Method, Measurement and Problem Solving Chapter 2-1 Method, Measurement and Problem Solving

I. What is Chemistry? A. Chemistry is the study of all matter and the changes it can undergo. B. Chemistry has been called the central science because it overlaps so many sciences. C. Chemical – any substance with a definite composition. Ex) dihydrogen monoxide = H2O

A common misperception of science is that science defines "truth A common misperception of science is that science defines "truth."  Science does not define truth, but rather it defines a way of thought.  It is a process by which experiments are used to answer questions.  This process is called the scientific method and involves several steps:

II. The Scientific Method: (2.2) A. A systematic approach to gathering knowledge. B. Steps to the Scientific Method: observation question hypothesis experiment conclusion *Note: All hypotheses must be able to be tested in order to be a true hypothesis.

Many Experiments  Natural Law  Theory (how nature behaves) (why nature behaves)

Any # to the zero power is 1 III. Scientific Notation: Shorthand way of expressing very large or very small numbers. (2.3) Power of 10 Equivalent # Reason 100 1 Any # to the zero power is 1 101 10 10 x 1 102 10 x 10 103 1,000 10 x 10 x 10 105 100,000 10 x 10 x 10 x 10 x 10 10-1 0.1 1/10 10-3 0.001 1/(10x10x10) = 1/1000 10-5 0.00001 1/(10x10x10x10x10) = 1/100,000

B. Express Numbers in Scientific Notation – move the decimal point so that there is only 1 non-zero digit to the left of the decimal point. Moving the decimal point left the power will be -, right the power will be +.

Try these examples: top of page 2 in the notes! 1) 2700 2) 0.0035 2,640,000,000 4) 0.010 C. Express Numbers in regular form – reverse the process. 5) 8.65 x 106 6) 9.73 x 10-8 Complete the front of the Scientific Notation Worksheet 2.7 x 103 3.5 x 10-3 1.0 x 10-2 2.64 x 109 8,650,000 0.000 000 0973

Small Numbers – negative exponents are all between 0 and 1 Large Numbers 1x10-10 1x10-1 1x102 4x101 1x100 = 1

1st Commandment of Chemistry: KNOW THY CALCULATOR! Find the “EE” key – it may be a 2nd function! If you have a graphing calculator look for the following keys: Find the (-) key.

Look at the calculator that is similar to yours… Find the “Exp” or “x10x” 1st Law of Chemistry: Know Thy Calculator! Look at the calculator that is similar to yours… Find the “(-)” or the “+/-” key.

Try these examples: Ex. #7) 8.08 x 10-5 - 2.07 x 10-6 = Ex. #8) 3.7 x 102 x 5.1 x 103 = Ex. #9) 7.87 x 10-5 1,887,000 or 1.887 x 106 5000 or 5 x 103

Origin of the Metric System During the18th century scientists measured the distance from the earth’s equator to the North Pole and divided it into ten million parts. This number is equal to exactly 1 meter.

The Meter The standard for the meter is kept in a safe in France. The meter stick is a replica of that standard. A meter is made up of 100 centimeters and 1000 millimeters.

Demo Volunteers!

= The Liter The liter is 1000 mL 10cm x 10cm x 10cm 1 liter = 1000 cm3 = 1 dm3 1 milliliter = 1 cm3 = 1 cc = 20 drops

The Gram Mass is the amount of matter in an object. 1 cm3 of water = 1 gram. The standard kilogram is kept under lock and key at the Bureau of International Weights and Measures in Sevres, France.

The Time standard During the 15th century a scientist named Galileo set the standard of time known as the second.

Why do we need standards????

Mars Climate Orbiter Mistake In December 1998 two different groups of scientists were working on calculations to land a probe on Mars. The American team did their calculations in the English system and the other team did their calculations in the metric system – the $125 million probe crashed onto Mars in September 1999.

Medication Dose Errors In 2004, doctors prescribed 0.75 mL of Zantac Syrup twice a day to a baby, but the pharmacist labeled the bottle, “Give 3/4 teaspoonful twice a day.” A teaspoon is about 4.9 mL… The mistake was 5 times the correct dose!

Length Relationships

IV. Metric System: (1.2) A. International System of Measurements (SI): standard system used by all scientists. It is based upon multiples of 10.

Measurement Unit Instrument Equation Derived Unit Mass gram triple beam balance ------------ --------------- length Meter meterstick time second watch Temperature Kelvin/ celcius thermometer Quantity mole ----------------------- Area m2/cm2 L x W cm2 Volume m3/cm3 Graduated cylinder LxWxH L Density g/cm3 ---------------------- D = M/V Pressure Atm/kPa barometer Force/area N/m2 Energy Cal or J Calorimeter ---------------- Cal/Joules

Prefix Abbreviation Meaning Scientific Notation Giga G 1,000,000,000 1 x 109 Mega- M 1,000,000 1 x 106 kilo- k 1,000 1 x 103 hecto- h 100 1 x 102 deka- da or dk 10 1 x 10 BASE UNIT meter/liter/gram 1 deci- d 0.1 1 x 10-1 centi- c 0.01 1 x 10-2 milli- m 0.001 1 x 10-3 micro- µ 0.000 001 1 x 10-6 nano- n 0.000 000 001 1 x 10-9 pico- p 0.000 000 000 001 1 x 10-12

D. Metric Conversions using the Factor-Label Method (Dimensional Analysis) Ex. #1) Convert $72 to quarters: Write the given with the units. Then look at the unit and use a conversion factor that relates to the unit you need. See page 3 in the notes

V. Uncertainty in Measurement: (2.3) 2.00cm .01cm A. Measurements are uncertain because: 1. Instruments are not free from error. 2. Measuring always involves some estimation. B. Estimating with a scale 1. Estimate 1 digit more than the instrument measures. 2. “” is used to show uncertainty. READ the length of the lines: 2.83cm .01cm Smallest graduations on the ruler are 0.1cm therefore you should measure to 0.01cm!

C. Precision: When the instrument gives you about the same results under similar conditions. D. Accuracy: When the experimental value is close to the true or actual value. The smaller the increments of measurement an instrument has, the more accurate it can be. E. An instrument is precise (numbers repeatable to a certain number of places) the operator makes it accurate (close to the right answer by using it correctly).

Ex. Precise, Accurate, Both or Neither (Accepted Value = 15g) 1. 200g, 1g, 40g neither 2. 78g, 80.g, 79g precise 3. 16g, 14g, 17g both precise and accurate

What is the goal for a game of darts? Hitting the Bulls Eye!

Reading a Metric Ruler

Meter sticks and paperclips!

Rulers 3.6 cm   3 4 5 3.6 cm   3 4 5 3.62 cm   3 4 5

How to use a graduated cylinder Read the meniscus

How to use a graduated cylinder 36.4 mL 19.0 mL 6.25 mL

More Graduated Cylinders 15.2 mL 8.69 mL 17 mL

Because the smallest increments on the graduated cylinder are 0 Because the smallest increments on the graduated cylinder are 0.1 mL, you estimate the .01 place… The cylinder reads 8.76 mL

130.510 g

Triple Beam Balance   100 200 10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 7 8 9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Reading a Triple Beam Balance

How to read a Triple Beam Balance 28.570 g Ohaus Triple Beam Balance Tutorial Reading A Triple Beam Balance Tutorial

How to read a Triple Beam Balance 109.076 g Ohaus Triple Beam Balance Tutorial Reading A Triple Beam Balance Tutorial

D. Factors in an Experiment Independent: most regular variable – goes on the X-axis Dependent: what you are testing – goes on the Y-axis Experimental Control: part of the experiment that stays the same. Dependent variable “Y” axis Independent variable “X” axis

Drawing a Graph in Chemistry: Label each axis with a name and a unit. Number by regular increments! This means by 1’s, 2’s, 5’s, 10’s etc. NOT by 3’s,7’s or 9’s! Unless otherwise noted include zero. Include a title that states what is being tested…this would include the dependent variable and any change that occurs for different trials. Include a key for different trials. This could be different colors or one in pen and one in pencil. Write a statement or conclusion on the graph that states; “This graph shows…” to explain the results of the experiment. If necessary, extend the graph (extrapolate) to predict additional data points with a dashed (-----) line. Title: How pressure changes with increased volume. Statement: This graph shows that pressure decreases with increased volume. Key: Trial 1 Trial 2

Graphing: How do you determine the best-fit line through data points Graphing: How do you determine the best-fit line through data points? The line may pass through some, all or none of the data points. y-variable x-variable

Are the data directly or indirectly related, is the general trend 1st degree (straight line) or 2nd degree (curved)?

Rules for Significant Digits! Can you think of a map of the United States? Then you can do significant digits! All nonzero digits are significant. All zeros between two nonzero digits are significant. All zeros to the left of an understood decimal point, but to the right of a nonzero digit are not significant. All zeros to the left of an expressed decimal point, and to the right of a nonzero digit are significant. All zeros to the right of a decimal point, but to the left of a nonzero digit are not significant. All zeros to the right of a decimal point and to the right of a nonzero digit are significant.

VI. Significant Digits A. Significant Digits include measured digits and estimated digits. Use Atlantic-Pacific Rule – imagine a US map decimal point decimal point Pacific Atlantic resent bsent

1100 2 significant digits 4 significant digits 1100. 8 significant digits 11.010000 2 significant digits 0.025 5 significant digits 0.00035000 1,000,100 5 significant digits Decimal Absent Start counting with the 1st nonzero digit and count all the rest. Decimal Present Start counting with the 1st nonzero digit and count all the rest.

B. Significant Digits in Addition and Subtraction Add or Subtract numbers. Answer must be based on the number with the largest uncertainty (look at least places.) Ex. 951.0 g 1407 g 23.911g 158.18 g + 2540.091g ? Which is the least precise place??? Round your answer to that place: tenths place ones place thousandths place hundredths place 2540.g

B. Multiplication and Division Multiply or Divide numbers. Round answer to the same number of significant digits as number with fewest significant digits. Ex #1) = Ex #2) V = L x W x H V= 3.05 m x 2.10 m x 0.75 m = 4 13.2 no units! 3 4.8 m3 3 3 2

Ex. #3) A = L x W A= 3200 cm x 2500 cm = ? Always write down the answer your calculator gives you, then round to the correct # of S.D. = 8,000,000 cm2 This only has 1 S.D. How many S.D. should the answer have? If you can’t round, write the number in scientific notation: = 8.0 x 106 cm2 2

VII. Important Formulas: Percent Error: Comparing a measurement obtained experimentally with an accepted value. It is always expressed as a positive %. % error = Ex.) If a student calculates the density of aluminum to be 2.5 g/cm3, and the accepted value is 2.7g/cm3, what was her % error?

Ex. ) If a student calculates the density of aluminum to be 2 Ex.) If a student calculates the density of aluminum to be 2.5 g/cm3, and the accepted value is 2.7g/cm3, what was her % error?

DENSITY Density is defined as mass per unit volume. It is a measure of how tightly packed and how heavy the molecules are in an object. Density is the amount of matter within a certain volume. Density is the amount of matter within a certain volume.

Which is less dense???

Units for density g/cm3 or g/ml Formula: M = mass V= volume D = density M = D x V V = M / D D = M / V

What if it’s an irregular shaped solid and not a liquid??? To find density: Find the mass of the object with the triple beam balance…you may have to subtract the mass of the container! Find the volume of the object – use a graduated cylinder for liquids and a centimeter ruler for regular solids. Divide : Density = What if it’s an irregular shaped solid and not a liquid???

Density of an Irregular solid: 1- Find the mass of the object 2- Find the volume of the object by water displacement!

B. (1.2) Density M=VD V= Ex.) If a metal block has a mass of 75.355 g and a volume of 22.0 cm3, what is the density? D = What is the density of water? 1.0 g/mL Would the above metal block float or sink in water???

VIII. Dimensional Analysis (The Factor-Label Method): (1.2) A. Uses unit equalities to convert between units. A unit equality is an equation that relates 2 units. Ex.) 12in = 1ft 60sec = 1min 1kg = 1000g B. Unit equalities are used to write conversion factors which are always equal to “1.” Ex)

digits in the answer is equal to the number in the given. C. The conversion factor is a definition, and therefore infinitely precise, so the number of significant digits in the answer is equal to the number in the given. Useful Chemistry Conversion Factors 1 in. = 2.54 cm 1 ft. = 12 in. 1 mile = 5280 ft. 1 min. = 60 s 1 hr. = 60 min. 1 atm = 760 mm Hg 1 atm = 101,325 Pa 1 cal. = 4.184 J 1 gal. = 3.785 L These conversion factors will NOT be given on the test. In addition you need to know the 6 basic metric prefixes.

Ex. #1) How many seconds are in 22.0 hours? Ex. #2) How many years are in 3 x 108 seconds? Ex. #3) If there are 9 dibs in 1 sob, 3 sobs in 1 tog, 1 tog in 6 pons, and 12 pons in 1 gob. How many gobs are in 27 dibs?

Ex #4) Calculate the number of feet in a 5. 00 km race. (1 inch = 2 Ex #4) Calculate the number of feet in a 5.00 km race. (1 inch = 2.54 cm)