2 - 1 Measurement The Metric System and SI Units Converting Units Uncertainty in Measurement...

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MeasurementMeasurement

The Metric System and SI UnitsThe Metric System and SI Units

Converting UnitsConverting Units

Uncertainty in MeasurementUncertainty in Measurement

Significant FiguresSignificant Figures

Measuring Volume and MassMeasuring Volume and Mass

Extensive and Intensive PropertiesExtensive and Intensive Properties

DensityDensity

Measuring Temperature and TimeMeasuring Temperature and Time

The Mole and Atomic and Formula MassesThe Mole and Atomic and Formula Masses

SI UnitsSI Units

Many different systems for measuring the world around us have developed over the years.

People in the U.S. rely on the English System.

Scientists make use of SI units so that we all are speaking the same measurement language.

Data, results and unitsData, results and units

DataDataMeasurements and observations.

ResultsResultsData obtained from an experiment.May be converted using known equations.

UnitsUnitsDefines the quantities being measured.All measurements must have units.

To communicate our results, we must use standard units

Units are importantUnits are important

45 000 has little meaning, just a number

$45,000 has some meaning - money

$45,000/yr more meaning - person’s salary

Measurements in chemistryMeasurements in chemistry

English units. English units. - Still commonly used in the United States.

Weight ounce, pound, ton

Length inch, foot, yard, mile

Volume cup, pint, quart, gallon

Not often used in scientific workNot often used in scientific work - Very confusing and difficult to

keeptrack of the conversions needed.

Measurement in chemistryMeasurement in chemistry

English units.English units. Vary in size so you must memorize many conversion factors.

Common English measures of volumeCommon English measures of volume1 tablespoon = 3 teaspoons1 cup = 16 tablespoons1 pint = 2 cups1 quart = 2 pints1 gallon = 4 quarts1 peck = 2 gallons1 bushel = 4 pecks

ExampleExample

How many teaspoons in a barrel of oil?

1 barrel of oil = 42 gallons1 gallon = 4 quarts1 quart = 4 cups1 cup = 16 tablespoons1 tablespoon = 3 teaspoons

1 bbl x 42 x 4 x 4 x 16 x 3galbbl

tblcup

tsptbl

= 32 256 tsp

Metric UnitsMetric Units One base unit for each type of measurement. Use a prefix to change the size of unit.

Some common base units.TypeType NameName SymbolSymbol

Mass gram g

Length meter mVolume liter L Time second

sEnergy joule J

Measurement in chemistryMeasurement in chemistry

Metric prefixesMetric prefixes

Changing the prefix alters the size of a unit.

PrefixPrefix Symbol Symbol Factor Factor

mega M 106 1 000 000

kilo k 103 1 000

hecto h 102 100

deka da 101 10

base - 100 1

deci d 10-1 0.1

centi c 10-2 0.01

milli m 10-3 0.001

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SI unitsSI units

SI - System InternationalSystem InternationalSystematic subset of the metric system.

Only uses certain metric units.Mass kilogramsLength metersTime secondsTemperature kelvinAmount mole

Other SI units are derived from SI base units.

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Example. Metric conversionExample. Metric conversion

How many milligrams are in a kilogram?

1 kg = 1000 g1 g = 1000 mg

1 kg x 1000 x 1000

= 1 000 000 mg

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Converting unitsConverting units

Factor label methodFactor label method

•Regardless of conversion, keeping track of units makes thing come out right

•Must use conversion factors- The relationship between two

•Canceling out units is a way of checking that your calculation is set up right!

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Common conversion factorsCommon conversion factors

English FactorFactor1 gallon = 4 quarts 4 qt/gal1 mile = 5280 feet 5280 ft/mile1 ton = 2000 pounds2000 lb/ton

Common English to Metric conversions FactorFactor

1 liter = 1.057 quarts 1.057 qt/L1 kilogram = 2.2 pounds 2.2 lb/kg1 meter = 1.094 yards 1.094 yd/m1 inch = 2.54 cm 2.54 cm/inch

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ExampleExample

Creatinine is a substance found in blood. If an analysis of blood serum sample detected 0.58 mg of creatinine, how many micrograms were present?

= 10-6 = micro = 10-6 = micro

0.580 mg = 580 g10-3 g1 mg( ) 1 g

10-6 g( )

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ExampleExample

A nerve impulse in the body can travel as fast as 400 feet/second.

What is its speed in meters/min ?

Conversions Needed

1 meter = 3.3 feet1 minute = 60 seconds

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m 400 ft 1 m 60 secmin 1 sec 3.3 ft 1 min

ExampleExample

m 400 ft 1 m 60 secmin 1 sec 3.3 ft 1 min?? = x x

?? = x x

mmin ....Fast7273

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Uncertainty in MeasurementUncertainty in Measurement

All measurements contain some uncertainty.

•We make errors

•Tools have limits

Uncertainty is measured with

AccuracyAccuracy How close to the true value

PrecisionPrecision How close to each other

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AccuracyAccuracy

Here the average valuewould give agood number but the numbersdon’t agree.

Large random error

How close our values agree with the true value.

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PrecisionPrecision

Here the numbersare close togetherso we have goodprecision.

• Poor accuracy.

• Large systematic

error.

How well our values agree with each other.

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Accuracy and precisionAccuracy and precision

Our goal!

Good precisionand accuracy.

These arevalues wecan trust.

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Accuracy and precisionAccuracy and precision

Predict the effect on accuracy and Predict the effect on accuracy and precision.precision.

•Instrument not ‘zeroed’ properly

•Reagents made at wrong concentration

•Temperature in room varies ‘wildly’

•Person running test is not properly trained

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Types of errorsTypes of errors

Instrument not ‘zeroed’ properlyReagents made at wrong concentration

Temperature in room varies ‘wildly’Person running test is not properly trained

Random

Systematic

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ErrorsErrors

SystematicSystematic

•Errors in a single direction (high or low).

•Can be corrected by proper calibration or running controls and blanks.

RandomRandom

•Errors in any direction.

•Can’t be corrected. Can only be accounted for by using statistics.

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Significant figuresSignificant figures

Method used to express accuracy and precision.

You can’t report numbers better than the method used to measure them.

67.2 units = three significant figures

Certain Digits

UncertainDigit

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The number of significant digits is independent of the decimal point.

255 25.5

0.0255

These numbersAll have three

significant figures!

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Significant figures: Significant figures: Rules for zerosRules for zeros

Leading zeros are notare not significant.0.421 - three significant figures

Leading zeroLeading zero

Captive zeros areare significant. 4012 - four significant figures

Trailing zeros areare significant.114.20 - five significant figures

Captive zeroCaptive zero

Trailing zeroTrailing zero

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Zeros are what will give you a headache!Zeros are what will give you a headache!

They are used/misused all of the time.

ExampleExampleThe press might report that the federal deficit is three trillion dollars. What did they mean?

$3 x 1012

or$3,000,000,000,000.00

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In science, all of our numbers are either measured or exact.

• ExactExact - Infinite number of significant figures.

• MeasuredMeasured - the tool used will tell you the level of significance. Varies based on the tool.

ExampleExampleRuler with lines at 1/16” intervals.A balance might be able to measure to

the nearest 0.1 grams.

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Significant figures:Significant figures:Rules for zerosRules for zeros

Scientific notationScientific notation - can be used to clearly express significant figures.

A properly written number in scientific notation always has the the proper number of significant figures.

0.00321321 = 3.213.21 x 10-3

Three SignificantFigures

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Scientific notationScientific notation

• Method to express really big or small numbers.

Format is Mantissa x Base Power

Decimal part ofDecimal part oforiginal numberoriginal number

DecimalsDecimalsyou movedyou moved

We just move the decimal point around.

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If a number is larger than 1If a number is larger than 1

•The original decimal point is moved X places to the left.

•The resulting number is multiplied by 10X.

•The exponent is the number of places you moved the decimal point.

1 2 3 0 0 0 0 0 0. = 1.23 x 108

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If a number is smaller than 1If a number is smaller than 1

•The original decimal point is moved X places to the right.

•The resulting number is multiplied by 10-X.

•The exponent is the number of places you moved the decimal point.

0. 0 0 0 0 0 0 1 2 3 = 1.23 x 10-7

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Most calculators use scientific notation when the numbers get very large or small.

How scientific notation is displayed can vary.

It may use x10n

or may be displayedusing an E.

They usually have an Exp or EEThis is to enter in the exponent.

cos tan

1.44939 E-2

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ExamplesExamples

378 000

3.78 x 10 5

8931.5

8.9315 x 10 3

0.000 593

5.93 x 10 - 4

0.000 000 4

4 x 10 - 7

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Significant figuresSignificant figuresand calculationsand calculations

An answer can’t have more significant figures than the quantities used to produce it.

ExampleExample How fast did you run if youwent 1.0 km in 3.0 minutes?

speed = 1.0 km / 3.0 min = 0.33 km / min +

cos tan

0.333333333

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Significant figures and calculationsSignificant figures and calculations

Addition and subtractionAddition and subtractionReport your answer with the same number of digits to the right of the decimal point as the number having the fewest to start with.

123.45987 g+ 234.11 g 357.57 g

805.4 g- 721.67912 g 83.7 g

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Significant figures and calculationsSignificant figures and calculations

Multiplication and division.Multiplication and division.Report your answer with the same number of digits as the quantity have the smallest number of significant figures.

Example. Density of a rectangular solid.Example. Density of a rectangular solid.25.12 kg / [ (18.5 m) ( 0.2351 m) (2.1m)

]= 2.8 kg / m3

(2.1 m - only has two significant figures)

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ExampleExample

257 mg

\__ 3 significant figures

120 miles

0.002 30 kg

23,600.01 $/yr

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Rounding off numbersRounding off numbers

After calculations, you may need to round off.

If the first insignificant digit is 5 or more,

- you round up

If the first insignificant digit is 4 or less,

- you round down.

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If a set of calculations gave you the following numbers and you knew each was supposed to have four significant figures then -

2.57995035 becomes 2.580

34.2004221 becomes 34.20

Rounding offRounding off

1st insignificant digit1st insignificant digit

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Measuring volumeMeasuring volume

VolumeVolume - the amount of space that an object occupies.

• The base metric unit is the liter (L)liter (L).

• The common unit used in the lab is the milliliter (mL)milliliter (mL).

• One milliliter is exactly equal to one cmcm33.

• The derived SISI unit for volume is the mm33 which is too large for convenient use.

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Measuring massMeasuring mass

MassMass - the quantity of matter in an object.

WeightWeight - the effect of gravity on an object.

Since the Earth’s gravity is relatively constant, we can interconvert between weight and mass.

The SI unit of mass is the kilogram (kg)kilogram (kg). However, in the lab, the gram (g)gram (g) is more commonly used.

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Extensive and intensive propertiesExtensive and intensive properties

Extensive propertiesExtensive propertiesDepend on the quantity of sample measured.

ExampleExample - mass and volume of a sample.

Intensive propertiesIntensive propertiesIndependent of the sample size.Properties that are often characteristic of the substance being measured.

ExamplesExamples - density, melting and boiling points.

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DensityDensity

Density is an intensive property of a substance based on two extensive properties.

Common units are g / cm3 or g / mL.

g / cm3

Air 0.0013 Bone 1.7 - 2.0

Water 1.0 Urine 1.01 - 1.03

Gold 19.3 Gasoline 0.66 - 0.69

Density = Mass

Volume

cm3 = mL cm3 = mL

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Example.Example.Density calculationDensity calculation

What is the density of 5.00 mL of a fluid if ithas a mass of 5.23 grams?

d = mass / volume

d = 5.23 g / 5.00 mL

d = 1.05 g / mL

What would be the mass of 1.00 liters of thissample?

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Example.Example.Density calculationDensity calculation

What would be the mass of 1.00 liters of the fluid sample?

The density was 1.05 g/mL.

density = mass / volume

so mass = volume x density

mass = 1.00 L x 1000 x 1.05

= 1.05 x 103 g

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Specific gravitySpecific gravity

The density of a substance compared to a reference substance.

Specific Gravity =

•Specific Gravity is unitless.

•Reference is commonly water at 4oC.

•At 4oC, density = specific gravity.

•Commonly used to test urine.

density of substancedensity of reference

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Specific gravity measurementSpecific gravity measurement

Hydrometer

Float height willbe based onSpecific Gravity.

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Temperature conversionTemperature conversion

Temperature - measure of heat energy.

Three common scales usedFahrenheit, Celsius and Kelvin.

oF = 32oF + (oC) X

oC = (oF - 32oF)

K = (oC + 273) X SI unitSI unit

5oC9oF

9oF5oC

1 K1oC

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Example. Example. ooF to F to ooC C

If it is 20 oF outside, what is it in oC ?

oC = (oF - 32oF) 5oC9oF

oC = (20oF - 32oF) 5oC9oF

oC = -6.7 (two significant figures in 20oF)

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Example. Example. ooF to KF to K

If the temperature is 75.0 oF, what is it in K?

First convert to oC

Then convert to K

oC = (75.0oF - 32) 59

= 23.9

K = 23.9oC + 273

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Measuring timeMeasuring time

The SI unit is the second (s).The SI unit is the second (s).

For longer time periods, we can use SI prefixes or units such as minutes (min), hours (h), days (day) and years.

Months are never used - they vary in size.

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Atomic massesAtomic masses

Atoms are composed of protons, neutrons and electrons.

Almost all of the mass of an atom comes from the protons and neutrons.

All atoms of the same element will have the same number of protons. The number of neutrons may vary - isotopes.

Most elements exist as a mixture of isotopes.

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IsotopesIsotopes

IsotopesIsotopes Atoms of the same element but having different masses.

Each isotope has a different number of neutrons.

Isotopes of hydrogen H H H

Isotopes of carbon C C C

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IsotopesIsotopes

Most elements occur in nature as a mixture of isotopes.

ElementElement Number of stable isotopesNumber of stable isotopesH 2C 2O 3Fe 4Sn 10

This is one reason why atomic masses are not whole numbers. They are based on averages.

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The atomic symbol & isotopesThe atomic symbol & isotopes

Determine the number of protons, neutrons and electrons in each of the following.

PP31311515 BaBa

138138 5656 UU

238238 9292

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Atomic massesAtomic masses

As a reference point, we use the atomic mass unit (u) - 1/12th of a 12C atom.

Using this relative system, the mass of all other atoms can be assigned.

Examples 7Li = 7.016 004 u14N = 14.003 074 01 u29Si = 28.976 4947 u

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Average atomic massesAverage atomic masses

• Most elements exits as a mixture of isotopes.

• Each isotope may be present in different amounts.

• The masses listed in the periodic table reflect the world-wide average for each isotope.

One can calculate the average atomic weight of an element if the abundance of each isotope for that element is known.

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Example.Example.Silicon exists as a mixture of three isotopes.

Determine it’s average atomic mass based on the following data.

Isotope Mass (u) Abundance28Si 27.976 9265 92.23 %29Si 28.976 4947 4.67 %30Si 29.973 7702 3.10 %

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92.23100

(27.976 9265 u) = 25.80 u

4.67100

(28.976 4947 u) = 1.35 u

3.10100

(29.973 7702 u) = 0.929 u

Average atomic mass for silicon = 28.08 u

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The moleThe mole

Number of atoms in 12.000 grams of 12C

1 mol = 6.022 x 1023 atoms mol = grams / formula

weight

Atoms, ions and molecules are too small to directly measure - measured in uu.

Using moles gives us a practical unit.

We can then relate atoms, ions and molecules, using an easy to measure unit - thethe gramgram.

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The moleThe mole

If we had one mole of water and one mole of hydrogen, we would have the name number of molecules of each.

1 mol H2O = 6.022 x 1023 molecules

1 mol H2 = 6.022 x 1023 molecules

We can’t weigh out moles -- we use grams.

We would need to weigh out a different number of grams to have the same number of molecules

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Moles and massesMoles and masses

Atoms come in different sizes and masses.

A mole of atoms of one type would have a different mass than a mole of atoms of another type.

H - 1.008 u or grams/molO - 16.00 u or grams/molMo - 95.94 u or grams/molPb - 207.2 u or grams/mol

We rely on a straight forward system to relate mass and moles.

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Masses of atomsMasses of atomsand moleculesand molecules

Atomic massAtomic mass

•The average, relative mass of an atom in an element.

Atomic mass unit (u)Atomic mass unit (u)

•Arbitrary mass unit used for atoms.

•Relative to one type of carbon.

Molecular or formula massMolecular or formula mass

•The total mass for all atoms in a compound.

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Molar massesMolar masses

Once you know the mass of an atom, ion, or molecule, just remember:

Mass of one unit - use u

Mass of one mole of units - use grams/mole

The numbers DON’TDON’T change -- just the units.

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Masses of atomsMasses of atomsand moleculesand molecules

HH22OO - water

2 hydrogen 2 x 1.008 u1 oxygen 1 x 16.00 u

mass of molecule 18.02 u18.02 g/mol

Rounded off basedon significant figuresRounded off based

on significant figures

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Another exampleAnother example

CHCH33CHCH22OHOH - ethyl alcohol

2 carbon 2 x 12.01 u6 hydrogen 6 x 1.008 u1 oxygen 1 x 16.00 u

mass of molecule 46.07 u46.07 g/mol

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Molecular mass vs. formula massMolecular mass vs. formula mass

Formula massFormula massAdd the masses of all the atoms in formula

- for molecular and ionic compounds.

Molecular massMolecular massCalculated the same as formula mass

- only valid for molecules.

Both have units of either u or grams/mole.

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Formula mass, FMFormula mass, FM

The sum of the atomic masses of all elements in a compound based on the chemical formula.

You must use the atomic masses of the elements listed in the periodic table.

CO2 1 atom of C and 2 atoms of O

1 atom C x 12.011 u = 12.011 u2 atoms O x 15.9994 u = 31.9988 u Formula mass Formula mass == 44.010 u44.010 u

or or g/mol g/mol

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Example - (NHExample - (NH44))22SOSO44

OK, this example is a little more complicated.

The formula is in a format to show you how the various atoms are hooked up.

( N H ( N H 4 4 ) ) 2 2 S O S O 44

We have two (NH4+) units and one SO4

2- unit.

Now we can determine the number of atoms.

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Ammonium sulfate contains2 nitrogen, 8 hydrogen, 1 sulfur & 4

oxygen.

2 Nx 14.01 = 28.028 H x 1.008 = 8.0641 S x 32.06 = 32.064 O x 16.00 = 64.00

Formula massFormula mass = 132.14= 132.14The units are either u or grams / mol.

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How many atoms are in 20.0 grams of ammonium sulfate?

Formula weight = 132.14 grams/molAtoms in formula = 15 atoms / unit

moles = 20.0 g x = 0.151 mol1 mol

132.14 g

atoms = 0.151 mol x 15 x 6.02 x1023 atomsunit

unitsmol

atoms = 1.36 x1024

2 - 1 Measurement The Metric System and SI Units Converting Units Uncertainty in Measurement...

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