matter, measurement & problem solving chapter 1 version 9.0 1

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Matter, Measurement & Problem Solving

Chapter 1

Version 9.0

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Chemistry is often called “the central science”

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Chemistry is the study of matter.

Matter is anything that has mass andoccupies space.

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The Three States of Matter

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Atoms are the building blocks of matter.

A carbon atom

Molecules – more than oneatom bonded together

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Classifying Matter - Some Definitions

• Substance – composed of matter and may be pure or impure

• Pure substance – only a single type of matter is present– Examples: Water and table salt

• Impure substances – when two or more pure substances are intermingled with each other.

• Impure substances may also be called mixtures. Their composition may or may not vary.– Soil, salt solution

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Pure Substance or Impure Substance?

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Pure Substance or Impure Substance?

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Classifying Matter - Some Definitions

• Elements – a substance that cannot be chemically broken down into simpler substances– On the molecular level, each element is composed

of only one kind of atom

Pure gold is an “elemental” substance

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Figure 1.6a

Each element is composed of only onetype of atom.

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Classifying Matter - Some Definitions• Compounds – substances composed of two or more

elements, i.e., they contain two or more kinds of atoms.– Ex. – water, composed of hydrogen atoms (2) and

oxygen atom (1)

Mixtures

• A mixture is any intimate combination of two or more components.

• Can be classified as heterogeneous or homogenous.– Heterogeneous mixture

• The mixing of components is visually non-uniform. • Regions of different composition exist.

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Homogeneous Mixtures

• Homogeneous mixture – Mixing is uniform, same composition throughout– A solution is a homogenous mixture of two or

more substances

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Brass – a mixture (alloy) of copper and zinc

Air

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Flow Chart for Classification of Matter

FiltrationDecantingExtractionSublimation

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Separation of Mixtures

We can separate a mixture into its components by taking advantage of the differences in their properties

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Simple distillation

Paper chromatography

Separation of Mixtures

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Practice Problem

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Properties of Matter

• Property – any characteristic that allows us to recognize a particular type of matter and to distinguish it from other types of matter

• Every substance has a unique set of properties• The properties of matter may be categorized

as physical or chemical

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Properties of Matter

• Physical properties: may be observed without changing the identity and composition of the substance – color, odor, density, melting pt., boiling point, hardness, etc.

• Chemical properties: describe the way a substance may change, or react, to form other substances. Example: flammability, the ability of a substance to burn in the presence of oxygen. Other examples include corrosiveness, acidity, and toxicity.

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Physical & Chemical Changes

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Practice ProblemMatter has both physical and chemical properties and can undergo physical or chemical changes. Physical properties are those that a substance displays without changing its composition, whereas chemical properties are evident only during a chemical change (also called a chemical reaction). In contrast, when a substance undergoes a physical change, it may change appearance, but not its composition.

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Properties of Matter

• Intensive properties – do not depend on the amount of the sample (mass) being examined– May be used to identify substances

• Temperature, melting pt, density, etc.

• Extensive properties – depend on the quantity of the sample– Relate to the amount of substance

• Mass, volume, enthalpy, internal energy, etc.

Important Units for Chem 210

• The 7 base units of the System International• m = meter• kg = mass• mol = number or count (atoms, ions, molecules,etc.)• K = Kelvin = unit for temperature• s = seconds• cd = candela (luminous intensity)• A = ampere (electric current)

• Examples of “derived” units:• 1 Joule = 1 J = 1 kg·m2/s2

• 1 Newton = 1 N = 1 kg·m/s2

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4 grams = 4 g

The numerical part

The unit, dimension or label

Measurements have two parts

Scientific Notation

Scientific Notation

Scientific Notation

Scientific Notation

Scientific Notation

Unit or Metric Prefixes & Prefix Multipliers

Metric prefix Metric abbrev.

Prefix multipliers

Prefix multipliers in sci. notation

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Unit or Metric Prefixes & Prefix Multipliers

Metric prefixes may be used in combination with “base” units :

Base units : g (grams), s (seconds), m (meters), L (Liters)

Example: 3 kg = 3 kilograms

Prefix multiplier is k = kilo Base unit = g = gram

Using Prefix Multipliers

X 10-6

1 x 10-6 s = 0.000006 s

7.3 x 10-6 s = 0.0000073 s

Measurements

Measurements

Scientific measurements (unless they are exact!) are reported so that every digit is certain except the last, which is estimated.

certainestimated

certain

estimated

certain estimated

Some Measurements are Exact

However…..most measurements are not exact

Precision

Precision of a Measurement Precision of a Series of Measurements

Depends on the instrument used to make the measurement

How close a series of measurementsare to one another or how reproducible they are

Precision

Precision – Series of Measurements

Which student is most precise?

How do you mathematically calculate precision?

Precision – Series of Measurements

How do you mathematically calculate precision?

1. For each student, determine the mean mass value (average mass value) of the trials 2. For student A, determine the deviation from the mean for each trial (if this value is

negative then take the absolute value). Repeat for students B & C.3. For student A, determine the average deviation from the mean by summing the results

from step 2 and dividing by the number of trials. Repeat for students B & C.

Precision – Series of Measurements

How do you mathematically calculate precision? Example – Student A

Mean value = (10.49 + 9.79 + 9.92 + 10.31 )/ 4 = 10.13 g

Deviation from mean , trial #1 = │10.49 – 10.13│ = 0.36 Deviation from mean, trial #2 = │9.79 – 10.13│= 0.34 Deviation from mean, trial #3 = │9.92-10.13│= 0.21 Deviation from mean, trial #4 = │10.31-10.13│ = 0.18

Average deviation from mean = (0.36 + 0.34 + 0.21 + 0.18)/4 = 0.28 g

Accuracy

• The term accuracy refers to the nearness of a measurement to its accepted value. Another words, accuracy is how close a measured value is to the actual (true) value

Accuracy

If the true mass of the object is 9.80 grams, which student is most accurate?

Reading Instruments

Recording Measurements

• In any measurement, the number of significant figures is the number of digits believed to be correct by the person doing the measuring, it includes one estimated (uncertain) digit.

The number has 3 significant figures

Recording Measurements

• Digital and analog instruments may be used to record measurements

• Determining the estimated (or uncertain digit) for a measurement may be more challenging when you are using an analog instrument as opposed to a digital instrument.

Digital Instruments

• If you are using a digital instrument, we will assume for our class that the last digit on the display represents the uncertain or estimated digit.

Analog Instruments• When you are using an analog instrument you will need to

estimate the last place in your measurement• Determine the smallest division on the scale of your

instrument• The place between the smallest divisions is where you will

need to estimate• Mentally divide the smallest division into 10 equal spaces• Estimate the digit

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How Do We Show Uncertainty?

• When scientists make a measurement or calculate some quantity from their data, they generally assume that some exact or "true value" exists

• Scientists reporting their results usually specify a range of values that they expect this "true value" to fall within

• measurement = best estimate ± uncertainty• In any measurement, the number of significant figures is the

number of digits believed to be correct by the person doing the measuring, it includes one estimated (uncertain) digit.

• In this class we will assume that the uncertainty lies in the last digit written in the number.

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2.85 cm

These digits are certain

This digit is uncertainThe scientists best estimate(in red)

How Do We Show Uncertianty?

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How Do We Show Uncertainty?

In most cases we will assume an uncertainty of ± 1 in the position of the uncertain digit.

2.85 cm ± 0.01 cm

Best estimate + uncertainty = measurement

The measurement above means that the experimenter is confident that the actual value for the quantity being measured lies between 2.84 cm and 2.86 cm.

Measurements & Significant Figures

• Remember, scientific measurements are reported so that every digit is certain except the last, which is estimated

• We use “significant figures” to preserve the precision of a measurement

• In any reported measurement, the non-place-holding digits (the ones not marking the decimal point) are called significant figures (or significant digits)

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Rules for Significant Figures• Non-zero digits are always significant (this is easy, the

challenge is when zero’s are present)• Embedded zero’s are significant• Leading zero’s (all zero’s before the first non-zero digit) are not

significant.• A final zero or “trailing zero’s” in the decimal portion only are

significant.• The zero to the left of the decimal point on numbers less than

one is not significant. The zero is there by convention.• Trailing zero’s in a whole number an integer) are not

significant unless a decimal point is present.• For numbers written in exponential notation, the number of

significant digits is equal to the number of digits in the mantissa.

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Practice Problems – Significant Figures

exponent

coefficient, mantissa, or significand

Rounding

Rounding

Rounding

Show in standard decimal form and scientific notation

Rounding

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Arithmetic Operations with Significant Figures and Rounding – Addition & Subtraction

• When adding or subtracting a series of measurements, the result can be no more certain than the least certain measurement in the series.

• When adding and subtracting we focus on the precision of each number…….the number of decimal places.

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1555 inches + 0.001 inches + 0.2 inches

142 cm – 0.48 cm

Practice Problems – Addition & Subtraction

Complete the following arithmetic operations. First identify the least precisenumber in each problem.

142 cm – 0.48 cm

142 cm – 140.3 cm

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Multiplication & Division with Significant Figures

• For multiplication and division, focus on determining the number of significant figures in each number.

• The least number of significant figures in any number of the problem determines the number of significant figures in the answer.

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Practice Problems – Multiplication & Division

220. Hours x 3 = (the 3 is an exact number)

Perform the following arithmetic operations. First identify the number of significant figures in each number.

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Multistep Calculation

• In a multistep calculation, it is best not to do rounding until the end (avoid accumulating rounding error).

• Determine the correct number of significant figures at each step. Carry extra digits through until the end and then round.

• It is helpful to underline the last digit that should be retained in each step.

• Remember, for addition and subtraction, decimal places are counted; for multiplication and division, significant figures are counted.

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Multistep Calculation

Remember the order of arithmetic operations:

1) Parenthesis or grouping operations2) Exponents (powers) or roots3) Multiplication or division4) Addition or subtraction

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(125.6 – 36.21) / 14.62 = ?

89.39 / 14.62 = 6.114227086 = 6.11

(8.34 – 7.84)/ (15.05 * 2.01) = ?

0.50/ (15.05 * 2.01) = ?

0.50/ 30.2505 = 0.01652865 = 0.017

Examples – Multistep Calculations

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Practice Problem

An equality

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Practice Problems

1) How many grams are in 1.65 lb ? 1 lb = 453.6 g

2) How many milliliters are in 2.44 gallons?

1 Liter = 1000 mL (exact)

1 gallon = 3.785 Liters

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Practice Problems

If a wheelchair–marathon racer moving at 13.1 miles per hour expends energy at a rate of 665 Calories per hour, how much energy in Calories would be required to complete a marathon race (26.2 miles) at this pace?

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Practice Problems

A car engine has a displacement of 292 in3. How manyLiters is this?

1 inch = 2.54 cm (exact)1 cm3 = 1 mL1 L = 1000 mL

Dimensional Analysis – Picket Fence Approach

• Convert 245.6 Tm to cm– First generate conversion factors!

• Two conversion factors • Use Picket Fence approach to complete conversion

Dimensional Analysis – Picket Fence ApproachWrite down all conversion factors first!

Dimensional Analysis – Picket Fence Approach

Practice Problem

Convert 4.078 x 1020 fg to Gg

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Ratio Approach

How many hours are there in 30 min?We know there are 60 minutes in 1 hour.Set-up ratio: 1 h

60 minThe ratio for our unknown relationship should equal the known ratio as long as we use the same units. Set the known ratio equal to the unknown ratio.

1 hr = x hr 60 min 30 minCross multiply and solve for x

x hr * 60 min = 1 hr * 30 min x = 0.5 hr

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Practice Problems

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Practice Problems

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Temperature Scales

Temperatureof outer space is ~ 3 K

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Temperature Conversion Equations

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Density

A physical property of matter widely used to characterize substances

Density of a substance is the ratio of its mass (m) to its volume (V).

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Density

A substance floats if it is less dense, or has less mass per unit volume, than other components in a mixture.

Ice floats because it is about 9% less dense than liquid water. In other words, ice takes up about 9% more space than water, so a liter of ice weighs less than a liter water. The heavier water displaces the lighter ice, so ice floats to the top.

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Density• Water displacement can be used to find the volume of a

solid by placing the object in a known volume of water.• When the object is added to water, the measured total

volume increases. • This final volume is equal to the volume of the initial water

plus the volume of the solid object added.• To determine the volume of the water that is displaced by

the object, subtract the initial volume from the final volume.

• The volume of water displaced is equal to the volume of the solid object.

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Practice Problem

27.00 mL28.16 mL

You add an iron key, of mass 9.1 g, to 27.00 mL of water and observe that the volume of iron and water together is 28.16 mL. Calculate the density of iron.

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Practice Problem

What is the mass of a lead block that measures 6.5 cm x 9.0 cm x 1.5 cm?

The density of lead is 11.3 g/cm3

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The Scientific Method

• The general process of advancing scientific knowledge by making experimental observations and by formulating hypotheses, theories and laws.

• Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge.

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The Scientific Method

• Scientific Law – a description of an observed phenomenon.

• Laws exist in nature and may be discovered.– Kepler’s Laws of Planetary Motion

• Describe the motion of planets• Does not explain why they are that way!• May be verbal statement or mathematical equation

– Newton’s Law of Universal Gravitation

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Scientific Method

• Scientific Theory - a scientific explanation of an observed phenomenon.– Theories actually explain why things are the way

they are– Theories may evolve over time– The value of a theory is the ability to make useful

predictions.

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Evolution of Atomic Theory

Democritus, 460-370 BC John Dalton’s atomic theory

J.J. Thomson’s “Plum puddingmodelBohr’s model

Modern Quantum Theory

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The Scientific Method

• Hypothesis – a proposed explanation made on the basis of limited evidence as a starting point for further investigation

• A hypothesis may evolve into a theory• Typically written in the form – "If ___________, then ___________.

This part is called the independent variable. The independent variable is just whatever you are going to do to solve the problem.

This part is the dependent variable. The dependent variable is what you think will happen when you do whatever the independent variable is.

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The Scientific Method

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Practice Problems

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Laws of Exponents