Chapter 2 – Measurement and Calculations

transcript

Taken from Modern Chemistry written by Davis, Metcalfe, Williams

& Castka

Scientific Method

– Describe the purpose of the scientific method.– Distinguish between qualitative and quantitative

observations.– Describe the differences between:

– Hypotheses– theories – and models

Section 1 - Objectives

Section 2-1The Scientific method is a logical approach to

solving problems by observing and collecting data, creating a hypothesis, testing the same, and formulating theories that are supported by data.

1. Not sleeping at night , something, before I go to bed is impacting my sleep

2. List the foods I eat and activities I take part in3. Hypothesis that by eliminating something I will get a better nights sleep4. Test the same5. Come up with theory supported by data

Section 2-1 (continued)

Observing and Collecting DataObserving is using our senses to obtain

information (data).

The data fall into to categories:– Qualitative – descriptive (the ore has a red-brown

color)– Quantitative - numerical (the ore has a mass of

25.7 grams)

A system is a specific portion of matter in a given region of space that has been selected for study during an experiment or observation

A hypothesis is a testable statement.“if...then”

Formulating Hypothesis

•If I raise the temperature of a cup of water, then the amount of sugar that can be dissolved in it will be increased.

•If the size of the molecules is related to the rate of diffusion as they pass through a membrane, then smaller molecules will flow through at a higher rate.

Testing a hypothesis requires experimentation.

Testing Hypothesis

•If I raise the temperature of a cup of water, then the amount of sugar that can be dissolved in it will be increased. (The scientist will use 10 separate cups of water and increase the temperature in each by 5° C and then measure how much sugar will go into solution.)

•If the size of the molecules is related to the rate of diffusion as they pass through a membrane, then smaller molecules will flow through at a higher rate.•(The scientist will use 1 membrane and 5 different size molecules and then measure how the diffusion rate through the membrane.)

A model in science is often used as an explanation of how phenomenon occur and how data or events are related.

Theorizing

A theory is a broad generalization that explains a body of facts or phenomena.

Experimental Design – POGIL POGIL

Units of Measurement

Notes on section 2.2 only pages 33-38.

Section 2 - Homework

Units of Measurement

– Distinguish between: – A quantity– A unit– And a measurement standard.

– Identify SI units for:– Length– Mass– Time– Volume – Density

– Distinguish between mass and weight– Perform density calculations– Transform a statement of equality to a conversion

factor.

Section 2 - Objectives

Section 2-2Measurements represent quantities.A quantity is something that has a magnitude and a

size or amount.

My mass and height

Le Systeme International d’Unites or SI

Different 75 000 is what we in the U.S. would know as 75,000

Commas in other countries represent decimal points.

SI Measurements

Mass is a measure of the quantity of matter. SI Standard is the kilogram (kg).

SI Base Units - MassMass

~2.2 pounds

The gram (g) which is 1/1000th of a kilogram is more commonly used for smaller objects.

Mass should not be confused with weight.

Weight is a measure of the gravitational pull on matter

SI Base Units – MassMass (continued)

Mass is measured with a balance. Weight is measured with a

spring scale..

SI standard is the meter (m).

SI Base Units – LengthLength

To express longer distances the kilometer (km) is used, = 1000 meters

1 meter = 39.3701 inches

Combinations of SI base units form derived units.

Derived SI units

EXAMPLES

m2 = length x widthOthers are given there own name…

kg/m∙s2 This is a pascal (Pa) and it is used to measure pressure.

Volume is the amount of space occupied by an object.

Derived SI Units (continued) – VolumeVolume

The derived SI unit for volume would be a m3

Instead scientist often us a non-SI unit called the liter (L) which is equal to one cubic decimeter.

1 L = 1.05669 quarts

Density is the ratio of mass to volume, written as mass divided by volume..

Derived SI Units (continued) – DensityDensity

D = m/v

Earth based reference

The density of H2O @ 4 ° C = 1 g/cm3

We are going to practice by finding the

Derived SI Units– Density Density (continued)

A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to another.

General equation

Conversion Factors

We can deriver a conversion factor when we know the relationship between the factors we have and the units we what.

Conversion Factors - Deriving Conversion FactorsDeriving Conversion Factors

Practice

Conversion Factors - Deriving Conversion FactorsDeriving Conversion Factors

HW / Classwork (depends) – Section review bottom of page 42 questions 2-5 all

Conversion Factors – Metrics (step method)Metrics (step method)

The next slide will teach you about:

King henry died by drinking chocolate milk under no pressure

Decimal Moves to right

Decimal Moves to left

SmallerUnits

LargerUnits

Remember

The decimal moves the way you are

steppingDeci- (d)

10-1Centi- (c)

10-2Milli- (m)

Deka- (da)10

Hecto- (h)102

Kilo- (k)

____________

Liters

Meters

Micro (µ)

10-6nano- (n)

10-9pico (p)

Decimal Moves to right

Decimal Moves to left

SmallerUnits

LargerUnits

Remember

The decimal moves the way you are

steppingDeci- (d)

10-1Centi- (c)

10-2Milli- (m)

Deka- (da)10

Hecto- (h)102

Kilo- (k)

____________

Liters

Meters

Micro (µ)

10-6nano- (n)

10-9pico (p)

Step Practice HW

Using Scientific Measurements

– Distinguish between accuracy and precision.– Determine the number of significant figures in

measurements.– Perform mathematical operations involving

significant figures. – Convert measurements into scientific notation.– Distinguish between inversely and directly

proportional relationships

Section 3 - ObjectivesHW Notes on this section with

these objectives in mind

Section 2-3 Accuracy and Precision

Accuracy refers to the closeness of measurements to the correct or accepted value.

Precision refers to the closeness of a set of measurements made in the same way.

Accuracy and Precision (continued) – Percent ErrorPercent Error

Percent error = ----------------------------------------------------- x 100( VALUEACCEPTED – VALUEEXPERIMENTAL)

VALUEACCEPTED

% error is positive (+) when the VALUEACCEPTED is greater than VALUEEXPERIMENTAL

% error is negative (-) when the VALUEACCEPTED is less than VALUEEXPERIMENTAL

Accuracy and Precision (continued) – Percent ErrorPercent Error

Percent error = ----------------------------------------------------- x 100( VALUEACCEPTED – VALUEEXPERIMENTAL)

VALUEACCEPTED

EXAMPLE 1(time estimation)

EXAMPLE 2(penny density)

Section 2-3 (continued)Accuracy and Precision (continued) – Error in MeasurementError in Measurement

Some error or uncertainty always exists in any measurement.

ReasonsSkill of measurerconditions (temperature, air pressure,

humidity etc)Instruments themselves

Accuracy and Precision – Error in MeasurementError in Measurement

ONLY NEED TO COPY THE RED

Ways to Improve Accuracy in Measurement1. Make the measurement with an instrument that has the highest level of

precision. The smaller the unit, or fraction of a unit, on the measuring device, the more precisely the device can measure. The precision of a measuring instrument is determined by the smallest unit to which it can measure.

2. Know your tools! Apply correct techniques when using the measuring instrument and reading the value measured. Avoid the error called "parallax" -- always take readings by looking straight down (or ahead) at the measuring device. Looking at the measuring device from a left or right angle will give an incorrect value.

3. Repeat the same measure several times to get a good average value. 4. Measure under controlled conditions. If the object you are measuring could

change size depending upon climatic conditions (swell or shrink), be sure to measure it under the same conditions each time. This may apply to your measuring instruments as well.

(continued)

Using Scientific Measurements

– Determine the number of significant figures in measurements.

– Perform mathematical operations involving significant figures.

Section 2.3 (second) - Objectives

HW Notes on this section with

these objectives in mind

Pgs 46-50

Accuracy and Precision – POGIL POGIL

Up to Problem # 22

Section 2-3

Significant figures (‘Sig figsSig figs’) in a measurement consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated.

Section 2-3 Significant Figures – Determining the number of significant – Determining the number of significant

digitsdigits 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are

ALWAYS significant.

2) ALL zeroes between non-zero numbers are ALWAYS significant.

3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant.

4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant.

EXAMPLES

12 eggs

2001 Dalmations

172.00 Kg

10000. L

Section 2-3 Significant Figures – Determining the number of – Determining the number of

significant digits significant digits (continued)

Number # Significant Figures Rule(s)48,923 5 13.967 4 1

900.06 5 1,2,40.0004 (= 4 E-4) 1 1,4

8.1000 5 1,3501.040 6 1,2,3,4

3,000,000 (= 3 E+6) 1 110.0 (= 1.00 E+1) 3 1,3,4

Section 2-3 Significant Figures – Rounding – Rounding (continued)

Digit following Last digit Example

Round to 3 Sig Figs

greater than 5 Increased by 1 42.68 g 42.7 g

Less than 5 Stay the same 42.32 m 42.3 m

5, followed by nonzero Increased by 1 2.7851 cm 2.79 cm

5, not followed by nonzero

AND preceded by an odd digit

Increased by 1 4.635 kg 4.64 kg

5, not followed by nonzero

AND preceded by an even digit

Stay the same 78.65 mL 78.6 mL

Section 2-3 Significant Figures – Sig Figs & Rounding – Sig Figs & Rounding (continued)

PRACTICE # 1(only front side)

PRACTICE # 2(only front side)

Section 2-3 Significant Figures (continued) – Addition or subtraction with – Addition or subtraction with

Significant FiguresSignificant Figures When adding or subtracting decimals, the

answer must have the same number of digits to the right of the decimal point as there are in the measurement having the FEWEST digits to the right of the decimal point.

Example

25.1 g 2.03 g______27.13 g as seen on a calculator, BUT using the above rule

you would round the answer to 27.1 g

Section 2-3 Significant Figures (continued) – Multiplication & Division – Multiplication & Division

with Significant Figureswith Significant Figures

For multiplication or division the answer can have no more significant figures than are in the measurement with the fewest number of

significant digits.

Density = mass ÷ volume

Example

3.05 g_______

8.47 mL= 0.360094451 g/mL CALCULATOR

ANSWER

But using the rule we go to 3 sig figs giving us 0.360 g/mL

WARNING: do not let your friend the calculator screw up your answer!

Section 2-3 Significant Figures (continued) – Conversion Factors & – Conversion Factors &

Significant DigitsSignificant Digits When using conversion factors there is no uncertainty – the conversion are exact.

Example

_______ 100 cm

m x 4.608 m = 460.8 cm

Practice BreakPractice break (the other sides & more)

HW in advance: Notes to the end of the chapter for Friday

PRACTICE # 1(only back side)

PRACTICE # 2(only back side)

TONIGHT’S HW

Section 2-3 Scientific Notation

In scientific notationscientific notation, numbers are written in the form M x 10n, where M is a number

greater than or equal to 1 but less than 10 and n is a whole number.

Examples

149 000 000 km 1.49 x 108 km

0.000181 m 1.81 x 10-4 m

1.49e8

1.81e-4

Section 2-3 Scientific Notation (continued) – Mathematical Operations – Mathematical Operations using Scientific Notation – addition & subtractionusing Scientific Notation – addition & subtraction

To add or subtract you must make the exponents the same

Examples - adding

1.49 x 104 km

1.81 x 103 km

14.9 x 103 km 1.49 x 104 km

1.81 x 103 km 0.181 x 104 km

16.71 x 103 km 1.671 x 104 km

EITHER OR

16.7 x 103 km Remember rounding 1.67 x 104 km

Section 2-3 Scientific Notation (continued) – Mathematical Operations – Mathematical Operations using Scientific Notation – addition & subtractionusing Scientific Notation – addition & subtraction

UNITS TOO (don’t get UNITS TOO (don’t get tripped up on this)tripped up on this)

Examples

1.49 x 105 km

5.02 x 104 m

Becomes 1.49 x 108 m

Becomes 0.00502 x 108 m

Becomes 1.49502 x 108 m

Rounding Becomes 1.50 x 108 m

Section 2-3 Scientific Notation (continued) – Mathematical Operations – Mathematical Operations using Scientific Notation – Multiplicationusing Scientific Notation – Multiplication

M factors are multiplied and ns are added

Remember general form M x 10n

Examples

1.49 x 108 m

1.81 x 10-4 m

2.969 x 104 m

2.97 x 104 m Rounded

Section 2-3 Scientific Notation (continued) – Mathematical Operations – Mathematical Operations using Scientific Notation – Divisionusing Scientific Notation – Division

M factors are divided and ns are subtracted

denominator from numerator

Examples

5.44 x 107 g

8.1 x 104 mol

= 0.6716049383 x 103 g/mol

_____________

= 6.7 x 102 g/mol

Section 2-3 Scientific Notation - Practice

PRACTICE

PRACTICE KEY

Joke BreakA man jumps into a NY City cab and asks the cab driver, “Do you know how to get to Carnegie Hall?”The cabbie turns around and says , “Practice, practice , practice!”

PRACTICE Adding & Subtracting

PRACTICEMultiplying & Dividing

PRACTICESig Figs

Key to Sig Figs

Significant Figures – POGIL POGIL HW

Chapter Review

Section 2-3 Direct & Inverse Proportions

Graphing Practice Graphing Practice

What the results should look like:

Chapter Summary Questions

HW – pages 60-6127, 31, 34, 36, 43, 48 & 57

Supplemental Scientific Notation Material

Density = Mass / Volume

5.03 g / 3.24 mL

= 1.552496...... g/mL

Rounded = 1.55 g/mL

0.603 L x 1000 ml/L

= 6.03 x 102 mL

((1.54 g/cm3 – 1.25 g/cm3) / 1.54 g/cm3) x 100%

= 18.8311.....%

Rounded = 18.8 %

Percent error = ----------------------------------------------------- x 100%( VALUEACCEPTED – VALUEEXPERIMENTAL)

VALUEACCEPTED

a) Fourb) Onec) Sixd) Three

a) 8.278 x 104 mg

b) 2.5766 x 10-2 kg

c) 6.83 x 10-2 m3

d) 8.57 x 108 m2

Density = Mass / Volume

57.6 g / 40.25 cm3

= 1.4310559....... g/cm3

Rounded = 1.43 g/cm3

a) 2 g fat = 15 calories1g = 7.5 Cal 8 Cal/g

a) 0.6 kgb) 2 x 105 μgc) One; the value 2 g limits the number of

significant figures for these data.

Supplemental Scientific NotationAdding (or substracting)

PRACTICE

Adding & Subtracting

Approximately, how much further from the sun is Saturn than Earth. Earth is approximately 9.3 × 107 miles from the sun and Saturn is approximately 8.87 × 108 miles from the sun.

(8.87 × 108) – (9.3 × 107)

= (8.87 × 101 × 107) – (9.3 × 107)

= (88.7 × 107) – (9.3 × 107)

= (88.7 – 9.3) × 107

= 79.4 × 107

= 7.94 × 101 × 107

= 7.9 × 108

Saturn is approximately 7.9 × 108 miles more from the sun than Earth is.

Supplemental Scientific NotationMultiplying & Dividing

PRACTICEMultiplying & Dividing

Chapter 2 – Measurement and Calculations

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