1 chemistry: atoms first julia burdge & jason overby chapter 1 chemistry: the science of change...

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Chemistry: Atoms FirstJulia Burdge & Jason Overby

Chapter 1

Chemistry:

The Science of Change

Kent L. McCorkle

Cosumnes River College

Sacramento, CA

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Chemistry: The Science of ChangeChemistry: The Science of Change1

1.1 The Study of Chemistry Chemistry You May Already Know The Scientific Method1.2 Classification of Matter States of Matter Mixtures1.3 The Properties of Matter Physical Properties Chemical Properties Extensive and Intensive Properties 1.4 Scientific Measurement SI Base Units Mass Temperature Derived Units: Volume and Density

1.5 Uncertainty in Measurement Significant Figures Calculations with Measured Numbers Accuracy and Precision

1.6 Using Units and Solving Problems Conversion Factors

Dimensional Analysis Tracking Units

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The Study of ChemistryThe Study of Chemistry

Chemistry is the study of matter and the changes that matter undergoes.

Matter is anything that has mass and occupies space.

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The Study of ChemistryThe Study of Chemistry

Scientists follow a set of guidelines known as the scientific method:

• gather data via observations and experiments

• identify patterns or trends in the collected data

• summarize their findings with a law

• formulate a hypothesis

• with time a hypothesis may evolve into a theory

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Classification of MatterClassification of Matter

Chemists classify matter as either a substance or a mixture of substances.

A substance is a form of matter that has definite composition and distinct properties.Examples: salt (sodium chloride), iron, water, mercury, carbon dioxide, and oxygen

Substances differ from one another in composition and may be identified by appearance, smell, taste, and other properties.

1.2

A mixture is a physical combination of two or more substances.

A homogeneous mixture is uniform throughout. Also called a solution. Examples: seawater, apple juice

A heterogeneous mixture is not uniform throughout. Examples: trail mix, chicken noodle soup 5


All substances can, in principle, exist as a solid, liquid or gas.

We can convert a substance from one state to another without changing the identity of the substance.

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Solid particles are held closely together in an ordered fashion.

Liquid particles are close together but are not held rigidly in position.

Gas particles have significant separation from each other and move freely.

Solids do not conform to the shape of their container.

Liquids do conform to the shape of their container.

Gases assume both the shape and volume of their container. 7


A mixture can be separated by physical means into its components without changing the identities of the components.

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The Properties of MatterThe Properties of Matter

There are two general types of properties of matter:

1) Quantitative properties are measured and expressed with a number.

2) Qualitative properties do not require measurement and are usually based on observation.

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A physical property is one that can be observed and measured without changing the identity of the substance.Examples: color, melting point, boiling point

A physical change is one in which the state of matter changes, but the identity of the matter does not change.Examples: changes of state (melting, freezing, condensation)

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A chemical property is one a substance exhibits as it interacts with another substance.Examples: flammability, corrosiveness

A chemical change is one that results in a change of composition; the original substances no longer exist.

Examples: digestion, combustion, oxidation

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An extensive property depends on the amount of matter.Examples: mass, volume

An intensive property does not depend on the amount of matter.Examples: temperature, density

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Scientific MeasurementScientific Measurement1.4

Properties that can be measured are called quantitative properties.

A measured quantity must always include a unit.

The English system has units such as the foot, gallon, pound, etc.

The metric system includes units such as the meter, liter, kilogram, etc.

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SI Base UnitsSI Base Units

The revised metric system is called the International System of Units (abbreviated SI Units) and was designed for universal use by scientists.

There are seven SI base units

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SI Base UnitsSI Base Units

The magnitude of a unit may be tailored to a particular application using prefixes.

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MassMass

Mass is a measure of the amount of matter in an object or sample.

Because gravity varies from location to location, the weight of an object varies depending on where it is measured. But mass doesn’t change.

The SI base unit of mass is the kilogram (kg), but in chemistry the smaller gram (g) is often used.

1 kg = 1000 g = 1×103 g

Atomic mass unit (amu) is used to express the masses of atoms and other similar sized objects.

1 amu = 1.6605378×10-24 g

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TemperatureTemperature

There are two temperature scales used in chemistry:

The Celsius scale (°C) Freezing point (pure water): 0°C Boiling point (pure water): 100°C

The Kelvin scale (K) The “absolute” scale Lowest possible temperature: 0 K (absolute zero)

K = °C + 273.15

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Normal human body temperature can range over the course of a day from about 36°C in the early morning to about 37°C in the afternoon. Express these two temperatures and the range that they span using the Kelvin scale.

Worked Example 1.1Worked Example 1.1

Strategy Use K = °C + 273.15 to convert temperatures from Celsius to Kelvin.

Solution 36°C + 273 = 309 K37°C + 273 = 310 K

What range do they span?310 K - 309 K = 1 K

Depending on the precision required, the conversion from °C to K is often simply done by adding 273, rather than 273.15.

Think About It Remember that converting a temperature from °C to K is different from converting a range or difference in temperature from °C to K.

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The Fahrenheit scale is common in the United States. Freezing point (pure water): 32°C Boiling point (pure water): 212°C

There are 180 degrees between freezing and boiling in Fahrenheit (212°F-32°F) but only 100 degrees in Celsius (100°C-0°C).

The size of a degree on the Fahrenheit scale is only of a degree on the Celsius scale.

TemperatureTemperature

Temp in °F = ( ×temp in °C ) + 32°F

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5

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A body temperature above 39°C constitutes a high fever. Convert this temperature to the Fahrenheit scale.


Solution Temp in °F = ( × 39°C ) + 32°F

Temp in °F = 102°F

Think About It Knowing that normal body temperature on the Fahrenheit scale is approximately 98.6°F, 102°F seems like a reasonable answer.

Temp in °F = ( × temp in °C ) + 32°F5

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5

9

Strategy We are given a temperature and asked to convert it to degrees Fahrenheit. We will use the equation below:

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Derived Units: Volume and DensityDerived Units: Volume and Density

There are many units (such as volume) that require units not included in the base SI units.

The derived SI unit for volume is the meter cubed (m3).

A more practical unit for volume is the liter (L).

1 dm3 = 1 L

1 cm3 = 1 mL

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d = densitym = massV = volume

SI-derived unit: kilogram per cubic meter (kg/m3)

Other common units: g/cm3 (solids)g/mL (liquids)g/L (gases)

Derived Units: Volume and DensityDerived Units: Volume and Density

The density of a substance is the ratio of mass to volume.

md =

V

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Ice cubes float in a glass of water because solid water is less dense than liquid water. (a) Calculate the density of ice given that, at 0°C, a cube that is 2.0 cm on each side has a mass of 7.36 g, and (b) determine the volume occupied by 23 g of ice at 0°C.

Solution (a) A cube has three equal sides so the volume is (2.0 cm)3, or 8.0 cm3

d =

(b) Rearranging d = m/V to solve for volume gives V = m/d

V =

Think About It For a sample with a density less than 1 g/cm3, the number of cubic centimeters should be greater than the number of grams. In this case, 25 cm3 > 23 g.

7.36 g8.0 cm3

23 g0.92 g/cm3

= 0.92 g/cm3

= 25 cm3


Strategy (a) Determine density by dividing mass by volume, and (b) use the calculated density to determine the volume occupied by the given mass.

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Uncertainty in MeasurementUncertainty in Measurement

There are two types of numbers used in chemistry:

1) Exact numbers:a) are those that have defined values

1 kg = 1000 g 1 dozen = 12 objects

b) are those determined by counting 28 students in a class

2) Inexact numbers:a) measured by any method other than counting

length, mass, volume, time, speed, etc.

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An inexact number must be reported so as to indicate its uncertainty.

Significant figures are the meaningful digits in a reported number.

The last digit in a measured number is referred to as the uncertain digit.

When using the top ruler to measure the memory card, we could estimate 2.5 cm. We are certain about the 2, but we are not certain about the 5.

The uncertainty is generally considered to be + 1 in the last digit.

2.5 + 0.1 cm

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When using the bottom ruler to measure the memory card, we might record 2.45 cm.

Again, we estimate one more digit than we are certain of.

2.45 + 0.01 cm26

Significant FiguresSignificant Figures

The number of significant figures can be determined using the following guidelines:

1) Any nonzero digit is significant.

2) Zeros between nonzero digits are significant.

3) Zeros to the left of the first nonzero digit are not significant.

112.1 4 significant figures

305 3 significant figures

0.0023 2 significant figure


0.000001 1 significant figure27

Significant FiguresSignificant Figures

The number of significant figures can be determined using the following guidelines:

4) Zeros to the right of the last nonzero digit are significant if a decimal is present.

5) Zeros to the right of the last nonzero digit in a number that does not contain a decimal point may or may not be significant.


100 1, 2, or 3 – ambiguous

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Determine the number of significant figures in the following measurements: (a) 443 cm, (b) 15.03 g, (c) 0.0356 kg, (d) 3.000×10-7 L, (e) 50 mL, (f) 0.9550 m.


Solution (a) 443 cm (b) 15.03 g

(c) 0.0356 kg (d) 3.000 x 10-7 L

(e) 50 mL (f) 0.9550 m

Strategy Zeros are significant between nonzero digits or after a nonzero digit with a decimal. Zeros may or may not be significant if they appear to the right of a nonzero digit without a decimal.

3 S.F. 4 S.F.

3 S.F. 4 S.F.

1 or 2, ambiguous 4 S.F.Think About It Be sure that you have identified zeros correctly as either significant or not significant. They are significant in (b) and (d); they are not significant in (c); it is not possible to tell in (e); and the number in (f) contains one zero that is significant, and one that is not. 29

In addition and subtraction, the answer cannot have more digits to the right of the decimal point than any of the original numbers.

102.50 + 0.231 102.731

143.29 - 20.1 123.19

← round to two digits after the decimal point, 102.73

← round to one digit after the decimal point, 123.2

← two digits after the decimal point← three digits after the decimal point

← two digits after the decimal point← one digit after the decimal point

Calculations with Measured NumbersCalculations with Measured Numbers

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In multiplication and division, the number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures.

1.4×8.011 = 11.2154

11.57/305.88 = 0.0378252

2 S.F.

← fewest significant figures is 2, so round to 114 S.F.

← fewest significant figures is 4, so round to 0.037834 S.F. 5 S.F.


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Exact numbers can be considered to have an infinite number of significant figures and do not limit the number of significant figures in a result.

Example: Three pennies each have a mass of 2.5 g. What is the total mass?

3×2.5 = 7.5 g


Exact(counting number)

Inexact(measurement)

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In calculations with multiple steps, round at the end of the calculation to reduce any rounding errors.Do not round after each step.

Compare the following:


1) 3.66×8.45 = 30.92) 30.9×2.11 = 65.2

1) 3.66×8.45 = 30.932) 30.93×2.11 = 65.3

Rounding after each step Rounding at end

In general, keep at least one extra digit until the end of a multistep calculation.

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Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) 317.5 mL + 0.675 mL, (b) 47.80 L – 2.075 L, (c) 13.5 g ÷ 45.18 L, (d) 6.25 cm x 1.175 cm, (e) 5.46x102 g + 4.991x103 g


Solution (a) 317.5 mL + 0.675 mL 318.175 mL

(b) 47.80 L - 2.075 L 45.725 L

Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits.

← round to 318.2 mL

← round to 45.73 L

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Worked Example 1.5 (cont.)Worked Example 1.5 (cont.)

Solution(c) 13.5 g 45.18 L

(d) 6.25 cm×1.175 cm


← round to 0.299 g/L= 0.298804781 g/L

3 S.F.

4 S.F.

← round to 7.34 cm2= 7.34375 cm2

3 S.F. 4 S.F.

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Worked Example 1.5 (cont.)Worked Example 1.5 (cont.)

Solution (e) 5.46 x 102 g + 49.91 x 102 g 55.37 x 102 g


= 5.537 x 103 g

Think About It Changing the answer to correct scientific notation doesn’t change the number of significant figures, but in this case it changes the number of places past the decimal place.

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An empty container with a volume of 9.850 x 102 cm3 is weighed and found to have a mass of 124.6 g. The container is filled with a gas and reweighed. The mass of the container and the gas is 126.5 g. Determine the density of the gas to the appropriate number of significant figures.


Solution 126.5 g – 124.6 g

mass of gas = 1.9 g

density =

Strategy This problem requires two steps: subtraction to determine the mass of the gas, and division to determine its density. Apply the corresponding rule regarding significant figures to each step.

← one place past the decimal point (two sig figs)

1.9 g9.850 x 102 cm3 ← round to 0.0019 g/cm3= 0.00193 g/cm3

Think About It In this case, although each of the three numbers we started with has four significant figures, the solution only has two significant figures.

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Accuracy and PrecisionAccuracy and Precision

Accuracy tells us how close a measurement is to the true value.

Precision tells us how close a series of replicate measurements are to one another.

Good accuracy and good precision

Poor accuracy but good precision

Poor accuracy and poor precision38

Accuracy and PrecisionAccuracy and Precision

Three students were asked to find the mass of an aspirin tablet. The true mass of the tablet is 0.370 g.

Student A: Results are precise but not accurate

Student B: Results are neither precise nor accurate

Student C: Results are both precise and accurate 39

Using Units and Solving ProblemsUsing Units and Solving Problems

A conversion factor is a fraction in which the same quantity is expressed one way in the numerator and another way in the denominator.

For example, 1 in = 2.54 cm, may be written:

1.6

1 in2.54 cm

2.54 cm1 in

or

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Dimensional Analysis – Tracking UnitsDimensional Analysis – Tracking Units

The use of conversion factors in problem solving is called dimensional analysis or the factor-label method.

Example: Convert 12.00 inches to meters.

12.00 in ×

Which conversion factor will cancel inches and give us centimeters?

1 in2.54 cm

2.54 cm1 in

or

= 30.48 cm

The result contains 4 sig figs because the conversion, a definition, is exact.

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The Food and Drug Administration (FDA) recommends that dietary sodium intake be no more than 2400 mg per day.


Solution2400 mg ×

Strategy The necessary conversion factors are derived from the equalities1 g = 1000 mg and 1 lb = 453.6 g.

1 lb453.6 g

453.6 g1 lb

or1 g

1000 mgor

1000 mg1 g

1 g1000 mg

1 lb453.6 g

× = 0.005291 lb

Think About It Make sure that the magnitude of the result is reasonable and that the units have canceled properly. If we had mistakenly multiplied by 1000 and 453.6 instead of dividing by them, the result(2400 mg×1000 mg/g×453.6 g/lb = 1.089×109 mg2/lb) would be unreasonably large and the units would not have canceled properly.

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An average adult has 5.2 L of blood. What is the volume of blood in cubic meters?


Solution5.2 L ×

Strategy 1 L = 1000 cm3 and 1 cm = 1x10-2 m. When a unit is raised to a power, the corresponding conversion factor must also be raised to that power in order for the units to cancel appropriately.

1000 cm3

1 L1 x 10-2 m

1 cm× = 5.2 x 10-3 m3

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Think About It Based on the preceding conversion factors, 1 L = 1×10-3 m3. Therefore, 5 L of blood would be equal to 5×10-3 m3, which is close to the calculated answer.

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Chapter Summary: Key PointsChapter Summary: Key Points1

The Scientific MethodStates of MatterSubstancesMixturesPhysical PropertiesChemical PropertiesExtensive and Intensive PropertiesSI Base UnitsMassTemperatureVolume and DensitySignificant Figures

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• Dimensional Analysis: One lap in an olympic swimming pool is 50 meters exactly (2 sig figs). If an athlete swims 81 laps in one practice, how far did he/she swim (in miles)?

• 1 inch = 2.54 cm (exactly)• 12 inches = 1 foot (exactly)• 1 mile = 5280 feet (exactly)

Group Quiz #1

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1 chemistry: atoms first julia burdge & jason overby chapter 1 chemistry: the science of change...

Documents

study of matter

form of matter

state of matter changes

si units

intensive properties

quantitative properties

study of chemistry chemistry

distinct properties