Measuring MatterMeasuring Matter

How can we keep track of all of How can we keep track of all of this “stuff”?this “stuff”?

Measuring Matter in Two WaysMeasuring Matter in Two Ways

Qualitative MeasurementsQualitative Measurements: which are : which are usually descriptive like observations.usually descriptive like observations.

Now it is important to start making…Now it is important to start making…

Quantitative MeasurementsQuantitative Measurements: are in the form : are in the form of numbers and units.of numbers and units.

The Powers of TenThe Powers of Ten

Picture a microscopic Picture a microscopic cell.cell.

Picture the galaxy.Picture the galaxy.

A Short History of Standard UnitsA Short History of Standard Units

Humans did not always have standards by which Humans did not always have standards by which to measure temperature, time, distance, etc. to measure temperature, time, distance, etc.

It wasn’t until 1790 that France established the It wasn’t until 1790 that France established the first metric system. first metric system.

The First Metric SystemThe First Metric SystemThe French established that one meter The French established that one meter was one ten-millionth of the distance of was one ten-millionth of the distance of the from the Equator to the North Pole. the from the Equator to the North Pole.

One second was equal to 1/86,400 of the One second was equal to 1/86,400 of the average day. average day.

Today’s StandardsToday’s Standards

The techniques used today to establish standards The techniques used today to establish standards are much more advanced than in 1790…are much more advanced than in 1790…

One meter is equal to the distance traveled by light One meter is equal to the distance traveled by light in a vacuum in 1/299,792,458 of a second.in a vacuum in 1/299,792,458 of a second.

One second is defined in terms of the number of One second is defined in terms of the number of cycles of radiation given off by a specific isotope cycles of radiation given off by a specific isotope of the element cesium. of the element cesium.

S.I. UnitsS.I. Units

The International System of Units is used The International System of Units is used ALMOST exclusively worldwide (the U.S. ALMOST exclusively worldwide (the U.S. is one the of the exceptions).is one the of the exceptions).

ALL science is done using S.I. units.ALL science is done using S.I. units.

The United States’ System of The United States’ System of MeasurementMeasurement

In 1975, the U.S. In 1975, the U.S. government government attempted to adopt attempted to adopt the metric system the metric system with little success.with little success.

The U.S. currently The U.S. currently uses the English uses the English System of System of Measurement.Measurement.

So why S.I.?So why S.I.?

So why S.I.?So why S.I.?

Decimals are more “computationally Decimals are more “computationally friendly”friendly”

Multiples of tenMultiples of ten Eliminate LARGE numbers by using Eliminate LARGE numbers by using

prefixesprefixes Scientifically basedScientifically based

Measurements and SI UnitsMeasurements and SI Units

Quantitative measurements must include a Quantitative measurements must include a numbernumber AND a AND a unitunit. .

Base units are used with prefixes to Base units are used with prefixes to indicate fractions or multiples of a unit. indicate fractions or multiples of a unit.

Try to fill in your table. Try to fill in your table.

Base UnitsBase UnitsBase UnitBase Unit SymbolSymbol Measures…Measures…

gramsgrams gg massmass

metermeter mm distancedistance

LiterLiter LL volumevolume

KelvinKelvin KK temperaturetemperature

degrees Celsiusdegrees Celsius °C°C temperaturetemperature

molemole molmol amount of a amount of a substancesubstance

secondsecond S or secS or sec timetime

ampereampere AA electric currentelectric current

candelacandela cdcd light intensitylight intensity

JouleJoule JJ energyenergy

PrefixesPrefixes

Prefixes combine with base Prefixes combine with base units to indicate fractions or units to indicate fractions or multiples of a unit.multiples of a unit.

PrefixesPrefixesPrefixPrefix SymbolSymbol Meaning Meaning mega-mega- MM 1 000 000 times larger1 000 000 times larger

kilo-kilo- KK 1 000 times larger1 000 times larger

Hecto-Hecto- HH 100 times larger100 times larger

deca-deca- DD 10 times larger than base unit10 times larger than base unit

Base UnitBase Unit

deci-deci- dd 10 times smaller than base unit10 times smaller than base unit

centi-centi- cc 100 times smaller100 times smaller

milli-milli- mm 1 000 times smaller1 000 times smaller

micro-micro- µµ 1 000 000 times smaller1 000 000 times smaller

nano-nano- nn 1 000 000 000 times smaller1 000 000 000 times smaller

pico-pico- pp 1 000 000 000 000 times smaller1 000 000 000 000 times smaller

femto-femto- ff 1 000 000 000 000 000 1 000 000 000 000 000 times smallertimes smaller

SI PrefixesSI Prefixes1 000 000 000 000 000 000 000 0001 000 000 000 000 000 000 000 0001 000 000 000 000 000 000 0001 000 000 000 000 000 000 0001 000 000 000 000 000 0001 000 000 000 000 000 0001 000 000 000 000 0001 000 000 000 000 0001 000 000 000 0001 000 000 000 0001 000 000 000 1 000 000 000 1 000 0001 000 0001 0001 00010010010100.10.10.010.010.0010.0010.000 0010.000 0010.000 000 0010.000 000 0010.000 000 000 0010.000 000 000 0010.000 000 000 000 0010.000 000 000 000 0010.000 000 000 000 000 0010.000 000 000 000 000 0010.000 000 000 000 000 000 0010.000 000 000 000 000 000 0010.000 000 000 000 000 000 000 0010.000 000 000 000 000 000 000 001

yotta-yotta-zetta-zetta-exa-exa-peta-peta-tera-tera-giga-giga-mega-mega-kilo-kilo-hecto-hecto-deca-deca-deci-deci-centi-centi-milli-milli-micro-micro-nano-nano-pico-pico-femto-femto-atto- atto- zepto-zepto-yocto- yocto-

YYZZEEPPTTGGMMkkhhdadaddccmmµµnnppffa a zzy y

More Details: LengthMore Details: Length

metersmeters centimeters (for smaller units of length)centimeters (for smaller units of length) millimeters (very small units of length)millimeters (very small units of length) kilometers (for large units of length)kilometers (for large units of length)

These are the most commonly used. These are the most commonly used.

More details: MassMore details: Mass

gramgram kilogramkilogram

Measured using balances.Measured using balances.

More details: VolumeMore details: Volume litersliters milliliters (for small volumes)milliliters (for small volumes) microliter (for extremely small volumes)microliter (for extremely small volumes) Measured using a graduated cylinder, Measured using a graduated cylinder,

pipet or buret (more accurate), volumetric pipet or buret (more accurate), volumetric flask or even a syringe. flask or even a syringe.

Volume is a derived units…Volume is a derived units…Some metric units are Some metric units are

derived from S.I. units.derived from S.I. units.

Volume is L x W x H = cm x cm x cm = cm3

One cm3 is the same as one mL.

Also, dm x dm x dm = dm3

One dm3 is the same as one L.

Conversions Using Factor Label Conversions Using Factor Label MethodMethod

Multiplying any number by an equality Multiplying any number by an equality does NOT change the value.does NOT change the value.

An equality is two measurements that are An equality is two measurements that are equal in amount but have different units equal in amount but have different units and numbers.and numbers.

Examples:Examples:

one dozen bagels = 12 bagelsone dozen bagels = 12 bagels

10 mm = 1 cm10 mm = 1 cm

Steps of Factor Label MethodSteps of Factor Label Method

1.1. Write down the units you are given.Write down the units you are given.2.2. Write X and a Line.Write X and a Line.3.3. Write unit you want to cancel on the Write unit you want to cancel on the

bottom of the line, the unit you want to bottom of the line, the unit you want to keep on the top of the line. Find and plug keep on the top of the line. Find and plug in your equality. (hint: the larger unit will in your equality. (hint: the larger unit will always get a 1 next to it)always get a 1 next to it)

4.4. Cancel units and do the math. Cancel units and do the math. 5.5. Voila!Voila!

Let’s do one together…Let’s do one together…

0.600L = _______mL

0.600L X mLL

10001

= 600 mL

1 L = 1000mL

TRY THE REST ON YOUR OWN !!!!

Temperature ScalesTemperature Scales

There are three temperature scales in use in this country that you need to be familiar with.

Temperature:Temperature:

A measure of A measure of the average the average kinetic energy kinetic energy of the particles of the particles in a sample.in a sample.

FahrenheitFahrenheit 18th-century German 18th-century German

physicist Daniel Gabriel physicist Daniel Gabriel FahrenheitFahrenheit

Based his scale on an Based his scale on an ice-salt mixture and ice-salt mixture and normal body temperaturenormal body temperature

Freezing point for water = Freezing point for water = 3232°F°F

Boiling point for water = Boiling point for water = 212°F212°F

Celsius ScaleCelsius Scale

Swedish guy, Anders Swedish guy, Anders Celsius in 174Celsius in 174

Freezing point at 0°C.Freezing point at 0°C. Boiling for water at Boiling for water at

100°C. 100°C. Below 0 is negative.Below 0 is negative.

Kelvin ScaleKelvin Scale English guy, William English guy, William

KelvinKelvin Measures Measures molecular molecular

movementmovement Theoretical point of Theoretical point of

ABSOLUTE ZERO is ABSOLUTE ZERO is when all molecular when all molecular motion stops motion stops (no negative (no negative numbers)numbers)

Divisions (degrees) are Divisions (degrees) are the same as in Celsiusthe same as in Celsius

Absolute ZeroAbsolute Zero

Theoretical point where there is absolutely Theoretical point where there is absolutely no movement of molecules in matter and a no movement of molecules in matter and a measure of ZERO ENERGYmeasure of ZERO ENERGY

This is not something that we ever This is not something that we ever witness, scientists have only theorized this witness, scientists have only theorized this pointpoint

Conversion Factors Conversion Factors

You need to know these conversion You need to know these conversion factors! factors!

K = °C + 273K = °C + 273

°C = K – 273°C = K – 273

On Table T

NOT on Table T

Practice Conversion ProblemsPractice Conversion Problems

Room temperature is approximately 23°C. What Room temperature is approximately 23°C. What is this temperature in Kelvin?is this temperature in Kelvin?

Ethanol has a boiling point of 351 K. That won’t Ethanol has a boiling point of 351 K. That won’t help us if we have a thermometer reading help us if we have a thermometer reading degrees Celsius, so convert it.degrees Celsius, so convert it.

Work on the conversion Work on the conversion problems in your packet…problems in your packet…

Uncertainty in MeasurementUncertainty in Measurement

Uncertainty in MeasurementUncertainty in Measurement

No measurement can be perfect.No measurement can be perfect. Scientists need to account for some Scientists need to account for some

degree of uncertainty in measurements.degree of uncertainty in measurements. Refer to terms Refer to terms accuracyaccuracy and and precisionprecision. . An ideal measuring device is accurate and An ideal measuring device is accurate and

precise and does not have a great deal of precise and does not have a great deal of uncertainty.uncertainty.

AccuracyAccuracy

Accuracy is when you are close to the actual value of what you are trying to measure (For example you throw three darts and they are all close to the bull’s eye).

PrecisionPrecision

Precision is a measure of how close each measurement is to the others. For example if you are at the driving range and all of the golf balls head towards the pond, that is precision (but not accuracy).

Uncertainty in Measurement Uncertainty in Measurement

Uncertainty occurs in every measurement Uncertainty occurs in every measurement made and must be accounted for.made and must be accounted for.

In chemistry, we use different tools, each of which has certain limitations.

We use the ± to indicate uncertainty in measurement.

Uncertainty EquationUncertainty Equation

YOU MUST MEMORIZE THIS YOU MUST MEMORIZE THIS EQUATION AS YOU WILL PERFORM IT EQUATION AS YOU WILL PERFORM IT ALMOST DAILY!ALMOST DAILY!

ΔF = (δF / δX1) ΔX1 + (δF / δX2) ΔX2 + …(δF / δXn) ΔXn

Just Kidding!Just Kidding!

However, there is a system we use in However, there is a system we use in chemistry that helps to minimize chemistry that helps to minimize uncertainty by only including those values uncertainty by only including those values that have certainty and one that is that have certainty and one that is uncertain.uncertain.

We call them SIGNIFICANT FIGURES!

Using Significant FiguresUsing Significant Figures

Why are significant figures important?Why are significant figures important? Have you ever multiplied two numbers Have you ever multiplied two numbers

and come up with a really LONG decimal?and come up with a really LONG decimal? Well, those numbers are INSIGNIFICANT Well, those numbers are INSIGNIFICANT

with respect to scientific calculations.with respect to scientific calculations.

And now for a short story…

Counting Sig FigsCounting Sig FigsThe Atlantic-Pacific RuleThe Atlantic-Pacific Rule

If the decimal is Absent (A), start If the decimal is Absent (A), start counting on the Atlantic (right) counting on the Atlantic (right) side. Go to the first NON-zero side. Go to the first NON-zero number and count everything number and count everything after that. after that.

If the decimal is Present (P), start If the decimal is Present (P), start counting on the Pacific (left) side. counting on the Pacific (left) side. Go to the first NON-zero number Go to the first NON-zero number and count everything after that. and count everything after that.

Quick Self-AssessmentQuick Self-Assessment

How many sig figs are in each of these numbers:How many sig figs are in each of these numbers:

98,000 m98,000 m0.123 L0.123 L0.00073 L0.00073 L8765 cm8765 cm40,506 m 40,506 m 20.00 mL20.00 mL

More PracticeMore Practice

Round each number to the number of sig figs Round each number to the number of sig figs shown in parentheses. shown in parentheses.

314.721 m (4)314.721 m (4)

0.001775 m (2)0.001775 m (2)

8792 m (2)8792 m (2)

Sig Figs in CalculationsSig Figs in Calculations

When adding or subtracting measurements, When adding or subtracting measurements, report to the LEAST number of DECIMAL report to the LEAST number of DECIMAL PLACES.PLACES.

For example:

12.52 + 349.0 + 8.24 = 369.76

You will report this with one decimal place as 369.8.

Sig Figs in CalculationsSig Figs in Calculations

When multiplying or dividing measurements, When multiplying or dividing measurements, you want to report the answer with the same you want to report the answer with the same number of sig figs as the measurement with number of sig figs as the measurement with the least number of sig figs.the least number of sig figs.

For example:

7.55 m x 0.34 m = 2.567 square meters

You will report this with 2 sig figs as 2.6 square meters because 0.34 m contains 2 sig figs.

Percent Error in ExperimentationPercent Error in Experimentation When trying to determine how accurate When trying to determine how accurate

your experimental value (“what you got in your experimental value (“what you got in the lab”) is compared with the theoretical the lab”) is compared with the theoretical (“what it is supposed to be”), we use a (“what it is supposed to be”), we use a simple formula.simple formula.

experimental – theoretical experimental – theoretical x 100% x 100%

theoreticaltheoretical

Theoretical VS Experimental

Example of Percent ErrorExample of Percent Error

When you calculate the density of When you calculate the density of chemical X experimentally you get 1.13 chemical X experimentally you get 1.13 g/mL. The actual density according to the g/mL. The actual density according to the literature is 1.16 g.mL. What is your literature is 1.16 g.mL. What is your percent error?percent error?

% %

DensityDensity

Density is a derived unit which is found by Density is a derived unit which is found by dividing a substances mass by its volume.dividing a substances mass by its volume.

Density EquationDensity Equation

D=M/VD=M/V

Common Units = g/mL or g/cmCommon Units = g/mL or g/cm33

Density Practice ProblemsDensity Practice Problems

1.1. A student measures the mass of a piece A student measures the mass of a piece of metal to be 4.0g and it has a volume of metal to be 4.0g and it has a volume of 1.5mL what is the density of this of 1.5mL what is the density of this metal?metal?

2.2. The Density of COThe Density of CO22 gas is 1.8 grams per gas is 1.8 grams per

liter. What is the mass of 0.2L of COliter. What is the mass of 0.2L of CO22

gas?gas?