Unit 1: Measurement and Conversions

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Scientific Notation Review

Often used to express very large or very small numbers. Also used to maintain correct number of significant figures.

Form: (# from 1 to 9.999) x 10 exponent 800 = 8 x 10 x 10 = 8 x 10 2 2531 = 2.531 x 10 x 10 x 10 = 2.531 x 10 3 0.0014

= 1.4 / 10 / 10 / 10 = 1.4 x 10 -3

Scientific Notation Practice

Change the given number to standard form.

000000187000000 1.87 x 10 –5 = 0.0000187

3.7 x 10 8 = 370,000,000 7.88 x 10 1 = 78.8

2.164 x 10 –2 = 0.02164

(-) exponent = number < 1 (+) exponent = number > 1

Scientific Notation Practice

Change the given number into scientific notation.

12,340 = 1.234 x 10 0.369 = 3.69 x 10 0.008 = 8 x 10 –3 –1 4 1,000,000,000 = 1 x 10 9

Significant Figures

about… A student is combining separate water samples, all of differing volumes, into one large bucket. Samples A, B and C are 25.5 mL, 16.37 mL and 51 mL, respectively. Once combined, what is the total volume of all the samples? 92.87 mL NO!

Because the samples were each measured with a different level of precision, we must factor that into our calculations by identifying what are called significant figures.

Measurement and Accuracy

• The last digit of any measured number is assumed to be an estimate (uncertain) • The second to last digit is assumed to be known with certainty (based on a line) A (25.5 mL) B (16.37 mL) C (51 mL) 26 60 50 25 16.4

16.3

Identifying Significant Figures

Counting SF’s in a number

Non-zero numbers:

ALWAYS count as SF .

Relative to the non-zero numbers

Zeroes

Left: NEVER count as SF (0.000345) Middle: ALWAYS count as SF (5001) Right: sometimes… w/ decimal point: count as SF (25.10) w/o decimal point: DO NOT count as SF (8200)

Exact Numbers

: IGNORE SF Counts (28 students in this class) Constants (1 mol = 6.022 x 10 23 ) Conversions (1 in = 2.54 cm)

How many Sig Figs?

Measurement Number of SF 1.

25 g

2

2.

0.030 kg 3.

1.240560 x 10 6 mg

7

4.

6 x 10 4 sec

2 1

5.

6.

7.

246.31 g 20.06 cm 1.050 m

5 4 4

Measurement Number of SF 8.

0.12 kg 9.

1240560. cm 10. 6000000 kg 11. 6.00 x 10 6 kg 12. 409 cm 13. 29.200 dm 14. 0.02500 g

2 7 1 3 3 5 4

Sig Figs with Calculations

Note: For any calculations, always perform the entire calculation without rounding, and then round the final answer.

Addition/Subtraction • Round the answer to the LEAST number of decimal places found (least precise)

11.31 + 33.264 + 4.1 = 48.674

→ rounded to 48.7

Multiplication/Division • Round the answer to the smallest number of SF found

5.282 x 3.42 = 18.06444 → rounded to 18.1 (3.42 only has 3 SF)

Back to the original question…

A student is combining separate water samples, all of differing volumes, into one large bucket. Samples A, B and C are 25.5 mL, 16.37 mL and 51 mL, respectively. Once combined, what is the total volume of all the samples? 25.5 mL + 16.37 mL + 51 mL = 92.87 mL 93 mL Could I write that as 93.0? NO!

More practice with SF

If you made measurements of three samples of water (128.7 mL, 18 mL and 23.45 mL), and then poured all of the water together in one, unmarked container, what total volume of water should you report? Support your answer.

128.7 mL + 18 mL + 23.45 mL = 170.15 mL

170. mL or 1.70 x 10 2 mL

Practice with Sig Fig Calculations

1.

A 2.

A 7 x 10 -6  8.74

x 10 -4 = -6.118 x 10 -9 report -6 x 10 -9 (1 SF) 4.356

x 10 6  1.2

x 10 -3 = 3.63 x 10 9 report 3.6 x 10 9 (2 SF) 3.

A 5.7

 9.863

= 15.563

report 15.6 (tenths place) 4.

A 20  3.73

= 16.27

report 20 (tens place) 5.

A 6.022

x 10 -5  5.1

x 10 -6 3 .

2 = 1.7225 x 10 -5 report 1.7 x 10 -5 (2 SF)

Complete calculation, and then follow order of operations to determine how many SF would be carried for each step

The Metric System

SI System

• The International System of Units – abbreviated

SI

from the French Le

S

ystème

i

nternational d'unités

• Based on the metric system (with small variations) • Based on powers of ten – Uses prefixes to differentiate between powers • Used in nearly country except U.S. (Liberia and Myanmar are some others…)

The International System of Units

Quantity Volume Length Mass Time Amount of substance Thermodynamic temperature Electric current Luminous intensity Name liter meter kilogram second mole Kelvin amperes candela Symbol L m kg s mol K amps cd Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3 rd Edition, 1990, page 16

Area and Volume:

Derived

Units

Area = length x width = 5.0 m x 3.0 m = 15 ( m x m ) = 15 m 2 Volume = length x width x height = 5.0 m x 3.0 m x 4.0

m = 60. ( m x m x m ) = 60. m 3

Derived

Units Commonly Used in Chemistry

Quantity Area Volume Force Pressure Energy Power Voltage Frequency Electric charge Name Symbol square meter m 2 cubic meter m 3 newton N pascal joule Pa J watt volt hertz coulomb W V Hz C

Prefixes in the SI System

The Commonly Used Prefixes in the SI System Prefix Symbol Meaning Power of 10 for Scientific Notation _______________________________________________________________________

mega-

M 1,000,000 10 6

kilo deci centi milli micro nano-

k d c m m n 1,000 0.1

0.01

0.001

0.000001

0.000000001

10 3 10 -1 10 -2 10 -3 10 -6 10 -9 Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118

Quantities of Mass

Giga Mega-

Kilo-

base

milli-

micro nano pico femto atomo-

10 24 g 10 21 g 10 18 g 10 15 g 10 12 g 10 9 g 10 6 g 10 3 g 10 0 g 10 -3 g 10 -6 g 10 -9 g 10 -12 g 10 -15 g 10 -18 g 10 -21 g 10 -24 g

Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25 Earth’s atmosphere to 2500 km Ocean liner Indian elephant Average human 1.0 liter of water Grain of table salt Typical protein Uranium atom Water molecule

Reporting Measurements

• Must use significant figures • Report what is known with certainty Using dashes • Add ONE digit of uncertainty beyond that Using estimation The implication is that for any measurement, the last digit is an estimate and uncertain, and the next to last is known with certainty Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

Practice Measuring

0 cm 1 2 3 4 5 4.5 cm 0 cm 1 2 3 4 5 4.54 cm Timberlake, Chemistry 7 th Edition, page 7 0 cm 1 2 3 4 5 3.0 cm

Measurement/Sig Fig Practice

Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water and explain your answers (the numbers given are as precise as possible): a. 128.7 mL b. 18 mL c. 23.45 mL Mark every 1 mL Mark every 10 mL Mark every 0.1 mL

Implied Range of Uncertainty

30 40 50 60 Implied range of uncertainty in a measurement reported as 50. cm ( ±5) 3 4 5 6 Implied range of uncertainty in a measurement reported as 5.0 cm ( ±0.5) 3 4 5 6 Implied range of uncertainty in a measurement reported as 5.00 cm ( ±0.05) Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

Reading a Meniscus

10 mL proper line of sight 10 8 reading correct 6 graduated cylinder

20 ? mL 10

Conversion Factors

equality: How many cm are in 1.32 meters?

1 m = 100 cm (or 0.01 m = 1 cm) applicable conversion factors: or 100 cm 1.32 m 100 cm 1 m 1 m = 132 cm We use the idea of

unit cancellation

to decide upon which one of the two conversion factors we choose.

Both ways are equally good!

1. How many kilometers is 15,000 decimeters?

OR… 15,000 dm 1 m 10 dm 1 km 1,000 m 15,000 dm ( ) ( 10 dm 1,000 m ) = 1.5 km

2. How many seconds is 4.38 days?

4.38 d ( ) 1 d ( 1 h ) ( ) 1 min = 378,432 s If we are accounting for significant figures, we would change this to… 3.78 x 10 5 s

3. Convert 41.2 cm 2 to m 2 41.2 cm 2 ( 100 cm ) = 0.412 m 2 = 0.412 cm

.

m WRONG!

Recall that… 41.2 cm 2 = 41.2 cm

.

cm 41.2 cm

.

cm ( 100 cm ) ( 100 cm ) = 0.00412 m 2 41.2 cm 2 ( (100) 2 cm 2 ) = 0.00412 m 2

4. Convert 41.2 cm 2 to mm 2 Recall that… 1 cm = 10 mm 2 41.2 cm 2 ( _____ 2 1 cm 2 ) = 4,120 mm 2

5. Convert to 480 cm 3 cm

.

cm

.

cm 480 cm to m 3 ( 100 cm ) ( 100 cm ) ( 100 cm ) = or 480 cm 3 ( 100 cm

3

) = or 480 cm 3 ( 3 _________ 1000000 cm 3 ) = 0.00048 m 3 4.8 x 10 -4 m 3

Comparison of English and SI Units

1 inch 2.54 cm Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119 1 inch = 2.54 cm

SI-US Conversion Factors

Conversion Factors Equality Length

2.54 cm = 1 in.

1 m = 39.4 in.

Volume

2.54 cm 1 in 39.4 in 1 m and and 1 in 2.54 cm 1 m 39.4 in.

946 mL = 1 qt 1 L = 1.06 qt 946 mL 1 qt 1.06 qt 1 L and and 1 qt 946 mL 1 L 1.06 qt

Mass

453.6 g = 1 lb 1 kg = 2.20 lb 453.6 g 1 lb 2.20 lb 1 kg and and 1 lb 453.6 g 1 kg 2.20 lb

Practical Conversions

Teachers get a lot of grief from normal workers because they only work 36 weeks a year. How many extra hours, per day, would a teacher have to put in to match the typical worker, assuming a teacher works 8 hrs per day for those 36 weeks?

What assumptions must we make?

Density Review  how tightly packed the particles are mass Density = volume  D  m V D m V Typical units: g/cm 3 for solids g/mL for fluids liquids and gases Glass: liquid or solid?

Monty Python’s take on analytical science and density with regard to witches…

Density Review

1. A sample of lead (Pb) has mass 22.7 g and volume 2.0 cm 3 . Find sample’s density.

m D  m V  22.7

g 2.0

cm 3 = 11 g cm 3 D V 2. Another sample of lead occupies 16.2 cm 3 of space. Find sample’s mass. V m = D V  11 g cm 3  16.2

cm 3  = 180 g

More Density Review Problems…

3. A 119.5 g solid cylinder has radius 1.8 cm and height 1.5 cm. Find sample’s density. 4. A 153 g rectangular solid has edge lengths 8.2 cm, 5.1 cm, and 4.7 cm. Will this object sink in water?

m 3. A 119.5 g solid cylinder has radius 1.8 cm and height 1.5 cm. Find sample’s density. 1.8 cm 1.5 cm D m V 2 SF V = p r 2 h = p (1.8 cm) 2 (1.5 cm) D  m V  119.5

15.2681

g cm 3 = 15.2681

cm 3 = 7.8

g cm 3

8.2 cm 4. A 153 g rectangular solid has edge lengths 8.2 cm, 5.1 cm, and 4.7 cm. Will this object sink in water? 5.1 cm 4.7 cm (Find object’s density and compare it to water’s density.) 2 SF V = l w h m = 8.2 cm (5.1 cm)(4.7 cm) D V = 196.554

cm 3 D  m V  153 196.554

g cm 3 = 0.78

g cm 3 < 1 No; it floats.

Will bowling balls sink or float in H

2

O?

If D BB > 1, it will sink If D BB < 1, it will float 21.6 cm in diameter V sphere = 4/3 p r 3 V = 4/3 p (10.8 cm) 3 V = 5,276.7 cm 3 m m = D V D V m = (1.0 g/cm 3 )(5276.7 cm 3 ) m = 5276.7 g Since the mass of a BB varies, let’s figure out at what mass it will sink v. float …or 11.6 lbs

Metric (SI) units Measurements Prefixes Uncertainty Length Mass Volume Density Timberlake, Chemistry 7 th Edition, page 40 Conversion factors Significant figures Problem solving with conversion factors