Topic 1

Chemistry and Measurements

What Is Chemistry?• Chemistry is the study of the composition, structure,

and properties of matter and energy and changes that matter undergoes.– Matter is anything that occupies space and has mass.

• Atoms – are the smallest units that we associate with the chemical behavior of matter ; atoms make up matter.

• Mass – is a measure of the quantity of matter that an object contains; mass does not vary with location, i.e. moon or earth object has same mass.

– Energy is the “ability to do work.” All chemical processes are accompanied by changes in energy.

Forms of energy• Potential energy – energy of position or arrangement

(composition) – “stored energy”• Kinetic energy – energy of motion

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Types of energy• Work• Heat

Specific heat of a substance is the amount of heat required to raise the temp of 1 g substance by 1oC. water – 1.00 cal or 4.182 J

g oC g oCheat absorbed (+) or release (-) = sp heat x mass x DT

DT = Tfinal - Tinitial

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How much heat in calories does it take to raise the temp of 225 g water from 25.0oC to 100.0oC?

      

sp heat x m x DT

This is an example of the type problem we will solve later in the course.

Experiment and Explanation

• Experiment and explanation are the heart of chemical research. – Chemists make observations under circumstances in which

variables such as temperature, amount of substance, etc. are controlled. Variables are controlled to design an experiment to give useful information leading to conclusions.

– An experiment is the observation of facts or events that can be described scientifically and were carried out in a controlled manner so that the results can be duplicated and rational conclusions obtained.

– After a series of experiments, a researcher may see some relationship or regularity in the results.

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Experiment and Explanation• If the regularity or relationship is fundamental

and we can state it simply, we call it a law.– A law is a concise statement or mathematical

equation about a fundamental relationship or regularity of nature.

– An example is the law of conservation of mass, which says that mass, or quantity of matter, remains constant during any chemical change (mass starting material = mass ending material).

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wood + air ash + gases

11.02 g 11.02 g

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Experiment and Explanation

• Explanations help us organize knowledge and predict future events.– A hypothesis is a tentative explanation of some

regularity of nature.– If a hypothesis successfully passes many tests, it

becomes known as a theory.– A theory is a tested explanation of some regularity

of nature.• Note: we cannot prove a theory is absolute. It is

always possible that further experiments will show the theory is limited or that a better theory is possible.

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Experiment and Explanation

The two aspects of science, experiment & explanation, lead us to what is called the

Scientific Method - the general process of advancing scientific knowledge through observation, laws, hypotheses, or theories .

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A representation of the scientific method.

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experiments

results

further exps

hypothesis

negative results positive results

theory

further exps

Matter: Physical State andChemical Constitution

• There are two principal ways of classifying matter:– By its physical state as a solid, liquid, or gas which

is dependent on the conditions, i.e. temperature, pressure.

– By its chemical constitution as an element, compound, or mixture.

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Solids, Liquids, and Gases• Solid: the form of matter

characterized by rigidity; a solid is relatively incompressible and has a fixed shape and volume.

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• Gas: the form of matter that is an easily compressible fluid; a given quantity of gas will fit into a container of almost any size and shape.

• Liquid: the form of matter that is a relatively incompressible fluid; liquid has a fixed volume but no fixed shape.

Elements, Compounds, and Mixtures

Physical change is a change in the form of matter but not in its chemical identity.

– Physical changes are usually reversible by physical means.

– No new compounds are formed during a physical change.

• Melting ice is an example of a physical change.– Species retain their chemical identities and can be

separated by some physical means.• i.e. dissolving one substance in another (salt in water)

can be reversed by distillation/evaporation11

• Chemical change, or chemical reaction, is a change in which one or more kinds of matter are transformed into a new kind of matter or several new kinds of matter.– Chemical changes are usually irreversible by physical means (can do by

chemical means).– New compounds are formed during a chemical change.– The rusting of iron is an example of a chemical change, iron and oxygen

form a new compound.

Substance – is a kind of matter that cannot be separated into other kinds of matter by any physical process.

iron + oxygen rust (Fe2O3)Rust is a substance that cannot be converted back into iron and oxygen by

any physical means.

Mixture – is a material that can be separated by physical means into two or more substances.

Salt (NaCl) in waterSalt and water can be separated through a physical means such as

evaporation or distillation; therefore, it is a mixture of two substances.12

Elements, Compounds, and Mixtures (cont’d)

• A physical property is a characteristic that can be observed for material without changing its chemical identity.– Examples are physical state of substance (solid, liquid,or

gas), melting point, and color.• A chemical property is a characteristic of a material

involving its chemical change. – A chemical property of iron is its ability to react with

oxygen to produce rust, a new substance with different properties from the starting substances.

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Elements, Compounds, and Mixtures (cont’d)

• Millions of substances have been characterized by chemists. Of these, a very small number are known as elements, from which all other substances are made.– An element is a substance that cannot be

decomposed by any chemical reaction into simpler substances.

– The smallest unit of an element is the atom.• Many identical atoms make up an element; the atom is

the repeating unit of identity for an element.14

Elements, Compounds, and Mixtures (cont’d)• Most substances are compounds (combination

of elements).– A compound is a substance composed of two or

more elements chemically combined (NaCl, H2O).– The smallest unit of a compound is the molecule.

• Many identical molecules make up a compound; the molecule is the repeating unit of identity for a compound.

– The law of definite proportions states that a pure compound, whatever its source, always contains definite or constant proportions of the elements by mass; unique composition for each compound but always the same for a particular compound. 15

i.e. NaClalways has39.3% Na & 60.7% Cl

Elements, Compounds, and Mixtures• Most of the materials we see around us are mixtures.

– A mixture is a material that can be separated by physical means into two or more substances.

– Unlike a pure compound which has a constant composition, a mixture has a variable composition.

– Mixtures are classified as heterogeneous (“coarse mixture”) if they consist of physically distinct parts or homogeneous (“solutions”) when the properties are uniform throughout.

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heterogeneous “distinct parts”

homogeneous “uniform”

Summary: Atomselementsmoleculescompoundssubstances

pure “definite proportions”

mixture “variable proportions”

HW 1 code: intro

• Chemical symbol is a one or two letter designation derived from the name of an element (based on English or Latin name).

• First letter of symbol is capitalized and second is always lower case.

Co vs CO The chemical symbol of Co is cobalt while the molecule CO is carbon monoxide. It makes a difference if you use upper or lower letters.

• Compounds are designated by combination of chemical symbols called a formula.– If more than one atom is to be indicated in a formula, a subscript

number is used after the symbol.CO has 1-C atom and 1-O atomCCl4 has 1-C atom and 4-Cl atoms

Note: you should learn the names/symbols of all the elements17

Because elements & compounds are so fundamental to the study of chemistry, it is useful to refer to them by symbols and formulas. Chemistry has its own language with symbols as letters, formulas as words, and chemical reactions as sentences.

Measurement and Significant Figures • Measurement is the comparison of a physical

quantity to be measured with a unit of measurement -- that is, with a fixed standard of measurement. It is important to give the unit of measure with a numeric value, i.e write 9.12 cm not just 9.12.– The term precision refers to the closeness of the

set of values obtained from identical measurements of a quantity (reproducibility).

– Accuracy refers to the closeness of a single measurements to its true value (truthfulness of data).

– Is it possible to have precision but be inaccurate?• Yes, you may have a systematic error causing all results

to be off by a similar amount. Just because you are precise, it doesn’t mean you are accurate. 18

missed bullseye everytime by similar distance – precise but inaccuate

• To indicate the precision of a measured number (or result of calculations on measured numbers), we often use the concept of significant figures.– Significant figures are those digits in a measured

number (or result of the calculation with a measured number) that include all certain digits plus a final one having some uncertainty (first digit basically guessing).

1930.22 cm

2 mL

1 mL

1.5 mL

Measuring device has divisions up to tenths place; therefore, the first uncertainty value (guessing) is the hundredths place. We are certain it is greater than 30.2 but less than 30.3 cm.

Measuring device has divisions up to ones place; therefore, the first uncertainty value (guessing) is the tenths place. We are certain it is greater than 1 but less than 2 mL.

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• Rules for Significant Figures (must learn):– All nonzero digits are significant.

i.e. 111 1286

– Zeros between significant figures are significant. i.e. 1001 20,006

– Zeros preceding the first nonzero digit are not significant. i.e. 0.0002

0.00206

– Zeros to the right of the decimal after a nonzero digit are significant.i.e. 0.00300 9.00 9.10 90.0

– Zeros at the end of a nondecimal number may or may not be significant. (Use scientific notation to indicate significant figures.)i.e. 900 900.

111 3 SF 1286 4 SF

1001 4 SF 20,006 5 SF

0.0002 1 SF 0.00206 3 SF

0.00300 3 SF 9.00 3 SF 9.10 3 SF 90.0 3 SF

could be 1, 2, or 3 SF 3 SF

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Scientific notation – is the representation of a number in the form A. x 10n, where A is a number (sign digits only) with a single nonzero digit to the left of the decimal point and n is an integer or whole number.

900

300,000,000 (let’s write with 3 SF)

0 0000301

843.4

0.00421

6.39 x 10-4

3.275 x 102

9 x 102 1 SF 9.0 x 102 2 SF 9.00 x 102 3 SF

3.00 x 108 3 SF

3.01x 10-5 3 SF

8.434 x 102 4 SF

4.21 x 10-3 3 SF

0.000639 3SF

327.5 4SF

HW 2HW 3code for both: sign

If you move the decimal place to the left until you have a single nonzero digit to the left of the decimal place, n will be a positive integer equal to the number of decimal places moved. In this case, the decimal is moving two decimal places and n = 2.We may write 900 as 1, 2, or 3 sign figures by using scientific notation to indicate the number.

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The decimal is moving 8 decimal places making n = 8, and I’ve selected to write with 3 sign digits..

If you move the decimal place to the right until you have a single nonzero digit to the left of the decimal place, n will be a negative integer equal to the number of decimal places moved. In this case, the decimal is moving to the right 5 decimal places and n = -5.

.

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Number of significant figures refers to the number of digits reported for the value of a measured or calculated quantity, indicating the precision of the value. [Basically means if all quantities have X sign fig can’t report final answer with more than X sign figs: measurement or calculation dictates sign figs.]

– When multiplying and dividing measured quantities, give as many significant figures as the least found in the measurements used.

2.1 x 3.52 =

– Which gets us to rounding: if the left most digit to be dropped is 5 or greater add 1 to last digit to be retained, if less than five, leave alone.

1.214 1.21– Multiple step calculation – typically, we keep a minimum of one

additional digit past the required sign figures during calculations; we call this the guard digit: 1.214 Sometimes we put a line under the actual last sign figure to indicate the correct sign figures in a number during the multiple step calculations. We drop the guard digit when the final answer is reported with correct sign figures.

– When adding or subtracting measured quantities, give the same number of decimals as the least found in the measurements used.

84.2 (3 SF)+22.321 (5 SF)106.521 106.5 (4 SF)

2 SF 3SF7.39 = 7.4

; therefore, answer must have 2 SF

Addition and subtraction doesn’t depend on number of sign digits in the calculation but instead in the least decimal place which in this case is the tenths place.Note if have steps involving both rules, you follow arithmetic rules to determine which rule to follow in each step: ( ), x /, + -

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3.38 – 3.012 = 0.368 = 0.37

2.4 x 10-3 + 3.56 x 10-1 = 0.0024+0.356 0.3584 = 3.58 x 10-1

2.568 x 5.8 = 14.9 = 3.56 = 3.64.186 4.186

4.18 – 58.16 x (3.38 – 3.01) =4.18 – 58.16 x (0.37) = 4.18 – 21.5 = -17.3 = -17

6.3 + 7.2 = 0.5256

13.5 = 25.69 = 25.7

0.5256

Subtraction; therefore, least decimal place dictates sign figures – hundredths place.

Addition; therefore, least decimal place dictates sign figures but notice the different powers of ten. Must change both to the same power or write the number out to easily determine the least decimal place.

Multiplication/division; therefore, least number of sign figures dictates sign figures. In this case the number 5.8 dictates it to be 2 sign figures. Note: the guard digit used in problem

This problem involves using both rules. We must follow order of operations and do the subtraction in the parentheses first (least decimal place), followed by the multiplication (least number), and finally the first subtraction (least decimal place).

This problem also involves using both rules. We must do the addition in numerator first (least decimal place), followed by division (least number).

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An exact number is a number that arises when you count items or when you define a unit (conversion 12 in = 1 ft).

– For example, when you say you have nine coins in a bottle, you mean exactly nine (9.00000…. - infinite).

– When you say there are twelve inches in a foot, you mean exactly twelve.

– Note that exact numbers have no effect on significant figures in a calculation.

Measurement and Significant Figures (cont’d)

HW 4code: math

SI Units and SI Prefixes

In 1960, the General Conference of Weights and Measures adopted the International System of units (or SI), which is a particular choice of metric units.

– This system has seven SI base units, the SI units from which all others can be derived.

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Table SI Base Units

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Quantity Unit SymbolLength Meter mMass Kilogram kgTime Second sTemperature Kelvin KAmount of substance Mole molElectric current Ampere ALuminous intensity Candela cd

Note: All other units are derived from these base units.

SI Units and SI PrefixesThe advantage of the metric system is that it is a decimal system.

– A larger or smaller unit is indicated by a SI prefix -- that is, a prefix used in the International System to indicate a power of 10.

– It is important to realize that the prefix is only a power of ten and not part of the unit; this means we can separate them when cancelling units and connect the prefix to other units in the calculation. We will demonstrate this later.

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LmmL

Table SI Prefixes

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Multiple Prefix Symbol1 x 106 mega M1 x 103 kilo k1 x 10-1 deci d1 x 10-2 centi c1 x 10-3 milli m1 x 10-6 micro m

1 x 10-9 nano n1 x 10-12 pico p

1 Mu = 1 x 106u = 1,000,000 u

1 ku = 1 x 103u = 1,000 u

100 cu = 1 u

1000 mu = 1 u

1,000,000 mu = 1 u

There are more prefixes, but these are the more common ones that you should memorize.

I suggest you memorize the following conversion factors to switch between units where u = L, m, g, etc.

Note: 1 x 106 may be represented on a calculator as 1 EE 6 or 1 exp 6.Basically, “x 10” is equivalent to the EE or exp button on calculator.

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Ex. Convert: 9.7 x 103 m km

7.85 x 10-2 g cg

1.6 x 106 mm Mm

HW 5code: convert

    

    

    

 

 

For conversions, you start off with the number and unit you want to convert in the numerator. Next, you multiply a conversion factor that allows you to cancel the unit in the denominator of the factor with the unit of the number in the numerator.

= 1.6 x 10-3 MmNote: could have shorten the calculation by combining conversion factors into one factor.

TemperatureThe Celsius scale (formerly the Centigrade scale) is the temperature scale in general scientific use.

– However, the SI base unit of temperature is the kelvin (K), a unit based on the absolute temperature scale.

– The conversion from Celsius to Kelvin is simple since the two scales are simply offset by 273.15o (1K change = 1oC change).

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FP water: 0oC BP water: 100oCNote: FP water is our reference temp that all other FPs are relative to.

  

00C = 273.15 K

Note: units cancel based on 1K:1oC conversion factor

TemperatureThe Fahrenheit scale is at present the common temperature scale in the United States.

– The conversion of Fahrenheit to Celsius (1.8oF change = 1oC change)., and vice versa, can be accomplished with the following formulas.

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FP water: 32oF BP water: 212oF  Degrees difference between FP and BP of water on oC and oF scales

Note: units cancel based on 1.8oF:1oC conversion factor

Rearranging to solve for oC

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Ex. Convert: 102.5oF oC and K

Ex. Convert: -78oC K and oF

HW 6code: temp

   

   

     

     

     

Note: 1.8 and 32 are exact numbers and do not affect sign figures. The final sign figs are based on the original decimal place of the temp.

Derived UnitsThe SI unit for speed is meters per second, or m/s.

– This is an example of an SI derived unit, created by combining SI base units.

– Volume is defined as length cubed and has an SI derived unit of cubic meters (m3).

– Traditionally, chemists have used the liter (L), which is a unit of volume equal to one cubic decimeter.

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1 L = 1 dm3 1 mL = 1 cm3

1000 L = 1 m3 1000 mL = 1 L

Conversions you should memorize.

Derived UnitsThe density of an object is its mass per unit volume,

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where d is the density, m is the mass, and V is the volume.

• Generally the unit of mass is the gram.• The unit of volume is the mL for liquids; cm3 for solids;

and L for gases.• Specific gravity of substance = density of substance @T density of water

 

H2O: 1.00 g/mL @ 25oC

Density is a physical property of a substance. It doesn’t matter the quantity of substance; the mass and volume can vary but their ratio, density, will always be constant for the substance.

A Density Example

A sample of the mineral galena (lead sulfide) weighs 12.4 g and has a volume of 1.64 cm3. What is the density of galena?

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Ethanol has a density of 0.789 g/mL. What volume of ethanol must be poured into a graduated cylinder to equal 30.3 g?

36HW 7

 V V Vd = m

    

     = 38.4 mL

  = 1 =

(30.3 g) 

= 38.4 mL

First, we must convert the density formula to solve for volume.

Another way to do this is to follow units and use the fact that density is a conversion factor with the components basically being equal to 1. We are converting grams to a volume term through using density as a conversion factor.code: density

Units: Dimensional Analysis

In performing numerical calculations, it is good practice to associate units with each quantity.

– The advantage of this approach is that the units for the answer will come out of the calculation.

– And, if you make an error in arranging factors in the calculation, it will be apparent because the final units will be nonsense.

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Units: Dimensional AnalysisDimensional analysis (or the factor-label method) is the method of calculation in which one carries along the units for quantities.

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– Suppose you simply wish to convert 20 yards to feet. We know that

– Note that the units have cancelled properly to give the final unit of feet. The proper way to arrange the conversion factor depends on the cancellation of units. In this case, we wanted yards to cancel.

feet 60 yard 1feet 3 yards 20

  = 1 =

Units: Dimensional Analysis

The ratio (3 feet/1 yard) is called a conversion factor and is an exact number.

– The conversion-factor method may be used to convert any unit to another, provided a conversion equation exists.

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Relationships of Some U.S. and Metric Units

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Length Mass Volume1 in = 2.54 cm 1 lb = 454 g 1 qt = 0.9464 L1 yd = 0.9144 m 1 lb = 16 oz 4 qt = 1 gal1 mi = 1.609 km 1 oz = 28.35 g1 mi = 5280 ft

Note: It is recommended that you memorize one set of conversion factors and work towards them to make the switch from U.S. to metric and vice versa.

How many meters are in 6.81 miles?

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HW 8code: units

We know that 1 in = 2.54 cmWe will go from miles ft in cm m

        

 

How many in2 are in 12.00 ft2 ?

  

 Note: the conversion factor is squared to cancel the units; the coefficient as well as the unit is squared.

= 1728 in2

Unit Conversion (using prefixes)

How many mg of sodium hydrogen carbonate are in 55.0 mL of a solution that contains 3.48 g/L of sodium hydrogen carbonate?

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Note: we can treat the prefix separately from the unit; in this case, the L cancels, and the m is combined with the final unit of g.

Note: Alternatively, we can do it the normal way by cancelling units one at a time ended up with the same answer.