types of observations and measurements

Types of Observations and Measurements

• We make QUALITATIVE observations of reactions — changes in color and physical state.

• We also make QUANTITATIVE MEASUREMENTS, which involve

numbers.

Stating a Measurement

• Measurements must include a quantity and a unit

4.356 g

Quantity Unit

Three targets with three arrows each to shoot.

Can you hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do they compare?

Can you define accuracy and precision?

•Accuracy is how close a

measurement is to a true value, within a 5% error

•Precision is how close several

measurements are to the same value; how reproducible data is

Accuracy and Precision

Which apply to the concept of Accuracy? Precision?

• Multiple measurements

–Precision

• Correct

–Accuracy

• Repeatable

–Precision

• Reproducible

–Precision

• Single Measurement

–Accuracy

• True Value

–Accuracy

Percent Error • The measure of inaccuracy of data is the

Percent Error

• % Error = actual - accepted

• accepted

• Accepted = Theoretical Value – The value you are expecting to get

– AKA: book value, accepted value

• Actual = Experimental Value – The value you get in an experiment

• Accuracy means < 5% error.

Percent Error

Example: Professor Bunsen conducts an experiment to calculate the density of a silver ring. He finds the density of the ring to be 9.8 g/mL. When he looks up the density of silver in his chemistry book, he finds that the density of silver is 10.5 g/mL. What is his percent error?

% Error = 9.8g/mL – 10.5g/mL X 100

10.5 g/mL

% Error = -6.67%

Scientific Notation

• Used for very large and very small numbers

• Examples: - 123

» 1.23 x 10 2

- 0.0456

» 4.56 x 10 -2

Scientific Notation

• A number between 1 and 10

• A power of 10

N x 10x

To change standard form to scientific notation…

1) Place the decimal point between the first two nonzero digits.

2) Raise 10 to the power which equals the number of places the decimal is moved

3) Leave POSITIVE exponent if the original number is greater than 1(you moved the decimal to the left), NEGATIVE if the number is less than 1 (if you moved it right).

Examples

• Given: 289,800,000

• Use: 2.898 (moved 8 places)

• Answer: 2.898 x 108

• Given: 0.000567

• Use: 5.67 (moved 4 places)

• Answer: 5.67 x 10-4

To change scientific notation to standard form…

• Simply move the decimal point to the right for positive exponent 10.

• Move the decimal point to the left for negative exponent 10.

(Use zeros to fill in places.)

Example

• Given: 5.093 x 106

• Answer: 5,093,000 (moved 6 places to the right)

• Given: 1.976 x 10-4

• Answer: 0.0001976 (moved 4 places to the left)

Learning Check

• Express these numbers in Scientific Notation:

1) 405789

4.05789x105

2) 0.003872

3.872x10-3

3) 3000000000

3x109

4) 2

2x100

5) 0.478260

4.78260x10-1

Significant Figures

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

Significant figures in a measurement include the known digits plus one estimated digit

Known + Estimated Digits

In 2.76 cm…

• Known digits 2 and 7 are 100% certain

• The third digit 6 is estimated (uncertain)

• In the reported length, all three digits (2.76

cm) are significant including the estimated

one

Sig. Figs. In Measurements

Use all the digits that are known plus

one last digit that is estimated

•

• 3.80 mm • Top ruler

• 1.5 cm

• Bottom Ruler

• 1.42


• Read bottom of meniscus

• 32.7 mL

• 8.45 mL


Counting Significant Figures

RULE 1. All non-zero digits in a measured number

are significant.

Number of Significant Figures

38.15 cm 4

5.6 ft 2

65.6 lb 3

122.55 m 5

Leading Zeros

RULE 2. Leading zeros in decimal numbers are

NOT significant.


0.008 mm 1

0.0156 oz 3

0.0042 lb 2

0.000262 mL 3

Sandwiched Zeros

RULE 3. Zeros between nonzero numbers are significant. Number of Significant Figures

50.8 mm 3

2001 min 4

0.702 lb 3

0. 405 m 3

Final Zeros

RULE 4. Final zeros in numbers without

decimals are NOT significant.


25,000 in. 2

200. yr 3

48,600 gal 3

25,005,000 g 5

2.500 4

Unlimited Significant Figures

RULE 5. There are unlimited significant figures

for counting numbers or defined constants:

Counting:

20 students in the class

Exact, Non-measured Quantities:

60 minutes = 1 hour

Sig Fig Questions

• How many sig figs are there in these numbers?

1) 3.24 3

2) 3,000,000 1

3) 4530 3

4) 4530. 4

5) 43.00 4

6) 23,050 4

7) 2.3050 5

8) 60 min = 1 h unlimited

Rounding with Sig Figs

• For rounding:

– Find the number that represents the last Sig Fig you need

– If it’s 5 round up, 4 keep same

• Round the following to 3 Sig Figs:

– 1) 5.000

– 2) 25.64

– 3) 7.296

– 4) 499.5699

Rounding with Sig Figs

• For rounding:

– Find the number that represents the last Sig Fig you need

– If it’s 5 round up, 4 keep same

• Round the following to 3 Sig Figs:

– 1) 5.000 5.00

– 2) 25.64 25.6

– 3) 7.296 7.30

– 4) 499.5699 500.

Significant Figures in Calculations

A calculated answer cannot be more precise than the measuring tool.

A calculated answer must match the least precise measurement.

Significant figures are needed for final answers from

1) adding or subtracting

2) multiplying or dividing

Adding and Subtracting Sig Figs

When adding and subtracting, use the LEAST NUMBER OF DECIMAL PLACES

25.2 one decimal place

+ 1.34 two decimal places

26.54

answer 26.5 one decimal place

Adding and Subtracting Sig Figs

In each calculation, round the answer to the correct number of significant figures.

A. 235.05 + 19.6 + 2.1 =

1) 256.75 2) 256.8 3) 257

B. 58.925 - 18.2 =

1) 40.725 2) 40.73 3) 40.7

Multiplying and Dividing Sig Figs

When multiplying and dividing, use the LEAST NUMBER OF SIG FIGS

Example:

1.13 x5.126 122 = 5.79 251 786

5.79 3 Sig Figs 7 Sig Figs

3 Sig Figs

Multiplying and Dividing Sig Figs

A. 2.19 X 4.2 =

1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 =

1) 61.58 2) 62 3) 60

C. 2.54 X 0.0028 =

0.0105 X 0.060

1) 11.3 2) 11 3) 0.041

Significant Figures

• Significant Figures Rules

–Only Round Once!

–Carry the results through then round final answer to correct sig figs

Dimensional Analysis

• Dimensional Analysis

–AKA Factor –Label method

–A method of converting one unit to another, using CONVERSION FACTORS


• Conversion Factors

–The ratios between 2 units

–Always equivalent to 1

–Ex: 12 in = 1 ft , so:

Always write out units!!!!

in 12

ft 1or

ft 1

in 12

• Conversion Factors

–Multiply by the one that:

»Has the unit to cancel on the bottom

»Has the unit you want on top


12

1x 2 like 1

mL

1x mL

have

want


• How many quarters are in 3 dollars?

3 dollars X 4 quarters =

1 dollar


• How many quarters are in 3 dollars?

3 dollars X 4 quarters = 12 quarters

1 dollar


• Your friend weighs 71.8 kg. Knowing there are 2.2 lbs in 1 kg, how many lbs does he weigh?

• 158 lbs


• You need to measure out 38.1 g of CH4. If 1 mole of CH4 has a mass of 16.05 grams, how many moles of CH4 do you measure?

• 2.37 moles


• If you run a 5.00 km race, how many feet did you travel? (1 mile = 1.6 km, 1 mile = 5280 ft)

• 16,500 ft


• A plane flies at 550. miles per hour. What is this speed in km/min? (1 mile = 1.6 km)

• 14.7 km/min

Measurement

SI System

Metric Prefixes

Conversion Factors

SI Units

• English system of units

– Used by US (lbs, in., oz., etc.)

• SI (AKA Metric System)

– Used by the rest of the world (incl. science)

– Why?

» It’s universal (used everywhere but US)

» Units are converted based on factors of 10

SI Units

SI Base Units

Quantity SI Base Unit Symbol

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of a

substance

mole mol

Luminous

Intensity

candela cd

Electric current ampere A

SI Derived Units

• Derived Units

–Result of combining SI units

–Examples: Area m2

Volume m3

Density kg/m3

Energy J (kg ·

m2/s2)

Molar Mass kg/mol

• Prefixes

– Identify the magnitude of the measurement

» Examples: kg, cm, mL

SI Units

Metric Prefixes G giga 1 000 000 000 109

M mega 1 000 000 106

k kilo 1 000 103

H hecto 100 102

da deka 10 101

Base unit Base unit 1 100

d deci 0.1 10-1

c centi 0.01 10-2

m milli 0.001 10-3

µ micro 0.000 001 10-6

n nano 0.000 000 001 10-9

p pico 0.000 000 000 001 10-12

SI Units

• SI unit conversions

–Compare unit to the base unit

»Ex: 1 cm = 10-2 m, therefore 102 cm = 1 m

»Ex: 1 km = 103 m, therefore 10-3 km = 1 m

–Use relationship to base to make conversion factor

»102 cm = 10-3 km

–Basically, change the sign of the magnitude!!!

SI Units Perform these SI conversions:

1)100 mm = ? cm

=10 cm

2)358 ds = ? µs

=35,800,000 µs

3)500. mL = ? hL

=0.00500 hL

4)0.0035 Mm = ? nm

=3.5 x 1012 nm

T G M K H da b d c m µ n p

SI Units

• Perform the following metric conversions:

• 35.7 mL to daL

• 8.12 nm to km

• 0.996 Gg to g

T G M K H da b d c m µ n p

Temperature Scales

• Fahrenheit

• Celsius

• Kelvin

Anders Celsius

1701-1744

Lord Kelvin

(William Thomson)

1824-1907

Calculations Using Temperature

K = °C + 273

°F = 9/5 °C + 32

°C = 5/9(°F - 32)

Learning Check

20) The normal temperature of a chickadee is 105.8°F. What is that temperature in °C?

1) 73.8 °C

2) 58.8 °C

3) 41.0 °C

Temperature Conversions

21) A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F?

DENSITY - an important

and useful physical property

Density mass (g)

volume (cm3)

Mercury

13.6 g/cm3 21.5 g/cm3

Aluminum

2.7 g/cm3

Platinum

22) Problem A piece of copper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cm3).

Density mass (g)

volume (cm3)

23) PROBLEM: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 mL of Hg?

First, note that 1 cm3 = 1 mL

Learning Check

24) The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass of 875 mL of octane?

Volume Displacement

A solid displaces a matching volume of water when the solid is placed in water.

33 mL

25 mL

Learning Check

25) An object was placed in a graduated cylinder. The water level rose from 50 mL to 55 mL. The mass of the object was 25 g. Determine the density.

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