Scientific Method and Measurements

Lecture 2

1/9-1/11

Dr. Jenkins

Lecture 2

CHEMISTRY

The Study ofMatter and its Properties,the Changes thatMatter Undergoes, and the EnergyAssociated withthose Changes

Prologue

Chemistry

Oceanography Atmospheric Sciences

Economics

PhysicsMedicine

Governments

Geology

Anthropology

Biology

Astronomy

Politics

People

Chemistry as the Central Science

The Scientific Method

An orderly and systematic approach to gathering information in order to answer questions about the world

Scientific MethodScientific Method

1. Observation – To observe any phenomenon in nature

2. Question – To formulate questions about the phenomenon observed

3. Hypothesis – To propose an educated guess as to the answer for the question

4. Experiment – To test the hypothesis

Scientific Method continued…Scientific Method continued…

5. Data/results – To gather and interpret information obtained from the experiment

6. Conclusion -To make a decision as to whether your results support or do not support your hypothesis.

7. Theory - A well-tested explanation for experimental data based on a set of hypothesis

Scientific Measurements

Significant Figures (2.2 - 2.5) Rules for Rounding (2.3)

Scientific Notation (2.6, 2.7)Uncertainty in measurements (2.1)

Metric System/Units (3.1 – 3.6)Dimensional Analysis

Significant Figures (1.3)Significant Figures (1.3)

Rules for Significant Figures:

1. Leading zeros are never significant. a) 0.0025 2 sig. fig.

2. Imbedded zeros a) 1.008 4 sig. fig.

3. Trailing zerosa) 100 1 sig. fig.b) 1.00 × 102 3 sig. fig.c) 1.10 3 sig. fig

4. All nonzero integers are significant

5. Exact numbers are numbers known with certainty and have an infinite number of significant figures.

a)numbers that arise when you count

3 cars, 5 books, 2.54 cm in 1 in

b)or when you define a unit

1 inch = 2.54 cm100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm1 kg = 1000 g, 1 LB = 16 oz1000 mL = 1 L; 1 gal = 4 qts.1 minute = 60 seconds

How many significant figures are in each of the following measurements?

24 mL 2 significant figures

3001 g 4 significant figures

1 in = 2.54 cm infinite

5 books infinite

560 kg 2 significant figures

1.8

PracticePractice

1. 3427 

2. 172

3. 3100.0

4. 0.0000455

5. 0.010560

6. 3.03 x 10-1

7. 0.00565 

8. 100,000

44

33

55

33

55

33

33

11

How many significant Figures Answers:

Significant Figures

1.8

Addition or Subtraction

The answer cannot have more digits to the right of the decimalpoint than any of the original numbers.

89.3321.1+

90.432 round off to 90.4

one significant figure after decimal point

3.70-2.91330.7867

two significant figures after decimal point

round off to 0.79

Significant Figures

1.8

Multiplication or Division

The number of significant figures in the result is set by the original number that has the smallest number of significant figures

4.51 x 3.6666 = 16.536366 = 16.5

3 sig figs round to3 sig figs

6.8 ÷ 112.04 = 0.0606926

2 sig figs round to2 sig figs

= 0.061

Significant Figures

1.8

Exact Numbers

Numbers from definitions or numbers of objects are consideredto have an infinite number of significant figures

The average of three measured lengths; 6.64, 6.68 and 6.70?

6.64 + 6.68 + 6.703

= 6.67333 = 6.67

Because 3 is an exact number

= 7

Rules for Rounding

In a series of calculations, carry the extra digits through to the final result, then round

If the digit to be removed… is less than 5, the preceding digit stays the

same (1.331.3) is equal to or greater than 5, the preceding

digit is increased by 1 (1.361.4)

Round-off the following to two decimal places:Round-off the following to two decimal places:

23.044 39 g23.044 39 g ==

65.891 mL65.891 mL = =

45.106 ms45.106 ms = =

30.1149 kg30.1149 kg = =

23.04 g23.04 g

45.11 ms45.11 ms

65.89 mL65.89 mL

30.11 kg30.11 kg

a) 4.53   + 2.2 =

b) 1113.0 – 14 =

c) 6.18  + 4.72 =  

d) 0.0045 -  1.03 =      

PracticPracticeePracticPracticee

6.73 rounded to 6.76.7

10991099

10.9010.90

-1.03-1.03

a) 4.53   x 2.2 =

b) 0.453 x 14,255 =

c) 6.18  ÷ 4 =  

d) 0.0045 ÷   1.03 =      

PracticPracticeePracticPracticee10. or 1.0 x 1010. or 1.0 x 1011

64606460

22

0.00440.0044

Scientific Notation (1.2)Scientific Notation (1.2)

Interactive Online Practice with Scientific Notation

http://www.aaamath.com/dec71i-dec2sci.html

1. Technique Used to Express Very Large or Very Small Numbers

2. Based on Powers of 10

PracticePractice

1. 3427 

2. 172

3. 3100.0 x 102

4. 0.0000455

5. 0.982 x 10-3

6. 3.03 x 10-1

7. 0.00565 

8. 1000 x 10-3

3.427 x 103.427 x 1033

1.72 x 101.72 x 1022

3.1000 x 103.1000 x 1055

4.55 x 104.55 x 10-5-5

9.82 x 109.82 x 10-4-4

3.03 x 103.03 x 10-1-1

5.65  x 105.65  x 10-3-3

1.000 x 101.000 x 100 0 = 1.000= 1.000

Convert to Scientific Notation: Answers:

More Practice at 1. http://lectureonline.cl.msu.edu/~mmp/

applist/sigfig/sig.htm2. http://www.edhelper.com/exponents1

4.htm

3. http://www.edhelper.com/exponents1

5.htm

When making measurements, scientists use a concept and a practice known as significant

figures (Sig. Figs.)

Uncertainty in Uncertainty in Measurements (1.2)Measurements (1.2)

Uncertainty in Uncertainty in Measurements (1.2)Measurements (1.2)

Uncertainty in Uncertainty in MeasurementMeasurement

A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Significant figures include an estimated digit that is always one place beyond the calibrations on any measuring instrument.

4.2 +/- 0.14.2 +/- 0.1

4.23 +/- 0.014.23 +/- 0.01

4.240 +/- 0.0054.240 +/- 0.005

Uncertainty in Measurement Uncertainty in Measurement

GraduateGraduated d

cylindercylinder

Read at the meniscusmeniscus-bottom of curve

due to adhesive forces where water molecules are more attracted to the glass surface than to each other (cohesive)

DO NOT READ DO NOT READ TOP OF TOP OF CURVE!!CURVE!!

Uncertainty in Measurement Uncertainty in Measurement

BeakerBeaker

1. Smallest division is 10 mL

2. The Last digit is uncertain—the uncertainty here is ± 1 mL

What is the Volume?

46 or 48 mL (estimate)

47 47 ± 1 mL (2 significant figures)± 1 mL (2 significant figures)(7 is uncertain)

Uncertainty in Measurement Uncertainty in Measurement

1. Smallest division is 1 mL

2. The Last digit is uncertain—the uncertainty here is ± 0.1 mL

What is the Volume?

36.5 36.5 ± 0.1 mL ± 0.1 mL (3 significant figures; 5(3 significant figures; 5 is uncertain)GraduateGraduate

d d cylindercylinder

Uncertainty in Measurement Uncertainty in Measurement

1. Smallest division is 0.1 mL

2. The Last digit is uncertain—the uncertainty here is ± 0.01 mL

What is the Volume?

20.38 20.38 ± 0.01 mL ± 0.01 mL (4 significant figures; 8(4 significant figures; 8 is uncertain)

BuretBuret

Uncertainty in LengthUncertainty in Length

9.2 ± 0.1

9.14 ± 0.01

Estimating the last digit in a measurement

This measurement should be read as 4.95 ± 0.05 cm. This measurement has 3 significant figures.

Reading a metric ruler correctly:

1.65 ± 0.05 cm

Reading a metric ruler correctly:

6.70 ± 0.05 cm

A. 6.3 ± 0.1 cm A. 6.3 ± 0.1 cm B. 6.35 ± 0.05 or 6.33 ± 0.02B. 6.35 ± 0.05 or 6.33 ± 0.02

AA

BB

Triple beam balance

Dial-a-gram balance

electronic/ digital balanceanalytical balance

Mass measurementsMass measurements

MassMassMassMass

measured in grams (g)1000 milligrams (mg) = 1 g1 kilogram (kg) = 1000 g

As with all measuring instruments, Sig. Fig. Rules must be followed when reading a balance.

How would you read this measurement?

105.05 +/- 0.02 gDivisions are 0.1 so uncertainty is +/- 0.01 (can be more)

Units of Measurement Units of Measurement (1.1)(1.1)Units of Measurement Units of Measurement (1.1)(1.1)

Measurements Consists of a number & a scale (units) 2 systems of measurement

1. English system (US)

2. Metric System (international)SI Units (Systeme International) A system of standard units of measurement

SI Units (Systeme International) A system of standard units of measurement

Systems of Units - Standards of Systems of Units - Standards of MeasurementMeasurement

1. The English System

12 in/ft 3 ft/yd 12 in/ft 3 ft/yd 5280 ft/mi5280 ft/mi

2. The Metric System - A decimal system

Common SI PrefixesCommon SI Prefixes

Name(symbol)

Meaning Scientific notation Numerical Value

giga (G) billion 1.0 x 109 1,000,000,000

mega (M) million 1.0 x 106 1,000,000

Kilo (k) thousand 1.0 x 103 1,000

Know the metric prefixes

Common SI PrefixesCommon SI Prefixes

Name(symbol)

MeaningScientific notation

Numerical Value

deci (d) One-tenth 1.0 x 10-1 0.1

centi (c) One-hundreth 1.0 x 10-2 1.01

milli (m) One-thousandth 1.0 x 10-3 0.001

Know the metric prefixes

micro (μ) One-millionth 1.0 x 10-6 0.000 001

nano (n) One-billionth 1.0 x 10-9 0.000 000 001

Measurement Metric unit SI unit

Length Meter (m) Meter (m)

Mass Gram (g)Gram (g) Kilogram (kg)

Time Second (s) Second (s)

Temperature Celsius (°C) Kelvin (K)

Volume Liter (L)Liter (L) Cubic meter (m3)

Units of MeasurementUnits of Measurement

LengthLength1000 millimeters (mm) = 1 meter

100 centimeters (cm) = 1 meter

10 decimeters (dm) = 1 meter

1decameter (dam) = 10 meters

1 hectometers (hm) = 100 meters

1kilometer (km) = 1000 meters (m)For example: Kilo means 1000 so the prefix kilo makes a unit 1000 times bigger and milli would make a unit 1000 times smaller

MassMass1kilogram (kg) = 1000 grams (g)1000 milligrams (mg) = 1 gram (g)

VolumeVolume1000 milliliters = l liter 1000 liters = 1 cubic meter (m3)1 ml = 1 cm3

Dimensional Analysis Dimensional Analysis and The Metric System and The Metric System (1.5) (1.5)

converting a given number from one unit to another

helps you solve mathematical problems when doing calculations involving measured

quantities, the units must be added, subtracted, divided, or multiplied just like the numbers

Conversion FactorsConversion Factors - - A fraction whoseA fraction whose numerator and denominator contain the samenumerator and denominator contain the samequantity expressed in quantity expressed in differentdifferent units units..

1 mile = 5280 ft1 mile = 5280 ft 1 mile5280 ft

= 5280 ft1 mile

= 11

1 cm = 0.01 m1 cm = 0.01 m1 cm 0.01 m

= 0.01 m1 cm

= 11

1 in = 2.54 cm1 in = 2.54 cm2.54 cm 1 in

= 1 in 2.54 cm

= 11

Dimensional AnalysisDimensional AnalysisDimensional AnalysisDimensional AnalysisHow many meters are in each of the following?How many meters are in each of the following?

21 km21 km 1023 mm1023 mm

21 km x 1000 m = 21 x 103 m =km

1023 mm x 1 m = 1000 mm

1.023 m

2.1 x 104 m

How many mL are in 64.0 fl oz?How many mL are in 64.0 fl oz?

1 qt = 32 fl oz1 qt = 32 fl oz 1 qt = 946 mL1 qt = 946 mL

64.0 fl oz x 1 qt x 946 mL = 1890 mL 32 fl oz 1 qt

How many mg are in 2.56 kg?How many mg are in 2.56 kg?

2.56 kg x 1000 g x 1000mg2.56 kg x 1000 g x 1000mg 1 kg 1 g1 kg 1 g = 2.56 x 10= 2.56 x 1066 mg mg

How many mL are in 3.456 L?How many mL are in 3.456 L?

(3.456 L)((3.456 L)(1000 mL1000 mL)) LL

= 3456 mL= 3456 mL

How many L are in 23.7 cmHow many L are in 23.7 cm33??

(23.7 cm(23.7 cm33)()( 1 mL 1 mL )()( 1 L_ _ 1 L_ _)) (1 cm(1 cm33)(1000 mL))(1000 mL)

= 0.0237 L= 0.0237 L

Temperature (1.1)

Celsius scale =CKelvin scale = KFahrenheit scale =F

Temperature Conversion Temperature Conversion

°C = (°F - 32) x 5/9

°F = (°C x 9/5) + 32

K = °C + 273.15 (K means Kelvin)

°C = K ─ 273.15

Convert 73.6Convert 73.6ooF to Celsius and Kelvin temperaturesF to Celsius and Kelvin temperatures..

ooC = (5/9)(73.6C = (5/9)(73.6ooF - 32) = (5/9)(41.6)F - 32) = (5/9)(41.6)

ooC = (5/9)(C = (5/9)(ooF - 32)F - 32) K = K = ooC + 273.15C + 273.15

= 23.1= 23.1ooCC

K = 23.1K = 23.1ooC + 273.15 = 296.3 KC + 273.15 = 296.3 K

32°F = 0°C = 273.15 K

Absolute zero - The temperature at which substances possess no thermal energy (theory), equal to -273.15°C

DensityDensity

VolumeMass

Density

Specific Gravity = Density of sample

Density of sample

Specific gravity is a ratio between the density of a substance and the density of water.

Homework due Next Wednesday at the beginning of Class

Homework due Next Wednesday at the beginning of Class

Do at least 25 of the question/problems from the “Question and Problem” sections of Chapter 1—You will turn this in for a homework grade. Choose from the odd numbers since the answers are given (check your answers) at the end of the chapter.

Make sure you review/understand the “Questions and Problems” located throughout Chapter 1.