chapter #1 measurement and chemical calculations

CHAPTER #1

Measurement and Chemical Calculations

What is Chemistry

Chemistry is the study of matter and its changes

What is Matter?

Matter is anything that occupies space and has weight.

Examples of Matter• Pens and pencils

• Paper

• Students

• Desks

• Cars

• Airplanes

Is Air Matter?

Air would be matter if it takes up space and has weight.

Is Air Matter?

Does it?

Is Air Matter?

Does it?

The space that air takes up is called the atmosphere.

Does air have weight?

Is Air Matter?

Does it?

The space that air takes up is called the atmosphere.

Does air have weight?

Yes air does have weight, if not, then it would flow into outer space.

Is Air Matter?Air would be matter if it takes up space and has weight.Does it?The space that air takes up is called the atmosphere.Does air have weight?Yes air does have weight, if not, then it would flow into outer space. One liter of air weighs 1.29 grams.

What are Changes?In the study of chemistry we talk about two different kinds of changes, physical and chemical

Physical change is a change to matter so that the identity is not altered; i.e. taste, smell….

What are Changes?In the study of chemistry we talk about two different kinds of changes, physical and chemical

Physical change is a change to matter so that the identity is not altered; i.e. taste, smell….

Chemical change is a change to matter so that its identity is changed; i.e. different smell, color, taste.

Examples of Physical Change

• Tearing paper; starts out paper and ends as paper

• Folding paper ; starts out paper and ends as paper

• Melting of ice ; starts out water and ends as water

• Evaporation of water ; starts out water and ends as water

Examples of Chemical Change• Wood burning; starts out as wood ends up as

smoke and ashes, different smell and taste, right?

• Steel rusting; starts out as steel ends up as rust, different smell and taste

• Healing of a wound; starts out a blood ends up as scar tissue, different color, taste and smell

Matter Continued

Is everything matter?

Matter Continued

Is everything matter? No, not everything we can think of has weight and takes up space.

Matter Continued

For example personality!

Matter Continued

For example personality! One might argue that personality takes up the space of ones brain or person, but…

Matter Continued

For example personality! One might argue that personality takes up the space of ones brain or person, but…not all personable people are overweight. Thus personality does not have weight, and is therefore not matter.

Matter ContinuedHow about thought? Again we might argue that thought takes up the space of ones brain and your mother told you about heavy thoughts, but….

Matter ContinuedHow about thought? Again we might argue that thought takes up the space of ones brain and your mother told you about heavy thoughts, but….If you get on the bathroom scale and start having heavy thoughts, your weight does not go up!

Matter ContinuedHow about thought? Again we might argue that thought takes up the space of ones brain and your mother told you about heavy thoughts, but….If you get on the bathroom scale and start having heavy thoughts, your weight does not go up! That means thought is not matter, so if someone studies thought, they are not doing chemistry.

Examples of Chemistry• The study of why wood burns

• The study of why cement does not burn

• The study of why nails rust

• The study of milk spoiling

These all fit the definition of chemistry since they deal with change and matter

History of Chemistry

Who were the first chemists?

History of ChemistryWho were the first chemists?

Cavemen

History of ChemistryWhat kind of matter and changes did the cavemen study?

History of ChemistryWhat kind of matter and changes did the cavemen study? Fire and food!

Archeologists have found evidence of fire in caves and animal bones too. Cooking meat makes meat chewable. Chewing raw meet wears out ones jaw.

History of ChemistryThe next group that left archeological evidence of chemistry were the Egyptians. Their chemistry involved mummies, textile dyes, ink, paper and paints most of which can be found inside the pyramids.

History of ChemistryThe first group of people to leave written records of their chemistry were the Greeks. From Greek writings, we can see that the Greeks made observations, and created reasons for these observations, called hypothesis. They did not attempt to prove their hypothesis by experimentation, thus their chemistry efforts were philosophical in nature as opposed to science in nature.

History of ChemistryThe first group of chemists to test hypothesis with experiments were the alchemists. Alchemists were a group of Europeans that were trying to change matter in to different kinds of matter. For example, they were trying to change lead into gold. The major results of their experiments were to prove most of the Greek ideas of chemistry to be false and to show a clear distinction between science and philosophy.

History of Chemistry

A major short coming of the Alchemists chemistry was irreproducible results, caused by lack of measurement understanding. For example, on day 1 mixing two kinds of matter produced black matter, while doing the same thing the next day produced red matter. The Alchemists were the first group of chemists to make observations, create hypothesis, and to test their hypothesis with experiments.

Modern Chemistry

Antoine Lavoisier was the founder of modern chemistry by making careful measurements.

Modern ChemistryLavoisier’s careful measurements now made experiments reproducible. Chemists in other countries could now do the same experiment and get the same results. This now allowed chemists to prove a hypothesis to be correct by experimentation, thus leading to the discovery of theories and laws.

Modern Chemistry

• Law of Conservation of Mass

• Atomic Theory

Lavoisier’s Theories and Laws

Scientific MethodIs a sequence of thoughts and

experiments containing the following:

• A hypothesis is a tentative and testable explanation for an observation or a series of observations.

• A scientific theory is a general explanation of widely observed phenomena that have been extensively tested.

Classification of Matter

Matter

Homogeneous Heterogeneous

SolutionsSubstances

Elements Compounds

Homogeneous matter looks the same everywhere with a microscope, but since we lack microscopes we will use our eyes and not our imagination. Heterogeneous matter does not look the same everywhere.

Homogeneous and Heterogeneous

Classification of MatterHomogeneous or Heterogeneous?

Wood Carpet Margarine Gold

Wood Carpet Margarine GoldHeterogeneous

Wood Carpet Margarine GoldHeterogeneous Heterogeneous

Wood Carpet Margarine GoldHeterogeneous Heterogeneous Homogeneous

Wood Carpet Margarine GoldHeterogeneous Heterogeneous Homogeneous Homogeneous

Classification of MatterSolution is a homogeneous random combination of two or more different types of matter.

For example a random amount of salt and water combined together produces a homogeneous mixture, called salt water. Random combination means some salt and some water.

Classification of MatterAny combination the produces a homogeneous result that is not randomly created is called a substance.

For example, combining two hydrogen atoms and one oxygen atom produces a compound of water, which is a substance. Or the combination of two oxygen atoms, gives a molecule of oxygen.

Homogeneous matter created by the same atom is called and element. Exact combinations of different elements is called a compound.

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand•Sea water•Tap water•Steel•Antimony•Air•Distilled water•Cement•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water•Tap water•Steel•Antimony•Air•Distilled water•Cement•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water-Heterogeneous•Tap water•Steel•Antimony•Air•Distilled water•Cement•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water-Heterogeneous•Tap water-Solution•Steel•Antimony•Air•Distilled water•Cement•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water-Heterogeneous•Tap water-Solution•Steel-Solution•Antimony•Air•Distilled water•Cement•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water-Heterogeneous•Tap water-Solution•Steel-Solution•Antimony-Element•Air•Distilled water•Cement•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water-Heterogeneous•Tap water-Solution•Steel-Solution•Antimony-Element•Air-Solution•Distilled water•Cement•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water-Heterogeneous•Tap water-Solution•Steel-Solution•Antimony-Element•Air-Solution•Distilled water-Compound•Cement•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water-Heterogeneous•Tap water-Solution•Steel-Solution•Antimony-Element•Air-Solution•Distilled water-Compound•Cement-Heterogeneous•Wine

Classification of MatterLabel the following examples of matter as heterogeneous, solution, compound or element.•Sand-Heterogeneous•Sea water-Heterogeneous•Tap water-Solution•Steel-Solution•Antimony-Element•Air-Solution•Distilled water-Compound•Cement-Heterogeneous•Wine-Solution

Classification of Matter• Types of Matter

1. Pure Substances have the same physical and chemical properties throughout.

2. Mixtures are composed of two or more substances (elements or compounds) in variable proportions.

Elements and Compounds• Most elements are not found in the world in the

pure form. They are found in compounds.

• Hydrogen is found in water, H2O, and other hydrogen containing compounds.

• The law of constant composition states that every sample of a compound always contains the same elements in the same proportions.

Pure SubstancesTwo Groups

1. An element is the simplest kind of material with unique physical and chemical properties.

2. A compound is a substance that consists of two or more elements linked together in definite proportions.

An Atomic View• An atom is the smallest particle of an element that

retains the chemical characteristics of that element.

• A molecule is a collection of atoms chemically bonded together having constant proportions.

Properties of Matter• Intensive property - a characteristic that is

independent of the amount of substance present.Examples: color, hardness, etc.

• Extensive property - a characteristic that varies with the quantity of the substance present.Examples: length, width, mass, etc.

State of Matter

• Solids have definite shapes and volumes.

• Liquids occupy definite volumes, but do not have definite shapes.

• Gases have neither a definite shape nor volume.

• Plasma, not found on earth, but stars, similar to a gas, but a mixture of subatomic particles

Examples

Making Measurements• Accurate measurements are essential for our

ability to characterize the physical and chemical properties of matter.

• Standardization of the units of measurements is essential.

All measurements contain two parts a number and a unit.

The number comes from a measuring device, such as a ruler, clock, or speedometer, to name a few examples of measuring devices. The unit is a word or abbreviated word describing the kind of measurement.

All measuring devices contain a scale. Scales contain space between the lines. The last number of a measurement, called a significant figure, is a guess as to the number between the lines.

About Measurements

About the Measurement Number

What is the measurement of the object below?

Object

What is the measurement of the object below? 11.64 cm

Object

The last figure of the measurement number is a guess and therefore measurements cannot be exact.

11.64 cmSince the last number is a guess most observerswould agree between 11.63-11.65 cm. This being the case 11.64 is usually expressed as 11.64±0.01 cm

Object

When we make a scientific measurement the last recorded number is always an estimate.

This means that the last recorded number will usually vary depending on who is estimating the last number. This produces uncertainty, or error in the measurement.

About the Measurement NumberThe closer together the lines are on the measuring scale the more

numbers that are required to describe the measurement, but the last

number is still always a guess. We refer to the number of numbers in

a measurement as the number of significant figures. The more

significant figures the higher quality of the measurement.

One of the confusing issues about numbers is zero, since it can be a

number, decimal position holder or both. If zero is to be considered both

a position holder and a number additional information about the

measurement mush be known.

Since zero is used as a decimal place holder, a number, or both. How do we determine if a zero is a number or a position holder when determining the number of significant figures for a measurement?

Consider dropping one or more of the zero digits. If dropping a zero changes the value of the measurement, then the zero is a decimal position holder and is not considered to be a number and therefore cannot be counted as a number in the significant figure count.

Consider the measurement of 100 cm. If one of the zeros is dropped then the measurement becomes 10 cm, which has a different value than the original 100 cm. If both zeros are dropped then the measurement becomes 1 cm which is not the same as the original 100cm, therefore only one number and one significant figure.

About Significant Figures

Now consider the measurement 100.0 cm. If the last zero is dropped the value of the measurement remains the same. Here the last zero does not space the decimal in this measurement. Since zeros are either decimal position holders, or numbers, then the zero in this case must be a number and counted in the significant figure count since is not a decimal spacer.

What about the zeros in the center of the measurement of 100.0 cm? Since the last zero is a number and the one at the beginning is a number then the center zeros are sandwiched by two numbers. Sandwiched zeros are always counted as significant figures, thus giving 100.0 cm four significant figures.

About Significant Figures

Significant Figure PraticeSometimes zeros can be both spacers and numbers. To differentiate between spacers and zeros, additional information must be given. Consider the following list of measurements and determine how many significant figures each measurement contains.

10.0 cm

101 cm

101.0 cm

1.00 X 10-3 cm

Measurements SigFigs

ExamplesSometimes zeros can be both spacers and numbers. To differentiate between spacers and zeros, additional information must be given.

Consider the following list of measurements and determine how many significant figures each measurement contains.

10.0 cm

101 cm

101.0 cm

1.00 X 10-3 cm

ReasonZero is a spacer for sure. Additional information required to see if it is a number

10.0 cm

101 cm

101.0 cm

1.00 X 10-3 cm

3 The last number is not a spacer, since dropping it the value is unchanged. The other zero is sandwiched.

10.0 cm

101 cm

101.0 cm

1.00 X 10-3 cm

3 Zero is sandwiched here

10.0 cm

101 cm

101.0 cm

1.00 X 10-3 cm

4 Zero is a spacer for sure. Additional information required to see if it is a number.

10.0 cm

101 cm

101.0 cm

1.00 X 10-3 cm

0.0010

4 Zero is a spacer for sure. Additional information required to see if it is a number.

3 Only look at the coefficient

2 The last zero is counted

MEASUREMNTS QUALITY • Accuracy-How close a measurement is to the true

value.

• Precision-How close multiple measurements of the same object are to each other. Or the number of significant figures.

Accuracy and Precision

In chemistry we use the international system of units. This is a modern version of the metric system.

Unfortunately this system of units is not widely used in everyday life in the USA.

Being able to use conversion factors and formulas to transform measurements between systems of units is extremely important.

This procedure is called unit analysis, most commonly referred to as conversions

Now About the Unit

Measurement Units Abbreviation

Mass grams g

Volume liters L

Distance meters m

Time seconds s

Some of the common units for measurements and their abbreviations are shown below.

A much more extensive table is given on page 17 of the text.

About the Metric Units

In chemistry we are often dealing with very large or very small quantities. To help with this a system of prefix modifiers has been developed to make measurements user friendly.

Prefix Abbreviation Coefficient

mega M 1000 000 (106)

kilo k 1000 (103)

deci d 0.1 (10-1)

centi c 0.01 (10-2)

milli m 0.001 (10-3)

micro μ 0.000001 (10-6)

Memorized Metric Prefixes

Application of Metric Prefixes

Length (m) Mass (g) Time (s)

103 m = km 103 g = kg 103 s = ks

10-2 m = cm 10-2 g = cg 10-2 s = cs

10-3 m = mm 10-3 g = mg 10-3 s = ms

10-6 m = µm 10-6 g = µg 10-6 s= µs

Note: The memorized number always is in front of the single letter.

There have been many serious incidents that have resulted from errors in converting between systems of units.

Air Canada Flight 143(Google it for more details)

Unit Conversions

Due to accidents, careful unit conversions are important.

$125 million Mars Climate Orbiter.Lost in Space.

Do you think there is the potential to make errors in the conversion of units for health care providers?

Unit Conversions

Yet another example of improper unit conversions

Conversion Problem Steps1. Write down the number and unit.2. Draw lines; a vertical line after the number an unit

and horizontal line below the number and unit. 3. Insert a fractional fact to cancel out the original unit.4. Compare the new unit to the asked for unit

a. If the same, you are done. b. If not the same, repeat step 3.

Sample Conversion Problems

1. How many grams are in 47.2 mg? 2. Change 702 cL to µL.

Step 1. Write down the number and unit.

47.2 mg

Step 2. Draw lines

47.2 mg

Step 2. Draw lines

47.2 mg

Step 3. Insert fractional fact crossing out original unit

47.2 mg

Step 2. Draw lines

47.2 mg

47.2 mgmg10-3 g

47.2 mg

Step 2. Draw lines

47.2 mg

47.2 mgmg10-3 g

Step 4. Compare new unit to the asked for unit.

47.2 mg

Step 2. Draw lines

47.2 mg

47.2 mgmg10-3 g

Step 4. Compare new unit to the asked for unit.A. If the same you are doneb. If not the same repeat step 3.

47.2 mg

Step 2. Draw lines

47.2 mg

47.2 mgmg10-3 g

= 0.0472 g

702 cL

Step 2. Draw lines

702 cL

702 cLcL10-2 L

702 cL

Step 2. Draw lines

702 cL

702 cLcL10-2 L

Not a match repeat step #3

702 cL

Step 2. Draw lines

702 cL

702 cLcL10-2 L

10-6 L

It’s a match, done

702 cL

Step 2. Draw lines

702 cL

702 cLcL10-2 L

10-6 L

It’s a match, done

= 7.02 x 106 μL

English/Metric ConversionsWhen converting between English and the metricsystems the following definitions should be used.• 2.54 cm = in• 946 mL = qt• 454 g = lbExample: Convert 155 lbs to kg.

155 lbs

155 lbs 454 glb

155 lbs 454 glb 103 g

kg= 70.37 kg

155 lbs 454 glb 103 g

kg= 70.37 kg = 70.4 kg

Sample English/Metric Conversion Problems1. Convert 708 pounds to kilograms.2. Convert 50.0 liters to gallons.3. Convert the density of water to pounds per

gallon.4. How many cubic meters are contained in 33

liters?5. The density of aluminum is 2.70 g/mL. Find

the thickness of aluminum foil that measures 2.0 cm by 5.66 cm.

ROUNDING When measurements are combined to provide information, can the calculated result be of a higher quality than the measurements?

ROUNDING When measurements are combined to provide information, can the information be of a higher quality than the measurements? No, information provide by combining measurements cannot have an accuracy, or precision greater than the measurement that provided the information.

Since information provided by combining measurements cannot have a higher quality than the measurements providing the information, then answers to problems must be rounded to give the same quality as the measurement with the least quality.

Rounding rules are designed to give answers the desired quality. They are posted on the course website and restated on the following slides.

Why Round After a Calculation

ROUNDING RULESRounding is the process of providing results that have the same quality as measurements with the least quality. Since there are different mathematical methods of combining measurements, then different rounding rules are required to provide sensible results of measurement combinations.

Addition and SubtractionRound the calculated answer so that it contains the same number of decimal places as the measurement with the least number of decimal places.

22.33 cm124 cm

Addition and SubtractionRound the calculated answer so that it contains the same number of decimal places as the measurement with the least number of decimal places.

22.33 cm124 cm146 cm

Multiplication and Division

Round the calculated answer so that it contains the same number of significant figures as the measurement with the least number of significant figures. In other words, if the measurement with the least number of significant figures contains two significant figures, then the rounded answer should contain two significant figures.

22.33 cmx 124 cm

Multiplication and Division

Round the calculated answer so that it contains the same number of significant figures as the measurement with the least number of significant figures. In other words, if the measurement with the least number of significant figures contains two significant figures, then the rounded answer should contain two significant figures.

22.33 cmx 124 cm2770 cm

LogarithmsRound the calculated answer so that it contains the same

number of decimal places as the measurement with the least

number of significant figures. In other words, if the

measurement with the least number of significant figures

contains two significant figures, then the rounded answer

should contain two decimal places.

Anti-logarithms

Round answer so that the number of significant figuresmatches the number of decimal places as the measurementwith the least number of decimal places. In other words, if themeasured number contains three decimal places, then theanswer should be rounded so that it contains three significantfigures.

Scientific Notation1. Place a decimal to the right of the

first nonzero number. 2. Place “X10” to the right of the

decimal number. 3. Count from the old decimal to the

new decimal. This number becomes the power of 10; negative power, if the number is less than one (if number starts with zero, then it is less than one)

Scientific Notation ExamplesConvert the following into scientific notation.

a. 454,000 mi

Step 1, place a decimal to the right of the first non-zero number.

= 4.54

a. 454,000 mi

Step 1, place a decimal to the right of the first non-zero number.Step 2, place X 10 after the number.

= 4.54 X 10

a. 454,000 mi

Step 1, place a decimal to the right of the first non-zero number.Step 2, place X 10 after the number. Step 3, count from the old decimal location to the new decimal location, this number of places becomes the power of 10.

= 4.54 X 105

a. 454,000 mi

Step 1, place a decimal to the right of the first non-zero number.Step 2, place X 10 after the number.Step 3, count from the old decimal location to the new decimal location, this number of places becomes the power of 10.

= 4.54 X 105 mi

Note: Be sure that the answer contains the same number of significant figures as the starting measurement

b. 0.00283 miStep 1, place a decimal to the right of the first non-zero number.

2.83 mi

b. 0.00283 miStep 1, place a decimal to the right of the first non-zero number.Step 2, place X 10 after the number.

2.83 X 10 mi

b. 0.00283 miStep 1, place a decimal to the right of the first non-zero number.Step 2, place X 10 after the number.Step 3, count from the old decimal location to the new decimal location, this number of places becomes the power of 10, unless the number is less than one, if so, then negative power

2.83 X 10-3 miNote: Be sure that the answer contains the same number of significant figures as the starting measurement

DENSITY

• What is heavier 5 pounds of lead or 5 pounds of feathers?

• What takes up more space, 5 pounds of lead or 5 pounds of feathers?

DENSITY

• What is heavier 5 pounds of lead or 5 pounds of feathers? Both the same. This is an old riddle to confuse density with weight

• What takes up more space, 5 pounds of lead or 5 pounds of feathers?

DENSITY

• What is heavier 5 pounds of lead or 5 pounds of feathers? Both the same. This is an old riddle to confuse density with weight

• What takes up more space, 5 pounds of lead or 5 pounds of feathers? Feathers, since they are less dense.

DENSITY UNITS

g/ml, g/cm3, (for solids and liquids), or

g/L for gases

We can determine the volume of irregularly shaped objects by displacement.

How can we determine the volume of a gas?

Gases fill whatever container they are placed in. So it’s the volume of the container !

Volume Determination

DENSITY PROBLEM SOLVING STRATEGYUse the four step unit analysis method from yesterday. Organize the measurements to give density units.

Sample Problems1. Calculate the density of a 4.07 g sample of rock that

displaces 1.22 mL of water.2. Calculate the density of a 4.22 g sample of wood that

measures 2.0 cm by 1.33 cm by 3.56 cm.3. Mercury has a density of 13.6 g/mL. Find the mass of 125

mL of mercury.4. Water has a density of 1.00 g/mL. Find the volume, in

liters, of a 3.22 kg sample of water.5. What does an object do in water with

a. A density greater than water?b. A density less than water?c. A density equal to water?

PERCENT CALCULATIONS

Percent is an simplified form of a fraction, which can be

used in the unit analysis process (four step method) as a

fractional fact

Percent has a mathematical

form of: = part

totalX 100

For example, if there are 37 red marbles and 68 green marbles,

then the total number of marbles is 105 marbles. The percent of

red marbles would be:

= 37105 X 100 = 35

Also, percent can be used as a fractional fact. For example

if there are 35% red marbles, then how many red marbles

would be in a collection of 687 total marbles?

35 red100 total

687 total = 240.45 marbles

Rounding?

Percent as a Fraction

Also, percent can be used as a fractional fact. For example if there are 35% red marbles, then how many red marbles would be in a collection of 687 total marbles?

35 red100 total

687 total = 240.45 marbles

Rounding? First of all marbles are counted and Have no significant figures. Since we do not haveFractional marbles, then this needs to be rounded to the nearest marble

Also, percent can be used as a fractional fact. For example if there are 35% red marbles, then how many red marbles would be in a collection of 687 total marbles?

35 red100 total

687 total = 240 marbles

Rounding? First of all marbles are counted and Have no significant figures. Since we do not haveFractional marbles, then this needs to be rounded to the nearest marble

The End

chapter #1 measurement and chemical calculations

study of matter

matter continuedhow

outer space

space of ones brain

liter of air weighs

different smell

different kinds of changes

different color

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