MeasuringWelcome to Chemistry 1:

A college preparatory course.

• Cellphone = NO!!!!

• Webpage

• Need to Buy– Scientific Calculator– Notebook or Binder

• Safety Contract – Signed

• Course Expectations– HW & Review (HW Bonus Points)– Make up missed work

• Notes

• Tests

– Getting Extra Help– Shoes in Locker– Letters of recommendation– “Are you a student, or just a kid who comes to

school?”

1. Three specific things you must do to be successful in this course.

2. Three things you must never do (academically) in this course.

Measuring

Hypothesis – testable, educated guess

Theory - repeatedly confirmed hypothesis that has predictive power.

Law – Theory with NO known exceptions

Scientific Method

Measuring

Hypothesis

Theory

Law

Measuring

Science changes!!!!!

MeasuringSpotting Bad Science

1.Based on Anecdotal EvidenceAnecdotal - From stories, not studies (no math)

2.Small Sample Size

3.Not published in Journals – not reviewed or tested

4.Broad ClaimsExample:  The Water Cure

Measuring

• Estimated place – every measurement must have ONE estimated place.

• One place past the smallest marking

Measuring

MeasuringMeasuring

MeasuringMeasuring

MeasuringMeasuring

MeasuringMeasuring

MeasuringMeasuring

Measuring

1. Label x and y axis including units

2. Mark Axis using a convenient scale

3. Title your graph “The Dependence of Y on X”

4. Mark dots with a small circle

5. Draw “Best Fit” line or curve

Graphing

Measuring

• Best Fit Line

a. Used ONLY for linear relationships.

b. Fits y = mx + b

m = slope

b = y-intercept

c. If graph is almost perfect line, same # dots above and below

X = independent variable (you can control)

Y = dependent variable (can’t control)

Graphing

Measuring

Measuring

Measuring

• Best Fit Curve

a. Used if points are clearly not linear.

b. Can be fit to higher order eqns:

y = mx2 + b

Graphing

Measuring

Measuring

Rectangle A = L X W

Triangle A = ½ B X H

Circle A = r2

Irregular Shape?

Graphing

Measuring

Measuring

• Use centimeters

• TWO decimal places, last one is the estimated place

• Write down the letter of your shape

• See me for the actual value

Graphing Lab

Measuring

1. What do chemists study/do?

2. What professions/college majors require a chemistry course?

3. Where is chemistry important in business/industry?

4. What household products are “chemicals”?

5. Where in history was chemistry important?

MeasuringScientific Notation

1. Descartes:1637 - “I think, therefore I am”

2. Powers of 10

100 = 1

101 = 10

102 = 10 X 10 = 100

103 = 10 X 10 X 10 =1000

MeasuringScientific Notation

200,000,000,000 stars (Andromeda):

2 X 100,000,000,000

2 X 1011 stars

MeasuringScientific Notation

3. A Helium atom masses

0.000,000,000,000,000,000,000,006,645g

6.645 X 10-24 g

Measuring

340

378,400

0.00234

0.000 000 000 0918

5.6 X 105

6.12 X 10-3

2.6 X 10-7

4 x 102

Scientific Notation

Measuring

43575,4000.0007230.000 000 0014 6.5 X 10-5

2.16 X 103

6.2 X 107

8 x 10-2

Scientific Notation

Measuring

There are ~900 students at Dallas

9 X 102 =90 X 101 =0.9 X 103 =

Scientific Notation

Measuring

Write 4500 in scientific notation with the following exponents:

X 103

X 102

X 105

X 104

Scientific Notation

Measuring

Write 4500 in scientific notation with the following exponents:

4.5 X 103

45 X 102

0.045 X 105

0.45 X 104

Scientific Notation

Measuring

Examples:

(2.0 x 102) + (3.0 x 103) = 3.2 X 103

(6.0 X 103) ÷ (3.0 x 10-5)=2.0X108

(2.0 x 107) - (6.3 x 105) = 1.9X107

Scientific Notation

Measuring

(4.0 x 105) x (3.0 x 10-1)=

(6.0 x 108) ÷ (3.0 x 105)=

(8.4x 1012) ÷ (8.4 x 109)=

NOTE: 103 = 1 X 103

Scientific Notation

Measuring

(4.0 x 105) x (3.0 x 10-1)=1.2 X105

(6.0 x 108) ÷ (3.0 x 105)= 2 X 103

(8.4x 1012) ÷ (8.4 x 109)= 1 X 103

NOTE: 103 = 1 X 103

Scientific Notation

MeasuringAccuracy and Precision

• Accuracy – how close the average of a set of measurements is to the accepted value (AAA)

• Precision – How close a set of measured values are to one another (reproducibility)

• Always compare to a textbook value

Measuring

XX XX

XXX

X

X X

X

X

X

X

X

X

Measuring

Percent Error – Measure of accuracy

% Error = Experimental – Accepted X 100Accepted

NOTE: “Experimental” =average of all trials

Percent Error

Measuring

A student measures the density of a sample of copper at 8.75 g/mL. The accepted value is 8.96 g/mL. Calculate the percent error.

MeasuringError Analysis: Range

Range - Measure of precision

Range = highest trial – lowest trial

Measuring

Example 1

A student measures the density of a sample of lead and does four trials (11.3, 10.5, 11.9, 10.8 g/cm3). Calculate the range and comment on precision.

MeasuringAccuracy and Precision

Students did trials to measure the density of a metal. The accepted density is 7.2 g/cm3. Were they accurate or precise?

Set 1 7.21 7.25 7.18

Set 2 6.40 7.90 7.30

Set 3 6.45 6.52 6.48

Measuring

1. Def - All of the measured values plus one estimated place

2. Examples

6 cm 6.0 cm 6.01 cm

0.005 mm 0.0050 mm 0.00500 mm

1340 kg 1340. kg 1340.0 kg

Significant Figures

Measuring

Numbers with a DecimalHow many sig figs? Also, write in sci.

notation:3.44 cm60.001 cm430.0 cm0.0032 cm0.00320 cm

Measuring

1. Often poor measurements

2. Examples: “Not left”

18,500 kg 120 ft

Numbers without a Decimal

Measuring

How many sig figs? Also, write in scientific notation:

10,500 cm

240 cm

120,000 cm

4 cm

45 cm

Numbers without a Decimal

How many significant figures are in the following? Also, write the numbers in proper scientific notation.

1508 cm20.003 lb300 ft300.0 ft0.00705 m0.007050 m12501250.1250.0

Measuring

Round the following to three sig figs:

32.45

32.449

0.0067530

0.003904

11,980

Significant Figures

Round to four significant figures:

598,937

0.00053254

5.37286

0.39201

0.39205

How many significant figures?

0.00200 0.0020 100.7450 144.0 2008.40 X 1010 9.000 X 10-5

Round to three significant figures:

54.649999 1.456 X 10-4

300.847 8.605 X 107

200.490.000567320.0045282

Measuring

1. Math answers are only as good as the worst measurement.

2. Example:

Determining the area of a room:

6.9 m by 10.478 m

3. Round AFTER you do the math.

Significant Figures and Math

Measuring

Addition/Subtraction Rule - Keep the least number of decimal places.

Examples:

7.56 0.0327

0.375 – 0.00068

+ 14.2203

Significant Figures and Math

Measuring

Multiplication/Division Rule – Answer contains the least # of TOTAL significant figures

Examples23.4 X 32.25 =

Significant Figures and Math

Measuring

11.688 4.0 =

7 cm X 7 cm =

4.68 X 1016 9.1 X 10-5 =

Significant Figures and Math

1. Multiple Operations – Round when you change between add/sub and mult/div

2. Examples

(0.56 X 11.73) + 22.34 =

(6.5688) + 22.34 =

(6.6) + 22.34 = 28.9

(12.45 – 11.643) X 2.68 =

(0.807) X 2.68 =

0.81 X 2.68 = 2.1708 = 2.2

160 X 3.445 =

19.64 + 0.466 =

4.856 X 10102.0 X 102=

(16.44 2.33) + 22.3 =

(7.055793991) + 22.3

7.06 + 22.3 = 29.36 = 29.4

Measuring

160 X 3.445 = 550

19.64 + 0.466 = 20.11

4.856 X 10102.0 X 102 = 2.4 X 108

(16.44 2.33) + 22.3 = 29.4

Significant Figures and Math

Measuring

19.64 - 14.465 =

320 X 0.04550 =

3.1415 X 1011 X 8.47 X 10-7=

(12.7 X 10.43) + 23.8 =

0.00320 X 10-4 (write in proper sci. not.)

Warm-Up

Measuring

1. Also called “exact” numbers

2. Have an infinite number of significant figures

3. Counting numbers and values in definitions.

4. Examples:

23 students Diameter = 2r

1 km=1000m

5. NEVER use exact numbers for determining sf.

Absolute Numbers

Measuring

Absolute numbers or measured values?

Y= X3 37 apples

1 m = 100 cm 50 people

2.85 grams 400 people

1 cm = 10 mm

Measuring

If we divide 1.66 lbs of candy among 3 people, how much candy will each person get? (Ans: 0.553 lbs/person)

What is the diameter of a circle whose radius is 3.835 m?

(Ans: 7.670 m)

Absolute Numbers

Measuring

1. What is the diameter of a circle with a radius of 2.567 cm?

2. If we buy 1.84 pounds of coffee and divide it among three people, how much coffee will each person get?

3. How many centimeters is 7.565 meters?

4. How would you divide 12.35 kg of candy among eight children?

Measuring

Qualitative – data with no number

Quantitative – data with a number

Metric

Measuring

1. SI System – Le System International d’Unites

2. 1670 – Gabriel Mouton (French Vicar)

3. 1795 – Adopted by France

Metric

Measuring

Measuring

4. Base ten scale

1000 m = 1 km (kilo) 100 m = 1 hm (hecto) 10 m = 1 dam (deca)

1 m = 1 m 1 m = 10 dm (deci) 1 m = 100 cm(centi) 1 m = 1000 mm (milli)

Metric

Measuring

Measuring

Fundamental Units (MKS)Length meterMass kilogramsTime second

Derived UnitsVolume liter (dm3)Energy Joules (kg m2/s2)

Metric

Measuring

Factor Label method55 cm = ? m0.055 L = ? mL0.00456 km = ? cm550 cm2 = ? m2

25 miles/hr = ? m/s

Metric

a. 129 hrs Days

b. 0.468 mkm

c. 825 cm2 in2

d. 0.00230 L mL

e. 0.468 m mm

f. 1245 cm km

g. 55.0 mi/hr km/hr

h. 55.0 mi/hr m/min

129 hrs Days 5.38 days

0.468 mkm 0.000468

825 cm2 in2 128 in2

0.00230 L mL 2.30 mL

0.468 m mm 468 mm

1245 cm km 0.01245 km

55 mi/hr km/hr 88.5 km/hr

55 mi/hr m/min 1470 m/min

Measuring

1 km = 103 m1 hm = 102 m1 dam = 101 m1 m = 1 m1 dm = 10-1

1 cm = 10-2

1 mm = 10-3 m

Metric

Convert using powers of ten

50 cm = ? m

5 mm = ? m

65 km = ? m

23.3 mL = ? L

0.0047 mm = ? m

0.876 L = ? mL

1. Round to 3 sf: 0.0050460

2. Calculate using sf (10.345 – 8.23) X 54

3. 65.0 m/s =? miles/hr

4. 584 cm3 = ? in3

5. 234 cm = ? Feet

6. 3.00 X 108 m/s = miles/s

7. 45.0 L/s = gallons/min

(1.00 inch = 2.54 cm)

(1.609 km = 1.00 mile)

(1.000 gallon = 3.785 L)

1. 0.00505

2. 110

3. 145 miles/hr

4. 35.6 in3

5. 7.68 Feet

6. 3.00 X 108 m/s = 186 000 miles/s

7. 713 gallons/min

(1.00 inch = 2.54 cm)

(1.609 km = 1.00 mile)

(1.000 gallon = 3.785 L)

Temperature

Measuring

Absolute Zero

• All atomic and molecular motion stops

• Coldest possible temperature?

• Liquid Nitrogen = 77 K (-196 oC)

• Dry Ice = 216 K (-56.6 oC)

Temperature

Measuring

Measuring

Measuring

Planck Temperature = 1.417 x 1032 K

(temperature of the Big Bang)

Measuring

Conversion FormulasF = 1.8 (oC) + 32K = C + 273C = K – 273

Temperature

Measuring

Ex: 24 oC = oF48oF = oC177 K = oC

Temperature

Measuring

102 oF oC-10.0 oC oF25 oC K177 K oF310 oF K

Temperature

Measuring

102 oF 39oC-10.0 oC 14 oF25 oC 298 K177 K -141 oF310 oF 427 K

Temperature

Measuring

25 oC oF50 oF K310 K oC10 K oC-15 oC K

Temperature

Measuring

25 oC 77 oF50 oF 283 K(10 oC)310 K 37 oC10 K -263 oC-15 oC 258 K

Temperature

Measuring

Page 39

15 a) 0.77 b) 13.0 c) 32 d) 326

21 a) 5000 m b) 1400 ft2 c) 1.21 in2

d) 100 yd

23 a) 7 b) 12.7 c) 1.49

Measuring

Page 40 (40-42, 53, 55, 57, 60)

42 a) 6.8 X 106 6800 6.8

b) 786 0.786 7.68X10-4

c) 4452 4.452 4.452 X 10-3

53) 384,300km 55) 0.376 qt

57) 114 g 60) 109 yd (10.9 yd)

Measuring

23 a) 7

b) 12.7

c) 1.49

42 a) 6.8 X 106 6800 6.8

b) 786 0.786 7.68X10-4

c) 4452 4.452 4.452 X 10-3

Measuring

Measuring

Sig Figs Review WS1 a=4 b=3c=2 d=4e=3 f=6 g=2h=32a) 20. e) 6.27 b) 960 f) 417 c) 55.2 g) 2.7 d) 5800

Measuring

B2) 3ft=1yd,

10 dm = 1 m

1.00 gal = 3.78 L

2.20 lb = 1.00 kg

B3) 15.5 miles

B4) $2.16, 9.72 oz

B5) 366 cm

B6) $8.94

Measuring

29

4.23 X 105

4.338 X 102

2.0 X 10-3

8.8 X 102

8 X 10-5

8.2 X 107

7.5 X 1013

1.06 X 10-6

Measuring

39

1.58 X 10-10

2.29 X 1010

3.69 X 10-6

3.15 X 1012

Measuring3. Most precise = 26.202, most acc = 26.8

5. a) 2 b) 3 c) 3 d) 3

e) 4 f) 5 g) 2 h) 2

9. a) 120 b) 28 c) 38,000 d) 0.47

e) 56 f) 0.040 g) 1,600,000 h) 320

11.a) 0.667 b) 0.400 c) 0.625 d) 3.25

15. a) 0.77 b) 13.0 c) 32 d) 326

24. a) 120 cm2 b) 394 ft2 c) 2 cm d) 2.3 in

25. a) 5000 m b) 1400 ft2 d) 1.21 in2 d) 100 yd

27. a) 7 b) 12.7 c) 1.49

Measuring28.a) 1.57 X102 b)1.57X10-1 c) 3.00 X10-2

d) 4.0 X107 e) 3.49 X10-2 f) 3.2 X 104

g) 3.2 X1010 h) 7.71 X10-4 i) 2.34 X 103

29. a) 4.23 X105 b) 4.338 X102 c) 2.0 X10-3

d) 8.8 X102 e) 8 X10-5 f) 8.20 X107

g) 7.5 X1013 h) 1.06 X10-6

32. a) 0.000475 b) 6550 c) 0.00788

d) 489,000 e) 4.75 f) 3.4

33.a) 0.064 b) 8340 c) 220 d) 0.00342

Measuring34. a) 4.89 X10-4 b) 4.56 X10-5 c) 7.8X 103

d)5.71 X10-2 e) 4.975 X108 f) 3.0 X 10-2

35. a) 7.8X10-10 b) 7.2X10-1 c) 3.450X1019

d) 2.8X1010 e) 6.9X10-14 f) 2.3X103

39. a) 1.58 X10-10 b) 2.29 X1010

c) 3.69 X10-6 d) 3.15 X1012

43.a) 4.56 X1016 b) 5 X10-9

c) 1.7 X10-14 d) 1.26 X1012

MeasuringWrite in Sci Notation Write the expanded number

4 X 102 0.000 05

5 X 10-3 2 000 000 000

6 X 104 0.144

3.4 X 10-3 150 000 000 000

7.5 X 1012 0.000 000 244

6.457 X 10-2 300 000

5.6 X 10-5 0.00045

4.5 X 102 45 000

Calculate in Sci Nota)3 X 105

b)2 X 103

c)4.3 X 103

d)6 X 107

e)2.5 X 10-6

f)1.664 X10-3

g)3.0 X 104

h) 8 X 10-4

i)1.6 X 101

j)1.16 X 107

How many signif figures?

Calculate using SFa)15.2 m) 91.0b)20. n) 4.1c)6 o) 0.0075d)19.4e)15f)3.1g)1.23h)4.27i)0.0102j)50k)49l)49.0

Multiple operations & SFa)20.b)960c)55.2d)5800

Abs. # Calculationsa)303 cm3

b)756.3 cmc)1.544 kg/childd)0.65 me)5.134 cmf)25.6 mlg)553 cm2

h)0.613 kg/person

MeasuringMetric Conversions

a) 250 cm

b) 57 cm

c) 0.42 m

d) 420 mm

e) 46.7 m

f) 72,000 ml

g) 2.3 cm

h) 8.955 g

i) 8.68 X 10-6 kg

j) 0.654 g

k) 6,000 mL

l) 1.2 dm

m) 5.678292 km y) 0.0012 mL

n) 0.088 L z) 2.3 mL

o) 19 mL

p) 3.9 m

q) 0.0234 L

r) 45 mL

s) 1.2 cm

t) 0.072 g

u) 0.0862 km

v) 2470 cm

w)340 mL

x) 4.8 cm

MeasuringTemperature Conversions

a) 298 K

b) 25 oC

c) 226 K

d) -196 oC

e) 62.2 oC

f) 309 K

g) 263 K

h) 59 oC

i) 127 oC

j) 176 K

k) 5273 K

l) -271 oC

m) 371 K

n) 18.3 oC

o) 239 K

p) 33 oC

q) 256 K

62.

71. Longer, 10.9 yards

102.a) 310 K b) 408 K c) -68oC

d) -231 oF e) 311 K d) 248 K

lbs g kg

1.72 780. 0.780

2.17 985 0.985

16.0 7260 7.26

MeasuringComplete the following chart (1.00 inch = 2.54 cm)

How many Dekameters is 456 cm?

Convert 60oF to Celsius and Kelvin

inches cm m

4.75

824

0.537

MeasuringComplete the following chart (1.00 inch = 2.54 cm)

How many Dekameters is 456 cm? 0.456 dam

Convert 60.0oF to Celsius and Kelvin 15.6oC, 289K

inches cm m

4.75 12.1 0.121

324 824 8.24

21.1 53.7 0.537

MeasuringA 43 G 400 (4 X 102)

B 5.5 H 35

C 306.9 I 30

D 2.21 J 25

E 7.7 K 40

F 10.88 L 165