Scientific Method Make observations _ Make a prediction _ Practically test the prediction Scientific law is a concise verbal statement or a mathematical.

Scientific Method Make observations _ Make a prediction _ Practically test the prediction Scientific law is a concise verbal statement or a mathematical equation that summarizes a broad variety of observations and experiences. Theory is an explanation of the general principles of certain phenomena, with considerable evidence or facts to support it. Exact numbers : exactly known values. Estimated numbers: values that have some uncertainty. Most of exact numbers have defined values (1000g is exactly 1 kg). Numbers obtained by measurement are always inexact. Measurements always have some degree of uncertainty because they are done by measuring devices. This uncertainty depends on the precision of the measuring device.

Accuracy is determined by the graduations found on the instrument
Accuracy is determined by the graduations found on the instrument. The smaller the increment between graduations, the more accurate the instrument is. The graduations are important, but the space between them also tells us something. If we look closely, we can estimate just where between the graduations our measurement lies. The last digit shown is uncertain. As a rule, you can assume that the manufacturer of a measuring instrument has calibrated the display so that the last digit you see is uncertain. (This isn't always true, but usually it is.)

20 ? 1.50 x 101 mL 15 mL ? 15.0 mL A student reads a graduated cylinder that is marked at mL, as shown in the illustration. Is this correct? NO Express the correct reading using scientific notation mL or 1.50 x101 mL 10

ACCURATE = Correct PRECISE = Consistent
Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = Correct PRECISE = Consistent Courtesy Christy Johannesson

Percent Error your value accepted value
Indicates accuracy of a measurement your value accepted value

Percent Error A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is g/mL.

% error = 2.9 % Percent Error
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 % Courtesy Christy Johannesson

Significant Figures 2.35 cm Indicate precision of a measurement.
Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm Courtesy Christy Johannesson

Significant Figures Counting Sig Figs (Table 2-5, p.47)
Count all numbers EXCEPT: Leading zeros Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson

Precision Accuracy check by check by using a repeating
Precision Accuracy reproducibility check by repeating measurements poor precision results from poor technique correctness check by using a different method poor accuracy results from procedural or equipment flaws.

Accuracy vs. Precision Systematic errors: reduce accuracy
Scientists repeat experiments many times to increase their accuracy. Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy Random errors: reduce precision (instrument) (person)

Numbers, which are the same regardless of who makes the measurement are called certain digits; if a number has to be estimated – it is an uncertain digit. All measurements are reported by recording all certain and the first uncertain digits. These digits are called significant figures. The estimated value is the final digit in a measured number. Exact numbers do not affect the number of significant figures. Constants : the speed of light is x 108m/s.

ACCURATE = Correct PRECISE = Consistent
Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = Correct PRECISE = Consistent Courtesy Christy Johannesson

Percent Error your value accepted value
Indicates accuracy of a measurement your value accepted value Courtesy Christy Johannesson

Percent Error A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. Courtesy Christy Johannesson

% error = 2.9 % Percent Error
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 % Courtesy Christy Johannesson

Significant Figures 2.35 cm Indicate precision of a measurement.
Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm Courtesy Christy Johannesson

Significant Figures Counting Sig Figs (Table 2-5, p.47)
Count all numbers EXCEPT: Leading zeros Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson

Counting Sig Fig Examples
Significant Figures Counting Sig Fig Examples 4 sig figs 3 sig figs 3. 5,280 3. 5,280 3 sig figs 2 sig figs Courtesy Christy Johannesson

(13.91g/cm3)(23.3cm3) = 324.103g 324 g Significant Figures 4 SF 3 SF
Calculating with Sig Figs Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = g 4 SF 3 SF 3 SF 324 g Courtesy Christy Johannesson

Significant Figures Calculating with Sig Figs (con’t) Add/Subtract - The # with the lowest decimal number determines the place of the last sig fig in the answer. 3.75 mL mL 7.85 mL 3.75 mL mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g  7.9 mL  354 g

Significant Figures Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm Courtesy Christy Johannesson

Practice Problems 5. (15.30 g) ÷ (6.4 mL) = 2.390625 g/mL  2.4 g/mL
Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL) 4 SF 2 SF = g/mL  2.4 g/mL 2 SF g g  18.1 g 18.06 g Courtesy Christy Johannesson

Scientific Notation 65,000 kg  6.5 × 104 kg
Converting into scientific notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent Only include sig. figs.

Scientific Notation Practice Problems 7. 2,400,000 g kg 9. 7  10-5 km  104 mm 2.4  106 g 2.56  10-3 kg km 62,000 mm Courtesy Christy Johannesson

The metric system was expanded in 1960 into the International System of Units (metric units are therefore sometimes called SI units). The major features of both systems are: · The use of decimals ; · A system of prefixes · Standards defined in terms of basic, unchanging physical properties

Length Volume L = 10 dL ( deciliter) 1 L = 1000 mL = 10 cm x 10 cm x 10 cm = 1000 cm3 Mass is a measure of the resistance of an object to a change in its state of motion. Weight is a response of mass to the force of gravity. Temperature It is very important to be able to express the temperature in all systems commonly used and to interchange between these systems. There are three systems for temperature measurement: Celsius, Kelvin and Fahrenheit scales.

Calculation Corner: Unit Conversion
1 foot = 12 inches 1 foot = 1 12 inches 12 inches = 1 1 foot

1 foot 12 inches 12 inches 1 foot “Conversion factors”

1 foot 12 inches 12 inches 1 foot “Conversion factors” 12 inches ( ) ( ) 3 feet = 36 inches 1 foot

( ) ______ How many cm are in 1.32 meters? equality: 1 m = 100 cm
(or 0.01 m = 1 cm) applicable conversion factors: ______ 1 m 100 cm ______ 1 m 100 cm or ( ) ______ 1 m 100 cm 132 cm X cm = 1.32 m = We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose.

Again, the units must cancel.
How many meters is 8.72 cm? equality: 1 m = 100 cm applicable conversion factors: ______ 1 m 100 cm ______ 1 m 100 cm or ( ) ______ 1 m 100 cm m X m = 8.72 cm = Again, the units must cancel.

Again, the units must cancel.
How many feet is inches? equality: 1 ft = 12 in applicable conversion factors: ______ 1 ft 12 in ______ 1 ft 12 in or ( ) ____ 1 ft 12 in 3.28 ft X ft = in = Again, the units must cancel.

( ) ( ) ____ ______ How many kilometers is 15,000 decimeters? 10 dm
1 km 1.5 km X km = 15,000 dm =

Simple Math with Conversion Factors

Example Problem Measured dimensions of a rectangle:
length (L) = 9.70 cm width (W) = 4.25 cm L W Find area of rectangle. A = L . W = (9.70 cm)(4.25 cm) = 41.2 cm 2 . cm

How many seconds is 4.38 days?
____ ( ) ( ) _____ ( ) ____ 24 h 1 d 1 h 60 min 1 min 60 s X s = 4.38 d 378,432 s = If we are accounting for significant figures, we would change this to… 3.78 x 105 s

Measured dimensions of a rectangular solid:
Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm H W Find volume of solid. L V = L . W . H = (15.2 cm)(3.7 cm)(8.6 cm) = 480 cm 3

( ) ( ) ( ) ( ) ( ) _____ _____ _____ _____ _________ 100 cm 1 m
Convert to m3. cm.cm.cm ( ) _____ ( ) _____ ( ) _____ 100 cm 1 m X m3 = 480 cm 3 2 100 cm 1 m 100 cm 1 m = or ( ) _____ 100 cm 1 m 3 X m3 = 480 cm3 = m3 or 1 m cm ( ) _________ 3 X m3 = 480 cm3 4.80 x 10-4 m3 =

Convert to m3... Measured dimensions of a rectangular solid:
Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm 0.152 m 0.037 m 0.086 m H W Find volume of solid. L V = L . W . H = (0.152 m)(0.037 m)(0.086 m) = m 3

Convert to mm3.

1 cm = 10 mm (1 cm)2 = (10 mm)2 1 cm2 = 100 mm2 (1 cm)3 = (10 mm)3
By what factor do mm and cm differ? 10 By what factor do mm2 and cm2 differ? 100 By what factor do mm3 and cm3 differ? 1,000 1 cm = 10 mm (1 cm)2 = (10 mm)2 1 cm2 = 100 mm2 (1 cm)3 = (10 mm)3 1 cm3 = 1000 mm3

Table 1.3 SI Prefixes Multiple Prefix Symbol 106 mega M 103 kilo k
10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro 10-9 nano n 10-12 pico p 2

Temperature The conversion of Fahrenheit to Celsius,
The Fahrenheit scale is at present the common temperature scale in the United States. The conversion of Fahrenheit to Celsius, 2

Density is one of the most important properties of matter, which is defined as the mass of a substance per unit of volume (units g/cm3; kg/m3).

Density INTENSIVE property of matter. EXTENSIVE - does NOT depend
Density is an INTENSIVE property of matter. - does NOT depend on quantity of matter. - color, melting point, boiling point, odor, density Brick Styrofoam Contrast with EXTENSIVE - depends on quantity of matter. - mass, volume, heat content (calories)

Properties of Matter volume: 100 mL 15 mL mass: 99.9347 g 14.9902 g
Pyrex Pyrex Extensive Properties volume: 100 mL 15 mL mass: g g Intensive Properties density: 0.999 g/mL 0.999 g/mL temperature: 20oC 20oC

? It appears that the brick is ~40x more dense than the Styrofoam.
Ask the students, "which weighs more...a ton of feathers or a ton of bricks?" You'll be surprised how many will answer "the bricks!" The students are confusing / misusing the terms density and mass. Styrofoam Brick

Styrofoam Brick M Mass D D = = Volume V Brick Styrofoam

Styrofoam Brick M Mass D V = = D V Mass = D * V

Density M V D = M M = D x V ass D V M D V = ensity olume

Archimedes Principle Vfinal = 98.5 cm3 - Vinitial = 44.5 cm3
After immersion Fishing sinker 98.5 cm3 Thread Before immersion Water 44.5 cm3 Vfinal = 98.5 cm3 - Vinitial = 44.5 cm3 Vfishing sinker = 54.0 cm3 Archimedes Principle: water displacement method to find the volume of an irregularly shaped object. The volume the water level increased is equal to the volume of the submerged object. The most famous application of buoyancy is due to Archimedes of Syracuse around 250 BC. He was asked to determine whether the new crown that King Hiero II had commissioned contained all the gold that he had provided to the goldsmith for that purpose; apparently he suspected that the smith might have set aside some of the gold for himself and substituted less-valuable silver instead. According to legend, Archimedes devised the principle of the “hydrostatic balance” after he noticed his own apparent loss in weight while sitting in his bath. The story goes that he was so enthused with his discovery that he jumped out of his bath and ran through the town, shouting "eureka" to the bemused people.

9. Some conversion problems require a U. S. -metric conversion factor
9. Some conversion problems require a U.S.-metric conversion factor. If a can of tomato juice is quart, how many milliliters are in the can? 10. What is the density of a 25.7 g piece of bone found at a crime scene? When the bone was placed in a graduated cylinder containing mL of water, the volume of the water rose to mL. 11. A 5.00 mL sample of urine weighs 5.45 g. What is the specific gravity of the sample of urine? 12. If the specific gravity of carbon dioxide is 1.96, how many mL will a 2.00 g sample of carbon dioxide occupy? 13. If a g sample of an ore is only 79.75% aluminum, how many grams of aluminum are present in the sample? 14. Olive oil has a density of 0.92 g/mL. The density of maple wood is 0.75 g/mL. The density of bone is 1.80 g/mL. The density of milk is 1.04 g/mL. When the four substances are mixed, which one or ones will float on the olive oil?

15. Olive oil has a density of 0. 92 g/mL
15. Olive oil has a density of 0.92 g/mL. The density of maple wood is 0.75 g/mL. The density of bone is 1.80 g/mL. The density of milk is 1.04 g/mL. When the four substances are mixed, which one or ones will float on the olive oil? 16. European cookbook contains a recipe for carrot cake that calls for 2.00 kg of carrots. How many pounds of carrots is this? (1 lb = 454 g) 17. The gap between two neurons in a rat's brain is estimated to be 2.08 x 10-3 nm. What is this distance in inches? 18. A nurse injects a patient with cc of a drug. How many mL of the drug was given? 19. If dL of blood was taken from a patient's arm, how many liters of blood was taken? 20. If 20.00% of the 150 students in a class voted to move the exam date forward, how many students wanted the earlier exam date?

Scientific Method Make observations _ Make a prediction _ Practically test the prediction Scientific law is a concise verbal statement or a mathematical.

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Scientific Method Make observations _ Make a prediction _ Practically test the prediction Scientific law is a concise verbal statement or a mathematical.

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