Chapter 3“Scientific

Measurement”

Olympic High SchoolChemistry - Mr Daniel

Credits: Stephen L. Cotton

Charles Page High School

Section 3.1Measurements and Their Uncertainty

OBJECTIVES:Convert measurements to scientific

notation.

Section 3.1Measurements and Their Uncertainty

OBJECTIVES:Distinguish among accuracy, precision,

and error of a measurement.

Section 3.1Measurements and Their Uncertainty

OBJECTIVES:Determine the number of significant figures

in a measurement and in a calculated answer.

Measurements Qualitative measurements are descriptive

words, such as “heavy” or “warm” Quantitative measurements involve

numbers (quantities), and depend on:

1) The reliability of the measuring instrument

2) the care with which it is read – this is determined by YOU!

Accuracy, Precision, and Error

It is necessary to make good, reliable measurements in the lab

Accuracy – how close a measurement is to the true value

Precision – how close multiple measurements are to each other (reproducibility)

Precision and Accuracy

Neither accurate

nor precise

Precise, but not

accurate

Precise AND

accurate

Accuracy, Precision, and Error

Error = accepted value – experimental value

Can be positive or negative

Accepted value = the correct value based on reliable references

Experimental value = the value measured in the lab

Accuracy, Precision, and Error

Percent error = the absolute value of the error divided by the accepted value, then multiplied by 100.

| error |

accepted valuex 100% error =

accepted (true) value

Chemistry

“Scientific Notation Review”

Olympic High School

Mr. Daniel

1. Scientific Notation

…Is also called Exponential Notation

Scientists often use very large or very small numbers 602 000 000 000 000 000 000 000

Called Avogadro’s Number 0.000 000 000 114 m

The radius of a bromine atom

1. Scientific NotationLarge numbers are very inconvenient, even difficult

Thus, very large or small numbers should be written in Scientific Notation

In Scientific Notation, the number is the product of two different components:

A coefficientExponent: A power of 10

1. Scientific Notation2300 is: 2.3 x 103

A coefficient is a number greater than or equal to one, and less than tenThe coefficient here is 2.3

The exponent is how many times the coefficient is multiplied by ten…The product of 2.3 x 10 x 10 x 10 equals 2300 (2.3 x 103)

1. Scientific NotationThe value of the exponent changes to indicate the number of places the decimal has moved left or right.12 000 000 =0.00356 =85 130 =0.000 05 =0.0342 =

1.2 x 107

8.513 x 104

5 x 10-5

3.42 x 10-2

3.56 x 10-3

1. Scientific NotationMultiplication and DivisionUse of a calculator is permitteduse it correctly

No calculator? Multiply the coefficients, and add the exponents:

(3 x 104) x (2 x 102) =

(3.5 x 106) x (4.0 x 1012) =6 x 106

1.4 x 1019

1. Scientific NotationMultiplication and Division• In division, divide the coefficients, and

subtract the exponent in the denominator from the numerator

3.0 x 105= 5 x 102

6.0 x 102

1. Scientific Notation•Addition and Subtraction

•Before numbers can be added or subtracted, the exponents must be the same

•Calculators will take care of this

•Doing it manually, you will have to make the exponents the same - it does not matter which one you change.

1. Scientific Notation

•Addition and Subtraction

(6.6 x 10-8) + (4.0 x 10-9) =

(3.42 x 10-5) – (2.5 x 10-6) =

7.0 x 10-8

3.2 x 10-5

(Note that these answers have been expressed in standard form)

Why Is there Uncertainty?Measurements are performed with instruments, and no instrument can read to an infinite number of decimal places

•Which of the balances shown has the greatest uncertainty in measurement?

Significant Figures!!

Significant Figures in Measurements

Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated.

Measurements must be reported to the correct number of significant figures.

Figure 3.5 Significant Figures - Page 67

Which measurement is the best?

What is the measured value?

What is the measured value?

What is the measured value?

Rules for Counting Significant Figures

Non-zerosNon-zeros alwaysalways count as count as significant figuressignificant figures::

34563456 kmkm hashas

44 significant figuressignificant figures

Rules for Counting Significant Figures

ZerosZerosCaptive zerosCaptive zeros alwaysalways count as count as

significant figures:significant figures:

16.07 cm16.07 cm hashas

44 significant figures significant figures

Rules for Counting Significant Figures

ZerosZerosLeading zerosLeading zeros nevernever count as count as

significant figures:significant figures:

0.0486 mL0.0486 mL has has

33 significant figures significant figures

Rules for Counting Significant Figures

ZerosZerosTrailing zerosTrailing zeros are significant only if the are significant only if the number contains a number contains a written decimal pointwritten decimal point::

9.300 g9.300 g has has9300 g 9300 g has has 9300. g9300. g has has

4 significant figures4 significant figures

4 significant figures4 significant figures2 significant figures2 significant figures

Rules for Counting Significant Figures

Two special situations have an Two special situations have an unlimitedunlimited number of significant figures:number of significant figures:

1.1. Counted itemsCounted itemsa)a) 23 people, or 425 thumbtacks23 people, or 425 thumbtacks

2.2. Exactly defined quantitiesExactly defined quantitiesb)b) 60 minutes = 1 hour60 minutes = 1 hour

Sig Fig Practice #1How many significant figures in the following?

1.0070 m 5 sig figs

17.10 kg 4 sig figs

100,890 L 5 sig figs

3.20 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 g 2 sig figs5 dogs unlimited

These come from measurements

This is a counted value

Significant Figures in Calculations

A calculated answer is only as accurate as the least accurate measurement from which it is calculated.

Just like a chain which is only as strong as the weakest link…

…sometimes, calculated values need to be rounded off.

Rounding Calculated Answers

A quick reminder about Rounding Determine how many significant figures are

needed Locate that final digit by counting from the left Is the next digit to the right less than 5?

No change to the final digit Is the next digit to the right 5 or greater?

Increase the final digit by 1

- Page 59

Round off each measurement to the number of significant figures shown in parentheses:

a) 314.721 meters (four)

b) 0.001775 meter (two)

c) 8792 meters (two)

314.7 meters

0.0018 meter

8800 meters

Rules for Significant Figures in Mathematical Operations

Multiplication and DivisionMultiplication and Division:: The number of The number of significant figures in an answer equals significant figures in an answer equals the number in the the number in the least accurateleast accurate measurement used in the calculation.measurement used in the calculation.

6.38 cm x 2.0 cm = 12.76 cm6.38 cm x 2.0 cm = 12.76 cm22 sigfig answer :sigfig answer :13 cm13 cm22 (2 sig figs) (2 sig figs)

Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm34.214409283 g/cm3 4.21 g/cm3

0.02 cm x 2.371 cm0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5871.786 lb·ft 5870 lb·ft

1.030 g x 2.87 mL 2.9561 g/mL 2.96 g/mL

Rules for Significant Figures in Mathematical Operations

Addition and SubtractionAddition and Subtraction: : The number The number of of decimal placesdecimal places in the answer equals in the answer equals the number of the number of decimal placesdecimal places in the in the least accurateleast accurate measurement. measurement.

6.8 cm +11.934 cm = 18.734 cm 6.8 cm +11.934 cm = 18.734 cm sigfig answer sigfig answer 18.7 cm (3 sig figs)18.7 cm (3 sig figs)

Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

*Note the zero that has been added.

Section 3.3The International System of Units

OBJECTIVES:List SI units of measurement and common

SI prefixes.Distinguish between the mass and weight

of an object.Convert between the Celsius and Kelvin

temperature scales.

International System of Units

Measurements depend upon units that serve as reference standards

The Metric system was first introduced by the French following the French Revolution

It was revised and renamed the International System of Units (SI), as of 1960.

The standards of measurement used in science are those of the SI.

International System of Units

SI has several advantages:

-Used world-wide

-Simple

-Based on powers of 10 There are eight base units which are

commonly used in chemistry: meter, cubic meter, kilogram, kelvin, second, joule, pascal and mole.

The Fundamental SI Units (Le Système International, SI)

(Liter)

(gram)

(ºCelsius)

(calorie)

Nature of Measurements

1 ) 1 ) numbernumber2 ) 2 ) unitunitExamples:Examples:

20 grams20 grams6.63 x 106.63 x 10-34-34 joules-seconds joules-seconds

Measurement - quantitative observation Measurement - quantitative observation consisting of consisting of 2 parts2 parts::

International System of Units

Derived units: These are not measured directly, but are calculated, showing the relationship between two other measurements: Speed = miles/hour (distance/time) Density = grams/mL (mass/volume)

Length In SI, the basic unit of length is the meter (m)

The meter is one ten millionth (0.000 000 1 ) the distance from the equator to the North Pole.

Or more accurately for the 21st century:

1 meter equals 1,650,763.73 wavelengths of light given off from an isotope of Krypton…

We make use of prefixes for units larger or smaller…

SI Prefixes Common to Chemistry

PrefixUnit

AbbreviationMeaning Exponent

Kilo- k thousand 103

Deci- d tenth 10-1

Centi- c hundredth 10-2

Milli- m thousandth 10-3

Micro- millionth 10-6

Nano- n billionth 10-9

Pico- P Trillionth 10-12

Learn These!!!

Converting Measurements in the SI

e.g. 1.2 mm= µm

1) Mark the value of prefixes of both units

1.2 mm= µm

2) Determine the difference in the number of place values of the two prefixes by subtracting. This is how many places the decimal is to be moved.

-3-(-6) =

10-3 10-6

+3

Converting Measurements in the SI(continued)

3) If the difference is a positive number, move the decimal place to the right to make the numerical value largerIf the difference is a negative number, move the decimal place to the left to make the numerical value smaller

The difference is positive (+3) therefore 1.2 becomes 1200

The final answer is 1200 µm

Volume The space occupied by any sample of matter. Calculated for a solid by multiplying the length x

width x height; thus derived from units of length.

SI unit = cubic meter (m3) Everyday unit = Liter (L), which is non-SI.

Note: 1000mL = 1 L

1mL = 1cm3

Devices for Measuring Liquid Volume

Graduated cylinders Pipets Burets Volumetric Flasks Syringes

The Volume Changes! Volumes of a solid, liquid, or gas will

generally increase with temperature

Therefore, measuring instruments are calibrated for a specific temperature, usually 20 oC, which is about room temperature

Units of Mass

Mass is a measure of the quantity of matter present Mass is constant, regardless of location

Weight is a force that measures the pull by gravity- it changes with location

Working with Mass The SI unit of mass is the kilogram (kg),

even though a more convenient everyday unit is the gram

It’s measuring instrument is the balance

Units of TemperatureTemperature is a measure of how hot or cold an object is based upon the kinetic energy (movement) of the atoms.

Heat is a form of energy which moves from objects at higher temperatures to objects at lower temperatures.

(Measured with a thermometer.)

Temperature Units

We use two units of temperature:Celsius – named after Anders CelsiusKelvin – named after Lord Kelvin

Units of Temperature

Celsius scale is defined by two readily determined temperatures:Freezing point of water = 0 oCBoiling point of water = 100 oC

Kelvin scale is based on the concept of Absolute Zero: the point at which there is no atom movement• absolute zero = 0 K (thus no negative values)

Temperature Continued…• Kelvin does not use the degree sign,

but is just represented by K

• The formulas to convert between Kelvin and Celsius:

• K = oC + 273• oC = K - 273

Units of Energy

Energy is the capacity to do work, or to produce heat.

Energy can also be measured, and two common units are:

1) Joule (J) = the SI unit of energy, named after James Prescott Joule

2) calorie (cal) = the heat needed to raise 1 gram of water by 1 oC

Units of Energy

Conversions between joules and calories can be carried out by using the following relationship:

1 cal = 4.184 J

Density Which is heavier- a kilogram of lead or a

kilogram of feathers? Many people will answer lead, but the

weight is exactly the same They are normally thinking about equal

volumes of the two The relationship here between mass and

volume is called density

Section 3.4Density

OBJECTIVES:Calculate the density of a material

from experimental data.Describe how density varies with

temperature.

Density

The formula for density is:

• units used: g/mL (g/cm3) g/L for gases

• Density is a physical property which does not depend upon sample size (intensive property)

Density =Mass

Volume

- Page 90Note temperature and density units

Density and Temperature

What happens to the density as the temperature of an object increases? Mass remains the same Most substances increase in volume as

temperature increases Thus, density generally decreases as the

temperature increases

Density and Water Water is an important exception to the

previous statement. Over certain temperatures, the volume of

water increases as the temperature decreases (Do you want your water pipes to freeze in the winter?) Does ice float in liquid water? Why?

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