PowerPoint The First

In which you will find information on: •the metric (SI) system of measurement

• uncertainty in measurements•how to count sig figs

Units of MeasurementUnits of Measurement

In every measurement there is aIn every measurement there is a

NumberNumber followed by a followed by a

UnitUnit from a measuring device from a measuring device

Numbers without a unit are Numbers without a unit are naked numbers naked numbers

(NN)!(NN)!

Some Tools for MeasurementSome Tools for Measurement

Which tool(s) Which tool(s) would you use to would you use to measure:measure:A. temperatureA. temperatureB. volumeB. volumeC. timeC. timeD. weightD. weight

Standards of MeasurementStandards of Measurement

When we measure, we use a measuring tool When we measure, we use a measuring tool to compare some dimension of an object to a to compare some dimension of an object to a standard.standard. For example, at one time the For example, at one time the

standard for length was the king’s standard for length was the king’s foot. What are some problems with foot. What are some problems with this standard?this standard?

What do we use in science?

• The metric system – based on units of 10

• Specifically, we use the SI system which has specific standards for 7 basic units

SI measurementSI measurement• Le Système international d'unités • The only countries that have not

officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly

• Metrication is a process that does not happen all at once, but is rather a process that happens over time.

• Among countries with non-metric usage, the U.S. is the only country significantly holding out. The U.S. officially adopted SI in 1866.

Information from U.S. Metric Association

UNITS OF MEASUREMENTUNITS OF MEASUREMENT

Use Use SI unitsSI units — based on the metric — based on the metric systemsystem

Length Length

MassMass

VolumeVolume

TimeTime

TemperatureTemperature

Meter, mMeter, m

Kilogram, kgKilogram, kg

Seconds, sSeconds, s

Celsius degrees, ˚CCelsius degrees, ˚Ckelvins, Kkelvins, K

Liter, LLiter, L

Didn’t I say there were SEVEN base Didn’t I say there were SEVEN base units?units?

Find the new ones!

What’s the most important What’s the most important measurement to chemists?measurement to chemists?

• The mole!• A mole is a measure of the # of particles in a

substance.• Analogy – 1 dozen eggs: 12 eggs as

1 mole atoms : 6.022 x 1023 atoms

Metric PrefixesMetric Prefixes• Used for convenience –Used for convenience – wouldn’t want to describe the mass of a penny in kilograms! wouldn’t want to describe the mass of a penny in kilograms!

• Kilo-Kilo- means 1000 of that unit means 1000 of that unit

– 1 kilometer (km) = 1000 meters (m)1 kilometer (km) = 1000 meters (m)

• Centi-Centi- means 1/100 of that unit means 1/100 of that unit

– 1 meter (m) = 100 centimeters (cm)1 meter (m) = 100 centimeters (cm)

– 1 dollar = 100 cents1 dollar = 100 cents

• Milli-Milli- means 1/1000 of that unit means 1/1000 of that unit

– 1 Liter (L) = 1000 milliliters (mL)1 Liter (L) = 1000 milliliters (mL)

Metric PrefixesMetric Prefixes

Metric PrefixesMetric Prefixes

Units of LengthUnits of Length• ? kilometer (km) = 500 meters (m)? kilometer (km) = 500 meters (m)

• 2.5 meter (m) = ? centimeters (cm)2.5 meter (m) = ? centimeters (cm)

• 1 centimeter (cm) = ? millimeter (mm)1 centimeter (cm) = ? millimeter (mm)

• 1 nanometer (nm) = 1.0 x 101 nanometer (nm) = 1.0 x 10-9-9 meter meter

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 nm0.094 nm

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 nm0.094 nm

Volume = length x length x lengthVolume = length x length x length

Chemistry In ActionChemistry In Action

On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat.

1 lb = 1 N

1 lb = 4.45 N

“This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

Uncertainty in MeasurementUncertainty in Measurement

• When making measurements, one must always estimate an extra decimal place (if it is a non-digital display)

• This extra place is uncertain

How many decimal places can you read on each of these?

Significant FiguresSignificant Figures

The numbers reported in a measurement are The numbers reported in a measurement are limitedlimited by the measuring tool by the measuring tool

Significant figures in a measurement include Significant figures in a measurement include the known digits plus one the known digits plus one estimatedestimated (uncertain) digit(uncertain) digit

Significant Figures and CalculationsSignificant Figures and Calculations

• Measurements in the lab must be made accurately!

• But what does that mean?

Reading a MeterstickReading a Meterstick

. l. l22. . . . I . . . . I. . . . I . . . . I33 . . . .I . . . . I . . . .I . . . . I44. . cm. . cm

First digit (known)First digit (known) = 2 = 2 2.?? cm2.?? cm

Second digit (known)Second digit (known) = 0.7 = 0.7 2.7? cm2.7? cm

Third digit (estimated) between 0.05- 0.07Third digit (estimated) between 0.05- 0.07

Length reportedLength reported == 2.75 cm 2.75 cm

oror 2.74 cm 2.74 cm

oror 2.76 cm2.76 cm

Known + Estimated DigitsKnown + Estimated Digits

In 2.76 cm…In 2.76 cm…

• Known digitsKnown digits 2 andand 7 are 100% certainare 100% certain

• The third digit 6 is estimated (uncertain)The third digit 6 is estimated (uncertain)

• In the reported length, all three digits (2.76 cm) In the reported length, all three digits (2.76 cm) are significant including the estimated oneare significant including the estimated one

Zero as a Measured NumberZero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm

What is the length of the line?What is the length of the line?First digit First digit 5.?? cm5.?? cmSecond digit Second digit 5.0? cm5.0? cmLast (estimated) digit is Last (estimated) digit is 5.05.00 cm0 cm

ALWAYSALWAYS estimate ONE place estimate ONE place pastpast the smallest mark! the smallest mark!

11.51

What happens when measurements What happens when measurements are used in calculations?are used in calculations?

• Measurements are only as good as the instruments used to make them!

• Imagine calculating the volume of a cube with three different rulers: 2.4 cm x 2.45 cm x 2.453 cm = 14.42364 cm3

• The answer has way too many digits! None of the rulers were able to measure all 5 decimal places!

• Instead, we use significant figures to show the accuracy of a measurement.

Counting Significant FiguresCounting Significant Figures

RULE 1. All non-zero digits in a measured number are RULE 1. All non-zero digits in a measured number are significant. Only a zero could indicate that rounding significant. Only a zero could indicate that rounding occurred.occurred.

Number of Significant Figures

38.15 cm38.15 cm 445.6 ft5.6 ft 2265.6 lb65.6 lb122.55 m122.55 m

333355

Leading ZerosLeading Zeros

RULE 2. Leading zeros in decimal numbers are RULE 2. Leading zeros in decimal numbers are NOTNOT

significant.significant.

Number of Significant Figures

0.008 mm0.008 mm 11

0.0156 oz0.0156 oz 33

0.0042 lb0.0042 lb

0.000262 mL 0.000262 mL ____

22

33

Sandwiched ZerosSandwiched Zeros

RULE 3. Zeros between nonzero numbers are RULE 3. Zeros between nonzero numbers are significant. (They can not be rounded unless they significant. (They can not be rounded unless they are on an end of a number.)are on an end of a number.)

Number of Significant Figures

50.8 mm50.8 mm 33

2001 min2001 min 44

0.702 lb0.702 lb

0.00405 m0.00405 m ____

33

33

Trailing ZerosTrailing Zeros

RULE 4. Trailing zeros in numbers without decimals are RULE 4. Trailing zeros in numbers without decimals are

NOT significant. They are only serving as place NOT significant. They are only serving as place

holders. holders. Number of Significant Figures

25,000 in. 25,000 in. 22

200. yr200. yr 33

48,600 gal48,600 gal

25,005,000 g 25,005,000 g

33

55

HOMEWORK EXERCISES

• These questions are due the next time our class meets.

1) For each of the following pieces of glassware, provide a sample measurement and discuss the number of significant figures and uncertainty.

CONTINUED…

HOMEWORK CONT’D

2) Which of the following are exact numbers?a. The elevation of Breckenridge, CO is 9600 ft.b. There are 12 eggs in a dozen.

3) How many sig figs are in each of the following?a. 12 b. 1098 c. 2.001 x 103

d. 0.00001014) Round each number to 3 sig figs.

a. 312.54 b. 0.00031254 c. 31, 254, 000