

Rule #3: Zeros after a decimal without a number in front are not significant.

0.045 g (2 sig figs)

Which zeros count?

Rule #4: Zeros between other sig figs do count.

1002 g (4 sig figs)

Rule #5: Zeroes at the end of a number after the decimal point do count

45.8300 g (6 sig figs)

Significant Figures

Pacific Ocean

When the decimal is Present, start counting with the first nonzero number on the left.

Keep counting until you fall off

Atlantic Ocean

When the decimal is Absent, start counting with the first nonzero number on the right.

Keep counting until you fall off.

Other Information about Sig Figs

Only measurements have sig figs.

A piece of paper is measured 11.0 inches tall.

Counted numbers are exact A dozen is exactly 12

Being able to locate, and count significant figures is an important skill.

Learning Check

A. Which answers contain 3 significant figures?

1) 0.4760 cm 2) 0.00476 cm 3) 4760 cm

B. All the zeros are significant in

1) 0.00307 mL 2) 25.300 mL 3) 2.050 x 103 mL

C. 534,675 g rounded to 3 significant figures is

1) 535 g 2) 535,000 g 3) 5.35 x 105 g

Learning Check

In which set(s) do both numbers contain the same number of significant figures?

1) 22.0 and 22.00

2) 400.0 and 40

3) 0.000015 and 150,000

4) 63,000 and 2.1

5) 600.0 and 144

6) 0.0002 and 2000

NO

NO

YES- 2

YES- 2

NO

YES-1

Calculations Using Sig Figs

Addition/ Subtraction

The least accurate measurement determines the accuracy of the answer.

Keep only as many decimal places as the least accurate measurement.

Ex: 12.01 + 35.2 + 6 = 53

Multiplication/ Division

The least precise measurement determines the accuracy of the answer.

Round your answer to the least number of significant figures in any of the factors.

Ex: 1.35 x 2.467 = 3.33

Another Example

First line up the decimal places

Then do the adding Find the estimated

numbers in the problem This answer must be

rounded to the tenths place

If 27.93 mL of NaOH is added to 6.6 mLof HCL, what is the total volume of your

solution?

27.96 mL+ 6.6 mL

34.6 mL

34.56 mL

135 cm x 32 cm = 4320 cm2

3 S.F. 2 S.F.Round off the answer to 4300 cm3 which is 2 sig

figs.

Example:

1. 2.19 m X 4.2 m =

A) 9 m2 B) 9.2 m2 C) 9.198 m2

2. 4.311 cm2 ÷ 0.07 cm = A) 61.58 cm B) 62 cm C) 60 cm

3. (2.54 mL X 0.0028 mL) =

0.0105 mL X 0.060 mL

A.) 11.3 mL B)11 mL C) 0.041mL

Learning Check

Percent Error

Percent error is a way for scientists to express how far off a lab value is from the commonly accepted value.

The formula is: % Error = |Accepted value – Experimental Value| x

100 %

Accepted Value

Percent Error

Example 1: Experimental Value = 1.24 g Accepted Value = 1.30 g

% Error = |Accepted value – Experimental Value| x 100 %

Accepted Value

% Error = |1.30 – 1.24| x 100 % 1.30

= 4.62 %

Wednesday- Exit Ticket

How many sig figs are in the following number

1.) 45.00 2.) 4,500 3.) 0.04500 4.) 0.000 00045

Day 3- Thursday

Why do we need common units?

It is important for scientists around the world to be able to communicate with each other!

If we all used a different set of units, communication would be different if not impossible.

Therefore...

International System of Units

The common system of units scientists have devised in order to communicate with each other even when they’re from different places is called the Systemme Internationale (International System in French) or SI.

This system has seven base units that are based on an object or event in the physical world.

SI Base Units

Quantity SI Base Unit Symbol

Time second s

Length meter m

Mass kilogram kg

Temperature Kelvin K

Amount of Substance

moles mol

Electric Current Ampere A

Luminous Intensity candela cd

Time

The SI base unit for time is the second, s.

How is this unit officially defined? The frequency of microwave radiation given off by a

cesium 133 atom is the physical standard used to establish the length of a second.

This is why atomic (cesium) clocks are more accurate than the standard clocks and stopwatches we normally used to measure time.

Length

The SI base unit for length is the meter, m. How is this unit officially defined?

A meter is the distance that light travels through a vacuum in 1/299792458 of a second.

If you need to measure length that is longer than this base unit… you’d measure in kilometers (km).

If you need to measure length that is a shorter distance than the base unit… you’d measure in centimeters (cm) or millimeters (mm).

Mass

Mass is the measure of the amount of matter in a sample.

The SI base unit for mass is the kilogram, kg.

How is this officially defined? The kilogram is defined by a platinum-iridium metal

cylinder stored in Sevres, France. A copy is kept at the National Institute of Standards and Technology in Gaithersburg, Maryland.

Mass

What units are you most likely to use to measure mass in lab? The masses measured

in lab are often much smaller than a kg, for those cases we use grams (g) or milligrams (mg)

Temperature

The SI base unit for temperature is the Kelvin, K.

This scale was calibrated so that changing one unit on the Kelvin scale is the same as changing a temperature by one degree Celsius.

Defining temperature points Celsius: 0° water freezes, 100° water boils Kelvin: 273 water freezes, 0 all motion stops

Temperature

Why was the Kelvin scale invented/ why is it useful? We needed an “absolute zero scale” so that we could do

calculations without negative numbers.

Convert between Kelvin and Celsius K = °C + 273 °C = K – 273

A third temperature scale that we will not use in the lab is Fahrenheit.

How do you convert between Celsius and this scale? °F = (1.8 x °C) + 32 °C = (°F-32) / 1.8

History of Temperature

Lord Kelvin Anders Celsius

Derived Units

Not all quantities can be measured with base units.

Example: the SI unit for speed is meters per second (m/s). Notice that this includes 2 base units- the meter

and the second.

A unit that is defined by a combination of base units is called a derived unit.

Volume

Volume is space occupied by an object.

The derived SI unit for volume is the cubic meter, m3, which is represented by a cube whose sides are all one meter in length.

This unit is much larger than what will commonly be needed in the lab so a more useful derived unit, the cubic centimeter, cm3 is used.

The unit cm3 works well for solid objects with regular dimensions, but not as well for liquids or for solids with irregular shapes. The metric unit for volume is the Liter, L.

What are the conversions between volume units? 1000m = 1 L; 1 cm3 = 1 mL; (memorize 1 cm3 1 mL)

Metric Dimensional Analysis

Trick Name/ Symbol Factor

King Kilo (K) 1000 or 103

Henry Hecto (H) 100 or 102

Died Deca (D) 10

By base 1

drinking deci (d) 1/10

chocolate centi (c) 1/100 or 1/102

milk milli (m) 1/1000 or 1/103

Micro (µ) 1/1000000 or 1/106

Nano (n) 1/1000000000 or 1/109

Mass, distance, time, volume, and quantity (amount) are the ones most common to chemistry.

These measurements each have their own base unit.

We want to know/measure

What it’s called

Standard system Metric Base Unit Abbreviation

How much something weighs

Mass Pounds, ounces, tons

Gram g

How long/short something is

Distance Inches, feet, miles Meter m

How much space something takes

up

Volume Pints, gallons, quarts, cups

Liter L

How long something takes

Time Seconds, minutes, hours

Second s

How many of something we

have

Quantity Dozen, gross Mole mol

#2

950 g = ________ kg

Symbol Factor

K 1000

H 100

D 10

b 1

d 1/10

c 1/100

m 1/1000

950 g x

kg

g

=

1

1000

0.95 kg

The greater unit gets the 1

#1

35 mL = _________ cL TWO prefixes = TWO

steps

35 mL x 1 L

1000

mL

x 100cL

1 L

The greater unit gets the 1

= 3.5 cL

Symbol Factor

K 1000 or 103

H 100 or 102

D 10

b 1

d 1/10

c 1/100 or 102

m 1/1000 or 103

μ 1/1000000 or 106

C

C

#8

0.005 kg= _________ dag TWO prefixes = TWO

steps

Symbol Factor

K 1000 or 103

H 100 or 102

D 10

b 1

d 1/10

c 1/100 or 102

m 1/1000 or 103

μ 1/1000000 or 106

0.005 kg

x 103 g

1 kg

C

x 106μg

1 g

The greater unit gets the 1

C

C

= 5x106 μg

Friday- Exit Ticket

Perform the following metric conversion

180 ns to ks 77.2 cm3 to L

Round the following number to 3 sig figs

45674

Extra Dimensional Analysis

Dimensional Analysis

Many problems in chemistry do not have a simple formula that you can plug the data into and get the answer. Instead, solving a chemistry problem requires planning, much like taking a trip. You must determine where you are going (what you are solving for) and how you are going to get there (what do you need to know to solve the problem).

Dimensional Analysis

In chemistry most data is in the form of a measurement. A measure contains two parts - the number and the UNIT!

Many problems involve converting measurements from one unit (or dimension) to another. These units help you to plan the solution to the problem you are trying to solve. The technique of converting between units is called DIMENSIONAL ANALYSIS.

Dimensional Analysis

When you use dimensional analysis to solve chemistry problems you will keep track of the units involved in the calculations you use. When you multiply or divide numbers with units you also multiply or divide the units. You cancel units the same way that you cancel the numerators and denominators of fractions.

A conversion factor is a relationship between different units of measure.

Dimensional Analysis

Give an example of a conversion factor and show 3 ways of writing it.

Inches and feet

Minutes and seconds

Dimensional Analysis

1. Write the given.

2. Set up your conversion factor your units will cancel out.

3. Multiply by factors on the top and divide by factors on the bottom.

Be sure your units are cancelling out and that the unit you’re left with is the desired unit.

Dimensional Analysis

How many inches are equal to 4.5 feet? How many steps? 1 (12 in = 1 ft)

4.50 ft

x 12 in

1 ft

= 54 in

Dimensional Analysis

How many dollars are in 140 dimes? How many steps? 1 (1 dollar = 10 dimes)

140 dimes

x 1 dollar

10 dimes

= 14 dollars

Dimensional Analysis

Pistachio nuts cost $6.00 per pound. How many pounds of nuts can be bought for $20.00? How many steps? 1 (1 pound = $6.00)

20 dollars x 1 pound

6 dollars

= 3.33 pounds

Dimensional Analysis

How much does 4.15 pounds of pistachio nuts cost? How many steps? 1 (1 pound = $6.00)

4.15 pounds

x 6 dollars

= 24.90 dollars

1 pound