Scientific Method and Measurement

Unit 1 : 

Unit 1 Scientific Method and Measurement

Hypothesis : 

Hypothesis is an educated guess is more specifically a descriptive model used to explain observations and to predict the outcome of an experiment based on these observations or previous knowledge Format: If (change in IV), then (change in DV)

Repeated Trials : 

Repeated Trials performing the same exact experimental procedure several times and comparing results makes the experiment more reliable reduces the effects of random errors

Observations : 

Observations process of using the senses to note and record facts about natural phenomenon

Data : 

Data observations that are recorded during an experiment can be qualitative or quantitative

Qualitative vs. Quantitative : 

Qualitative vs. Quantitative Qualitative: concerned with answering the questions: What? And how? Example: Determining whether or not iron is present in the water supply. Quantitative: concerned with answering the questions: How many? And how much? Example: Determining how much iron is in the water supply.

Measurements : 

Measurements Observations can be both quantitative and qualitative Measurements are always quantitative Measurements consist of 2 parts: a number and a unit example: 15 g NaCl

Types of Measurements Examples : 

Types of Measurements Examples 4 feet Blue chair Hot 100ºF Quantitative Qualitative Qualitative Quantitative

Variables : 

Variables factors that are changed during an experiment two kinds 1) independent 2) dependent

Types of Variables : 

Types of Variables Independent Variable: variable that is deliberately changed or manipulated by the individual conducting the experiment Dependent Variable: variable(s) that responded to the change of the independent variable can be determined by the data that is recorded (Dependent/Data)

Theory : 

Theory a thoroughly tested model that explains why certain experiments give certain results can never be proven Example: the kinetic molecular theory states that particles of all matter are in constant motion- these particles can not be seen by any type of microscope so this theory can’t really be proven

Scientific Law : 

Scientific Law concise statement that summarizes the results of a broad variety of observations and experiments can be proven but does not explain why a behavior is observed Example: Boyle’s Law states that when the mass of a gas remains constant, the volume of the gas varies inversely with its pressure

Constants and Control : 

Constants and Control Constants: factors that remain unchanged throughout an experiment Control: standard used for comparing experimental effects

Uncertainty in Measurements : 

Uncertainty in Measurements Need to make reliable measurements in the lab Accuracy – how close a measurement is to the true value - can be true of an individual measurement or the average of several measurements Precision – how close the measurements are to each other (reproducibility) - requires several measurements before precision can be ascertained

Slide 16: 

Let’s use a golf analogy…

Slide 17: 

Accurate? No Precise? Yes

Slide 18: 

Accurate? Yes Precise? Not enough info

Slide 19: 

Precise? No Accurate? Yes? No?

Slide 20: 

Accurate? Yes Precise? Yes

Precision Calculations : 

Precision Calculations Absolute Deviation Average Deviation Percent Deviation

Absolute Deviation : 

Absolute Deviation Calculated for each measurement the difference of each measurement from the mean or average Absolute Deviation = |Measured value – Mean|

Average Deviation : 

Average Deviation Calculated for each set of measurements Example: 3 trials for one level of an IV would be used to calculate average deviation for that level is the average (mean) of all of the absolute deviations

Percent Deviation : 

Percent Deviation Also called relative deviation Calculated for each set of trials for an IV level tells the scientist how reliable the instrument is for other measurements % Deviation = Average Deviation x 100 Mean

Random vs. Systematic Errors : 

Random vs. Systematic Errors Random errors: usually result from the experimenter's inability to take the same measurement in exactly the same way to get exact the same number - multiple trials tend to reduce impact of random errors over time Systematic errors: often due to a problem which persists throughout the entire experiment (error due to lab equipment or materials used) - multiple trials tend not to reduce impact as error is consistent across trials

Percent Error : 

Percent Error Used to determine the accuracy of an experiment Have to know true value of measurement the absolute value of the error divided by the accepted value, times 100% | accepted value – experimental value| accepted value x 100% % error =

Percent Error Terms : 

Percent Error Terms Accepted value – correct value based on reliable references Experimental value – the value measured in the lab

Uncertainty Example : 

Uncertainty Example A student decides to examine how many drops of water can fit on a penny. The student conducts the experiment three times, obtaining measurements of 25 drops, 29 drops, and 42 drops. When the experiment was repeated several hundred times, the average number of drops of water that fit on the penny was 51 drops. Calculate and evaluate the precision and accuracy of the student’s experiment. Trial 1: 25 drops Trial 2: 29 drops Trial 3: 42 drops Known value: 51 drops

Slide 32: 

Trial 1: 25 drops Trial 2: 29 drops Known value: 51 drops Trial 3: 42 drops Calculate absolute deviation for each trial: | 25 drops – 32 drops | = 7 drops | 29 drops – 32 drops | = 3 drops | 42 drops – 32 drops | = 10 drops 2) Calculate average deviation for the set of trials: (7 drops + 3 drops + 10 drops)/3 = 7 drops Calculate % deviation for the set of trials: % deviation = 7 drops/32 drops x 100 = 21.9% Precision Calcs

Slide 33: 

Trial 1: 25 drops Trial 2: 29 drops Known value: 51 drops Trial 3: 42 drops Calculate % error for the set of trials: - use average (32 drops) for experimental value % error = |51 drops – 32 drops| x 100 = 59.4% 32 drops Accuracy Calcs

Slide 34: 

% deviation = 21.9% % error = 59.4% - Precision for this experiment was good but could have been improved. - Accuracy for this experiment was poor. Uncertainty Example Analysis

Why use Scientific Notation? : 

Why use Scientific Notation? Example 1: 602,000,000,000,000,000,000,000 is Avogadro’s number (we’ll use it a lot in the spring). - A more convenient way to write Avogadro’s number is 6.02x1023 Example 2: 0.000000000000000000000006643 g is the mass of a proton. - A more convenient way to write the mass of a proton is 6.643x10-24 g. Scientific notation enables to write really big or really small numbers without all the zeros!

Scientific Notation : 

Scientific Notation Definition: expression of both large & small numbers using powers of 10 105  1.05x102 0.0105  1.05x10-2 0.0000064  6.4x10-6 640,000,000  6.4x108

Scientific Notation Rules : 

Scientific Notation Rules 1. Only one digit in front of the decimal 2. Power of 10 depends on two things: number of places decimal is moved direction decimal is moved If number is > 1: direction decimal moved is to the left - power of 10 is positive If number is < 1: direction decimal moved is to the right - power of 10 is negative

Scientific Notation Examples : 

Scientific Notation Examples Example 1: 238,000 Answer 2.38x105 Example 2: 0.00043 Answer 4.3x10-4 Example 3: 0.00289 Answer 2.89x10-3 Example 4: 7,400 Answer 7.4x103

Significant Figures : 

Significant Figures Measurements always have some degree of uncertainty Certain numbers: all the numbers in a measurement that can be absolutely determined Uncertain number: the one number estimated in the measurement Example: 3.45 cm Significant figures: all numbers recorded in a measurement

Significant Figures Rules : 

Significant Figures Rules 1. All nonzero integers count as significant figures 1457 has 4 sig figs 2. Three types of zeros: leading zeros captive zeros trailing zeros

Leading Zeros : 

Leading Zeros precede all nonzero digits never count as sig figs example: 0.00329 3 sig figs in measurement

Captive Zeros : 

Captive Zeros zeros that fall between nonzero digits always count as sig figs example: 23.09 4 sig figs in measurement

Trailing Zeros : 

Trailing Zeros zeros at the right end of a measurement (may or may not include a decimal) these are significant only if there is a decimal in the measurement example 1: 2500 2 sig figs (no decimal) example 2: 2500. 4 sig figs (decimal)

Measured Numbers and Sig Figs : 

Measured Numbers and Sig Figs numbers obtained using measuring devices always require the use of significant figures example: 4.506 g

Exact Numbers and Sig Figs : 

Exact Numbers and Sig Figs numbers determined by counting or by definition these numbers are considered to have an unlimited number of significant figures (will play a role in calculations) examples: 10 books; 1 in = 2.54 cm

Scientific Notationand Sig Figs : 

Scientific Notationand Sig Figs All digits included in scientific notation are significant figures examples: 1.0x10-1 has 2 sig figs (0.10) 2.00x102 has 3 sig figs (200.)

Scientific Notationand Sig Figs : 

Scientific Notationand Sig Figs When converting numbers from scientific notation to ordinary numbers - 0’s are used as placeholders examples: 5.4x10-3 has 2 sig figs (0.0054) 3.05x103 has 3 sig figs (3050) ***notice: no decimal because final 0 is a placeholder***

Sig Fig Practice : 

Sig Fig Practice The mass of the object was determined to be 2.090 g 4 significant figures (decimal) There are 12 inches in a foot definition; unlimited SF’s There are 25 seats in this classroom counted number; unlimited SF’s A piece of copper was measured to be 0.000520 m in diameter 3 significant figures The air pressure in this room is 750 mm Hg 2 significant figures (no decimal) The volume of water in the graduated cylinder is 2.50x102 mL 3 significant figures (decimal)

Rounding Numbers : 

Rounding Numbers Calculations tend to have more digits than needed following significant figures rules Accordingly, numbers must be “rounded off” to the correct number of sig figs using only the digit just past the required number of sig figs

Rounding Numbers Rules : 

Rounding Numbers Rules If digit to be removed is:  5: the digit preceding it does not change 1.43 rounds to 1.4  5: the digit preceding it is increased by 1 2.16 rounds to 2.2 and 4.45 rounds to 4.5 but 4.45 rounds to 4 if only 1 sig fig is required In a series of calculations: no rounding should occur until the final result (more on this later)

Rounding Examples : 

Rounding Examples Round the following to three significant figures: 2.2533  2.25 0.005945  0.00595 99.99  100. 6.323x102  6.32x102 1.395x10-1  1.40x10-1 Round the results of the following calculations to two significant figures: 300. + 40. = 340 or = 34 = 340 ! 54.3 x 0.014 = 0.76 (0.0582 x 3.1)/0.18 = 1.0 25.8/(0.018 x 2.05) = 7.0x102

Calculations Using Sig Figs : 

Calculations Using Sig Figs Addition/Subtraction smallest # of decimal places in answer = smallest # of decimal places of any of the original measurements ex: 12.11 + 18.0 + 1.013 2 DP 1 DP 3DP = 31.123 (calculator) = 31.1 (1 DP) ex: 0.6875 - 0.1 = 0.5875 = 0.6

Calculations Using Sig Figs : 

Calculations Using Sig Figs Multiplication/Division # of sig figs in answer = measurement with smallest # of sig figs ex: 4.56 x 1.4 = 6.384 3 SF 2 SF 4SF round to 2 SF = 6.4 ex: 8.315/298 = 0.0279027 = 0.0279 or 2.79x10-2

Significant Figures Calculation Practice : 

Significant Figures Calculation Practice 5.19 + 1.9 + 0.842 = ? Calculator: 7.932 Rounded: 7.9 1081 - 7.25 = ? Calculator: 1073.75 Rounded: 1074. 2.3 x 3.14 = ? Calculator: 7.222 Rounded: 7.2

Significant Figures Calculation Practice : 

Significant Figures Calculation Practice (3.60x10-3 x 8.123)/4.30 = ? Calculator: 0.0068006512 Rounded: 0.00680 only final answer is rounded because SF rules are the same for multiplication and division (1.33 x 2.8) + 8.41 (3.724) + 8.41 (3.7) + 8.41 = 12.11  12.1 rounding occurs here twice because SF rules differ for multiplication and addition

Units : 

Units Definition: the scale or standard being used to represent the results of an experiment Various systems exist today 1) English system 2) metric system 3) SI

English System : 

English System used primarily in the US includes units such as inches, feet, pounds, degrees Fahrenheit, and miles

Metric System : 

Metric System used in the majority of the industrialized world (except US) preferred for most scientific work includes units such as meters and grams

SI : 

SI stands for Système Internationale created in 1960 by an international agreement provided for a comprehensive system of units these units are based or derived from metric system

SI Base Units : 

SI Base Units Mass: kilogram (kg) Length: meter (m) Time: time (s) Temperature: Kelvin (K) Luminous intensity: Candela (Cd) Quantity: mole (mol) Electric current: Ampere (A)

SI Derived Units : 

SI Derived Units Volume: SI units are m3 also found in units of cm3 1mL = 1cm3; 1L = 1dm3 Energy: SI units are Joules (J) 1J = 1kg•m2/s2 Density: SI units are kg/m3 also found in units of g/cm3, g/mL, kg/L

Common Metric Prefixes : 

Common Metric Prefixes Base SI units are sometimes too large or too small to represent quantities appropriately Prefixes are used to change the unit’s size to a more appropriate quantity Examples include mm, cm, kg, and µL

Slide 64: 

Metric Prefixes, Symbols, & Examples Prefix Symbol Ex. w/Large Prefixes Ex. w/Small Prefixes mega M 1 Mg = 1,000,000g = 106g kilo k 1kg = 1,000g = 103g hecta h 1hg = 100g = 102g deca da 1dag = 10g = 101g o 1g = 100g 1g deci d 1g = 10dg 1dg = 0.1g = 10-1g centi c 1g = 100cg 1cg = 0.01g = 10-2g milli m 1g = 1,000mg 1mg = 0.001g = 10-3g micro µ 1g = 1,000,000µg 1µg = 0.000001g = 10-6g nano n 1g = 1,000,000,000ng 1ng = 0.000000001g = 10-9g pico p 1g = 1,000,000,000,000pg 1pg = 0.000000000001g = 10-12g move left move right

Slide 65: 

Estimating Measurements

Slide 66: 

1. Identify certain digits. 2. Identify smallest interval. 3. Identify uncertain digit. 4. Include appropriate units. 2 . 5 0 cm 0.1 /2 0.05

Slide 67: 

. 5 mL 5 2 Your turn...

Dimensional Analysis Terms : 

Dimensional Analysis Terms definition: changing between units using conversion factors conversion factor: ratio relating two different units example: 1 m/100 cm OR 100 cm/1 m equivalence statement: another way of writing a conversion factor example: 1 m = 100 cm Since these statements are based on definitions of quantities, they represent exact numbers and do not count towards significant figures These problems can be single step or multiple steps

Dimensional Analysis Steps : 

Dimensional Analysis Steps Step 1: Write what is given in the problem. Step 2: Set up conversion factor with equivalence statement so that units cancel. Step 3: Repeat step 2 as needed until units desired are obtained. Step 4: Solve the problem mathematically. Step 5: Apply significant figures and rounding rules as needed.

Dimensional Analysis Example 1 : 

Dimensional Analysis Example 1 How many meters are in 1.5 km? 1.5 km x km m 1 1000 = 1500 m OR 1.5x103 m

Dimensional Analysis Example 2 : 

Dimensional Analysis Example 2 2.5 g = ? cg 2.5 g x g cg 1 100 = 250 cg OR 2.5x102 cg

Dimensional Analysis Example 3 : 

Dimensional Analysis Example 3 How many mL are equivalent to 0.025 daL? 0.025 daL x daL L 1 10 = 250 mL L mL x 1 1000 daL  L  mL OR 2.5x102 mL

Dimensional Analysis Example 3 : 

Dimensional Analysis Example 3 How many mL are equivalent to 0.025 daL? 0.025 daL x daL mL 1 104 = 250 mL OR 2.5x102 mL

Dimensional Analysis Example 4 : 

Dimensional Analysis Example 4 5 µL = ? ML 5 µL x µL L 1 106 = 5x10-12 ML L ML x 1 106 µL  L  ML OR 0.000000000005 ML

Dimensional Analysis Example 4 : 

Dimensional Analysis Example 4 5 µL = ? ML 5 µL x µL L 1 106 = 5x10-12 ML L ML x 1 106 OR 0.000000000005 ML

Dimensional Analysis Example 5 : 

Dimensional Analysis Example 5 400. m2 = ? hm2 400. m2 x m hm 1 102 = 4.00x10-2 hm2 ( )2 ( )2 OR 0.0400 hm2

Dimensional Analysis Example 6 : 

Dimensional Analysis Example 6 How many cm/min are equal to 9.8 m/s? 9.8 m x m cm 1 102 = 59,000 cm/min OR 5.9x104 cm/min s x s min 1 60

Dimensional Analysis Example 7 : 

Dimensional Analysis Example 7 43.1 Cd/m3 = ? dCd/dam3 43.1 Cd x Cd dCd 1 10 = 431,000 dCd/dam3 OR 4.31x105 dCd/dam3 m3 x m dam 1 10 ( )3 ( )3

Temperature Scales : 

Temperature Scales Fahrenheit scale: used widely in the US and Britain; employed in most engineering sciences - unit of temperature: ºF Celsius scale: used in Canada and Europe; employed in physical and life sciences - unit of temperature: ºC absolute Kelvin scale: also employed in the sciences; can not be measured - unit of temperature: K

Comparison ofTemperature ScalesFigure 2.7 The Three Temperature Scales : 

Comparison ofTemperature ScalesFigure 2.7 The Three Temperature Scales

Temperature Equations : 

Temperature Equations °C  K Equation: TC + 273 = TK °C  °F Equation: 32 + 1.80(TC) = TF

Temperature Conversions : 

Temperature Conversions Example 1: The average temperature in school is 25ºC. What is this temperature in K and in ºF? 32 + 1.80(25ºC) = TF TF = 77ºF 25ºC + 273 = TK TK = 298K

Temperature Conversions : 

Temperature Conversions Example 2: The melting point of the element aluminum is 933 K. What is this temperature in ºC and in ºF? TC + 273 = 933 K TC = 660.ºC 32 + 1.80(660.ºC) = TF TF = 1220ºF

Temperature Conversions : 

Temperature Conversions Example 3: Many meals are reheated at 350.ºF. What is this temperature in K and in ºC? 32 + 1.80(TC) = 350.ºF TC = 177ºC 177ºC + 273 = TK TK = 450.K

Density : 

Density Definition: amount of matter present in a given volume of a substance Equation: density = mass/volume Density can have a variety of units, including g/mL, kg/L, g/cm3, and kg/m3 Specific Gravity: also used to describe a liquid’s density; defined as a liquid’s density/water’s density at 4ºC - no units since it is a ratio of densities

Density Problems : 

Density Problems Example 1: A student measures the mass of 23.5 mL of a certain liquid to be 35.062 g. What is its density? density = 35.062 g 23.5 mL = 1.49 g/mL

More Density Problems : 

More Density Problems Example 2: Iron has a density of 7.87 g/cm3. If the volume of iron is measured to be 75.0 mL, what is its mass? 7.87 g 75.0 cm3 (cm3) x = (7.87 g)(75.0 cm3) x = 590. g cm3 = x Since 1 mL = 1 cm3…

More Density Problems : 

More Density Problems Example 3: Mercury has a density of 13.6 g/mL. What volume of mercury must be taken to obtain 225 g of the metal? 13.6 g mL (13.6 g) x = (225 g)(mL) x = 16.5 mL x = 225 g

More Density Problems : 

More Density Problems Example 4: A student measures the mass of 23.5 mL of a certain liquid to be 35.062 g. What is its density in kg/dm3? density = 35.062 g 23.5 mL = 1.49 kg/L x kg 1 1000 g x mL 1000 L 1 Since 1 L = 1 dm3… = 1.49 kg/dm3

More Density Problems : 

More Density Problems Example 5: If the density of ethylene glycol, commonly known as antifreeze is 1.1 g/mL, how much ethylene glycol is present (in kg) if there is a total volume of 450 mL? 1.1 g 450 mL (mL) x = (1.1 g)(450 mL) x = 5.0x102 g mL = x x 1 1000 g kg = 0.50 kg

More Density Problems : 

More Density Problems Example 6: If the density of copper is 8.92x10-3 kg/dm3, what will be the volume (in mL) of a 62.5 cg sample of copper? 8.92x10-3 g mL (0.625 g)(mL) = (8.92x10-3 g) x x = 70.1 mL 1 kg/dm3 = 1 g/cm3 See examples 1 and 3! = 0.625 g x

More Density Problems : 

More Density Problems Example 7: A sample containing iron pellets (density = 7.87 g/cm3) is poured into a graduated cylinder initially containing 12.7 mL of water. This causes the water level in the cylinder to rise to 21.6 mL. What is the mass of this metal in mg? 7.87 g cm3 (cm3) x = (7.87 g)(8.9 cm3) x = 70. g x = 8.9 cm3 x 1 g mg 1000 = 7.0x104 mg v = 21.6 mL – 12.7 mL

More Density Problems : 

More Density Problems Example 8: 3.5 g of silver (density 10.5 g/cm3) is added to 25.0 mL of water in a graduated cylinder. To what volume reading will the water level in the cylinder rise once the silver is added? 10.5 g mL (10.5 g) x = (3.5 g)(mL) x = 0.33 mL x = 3.5 g volume: 0.33 mL = y – 25.0 mL y = 25.3 mL

NFPA Chemical Hazard Label : 

NFPA Chemical Hazard Label HEALTH SPECIAL REACTIVITY (STABILITY) FLAMMABILITY

NFPA Chemical Hazard Label : 

NFPA Chemical Hazard Label 2 3 4 Flammable vapor which burns readily Substance is stable

NFPA Chemical Hazard Label : 

Burns readily. NFPA Chemical Hazard Label Avoid water. May detonate with heat or ignition. Severe health risk. Diborane

NFPA Chemical Hazard Label : 

NFPA Chemical Hazard Label Complete Label for Phosphine

MSDS : 

MSDS Material Safety Data Sheet On file for all purchased chemicals. Includes all information shown on a chemical label and more. Different formats are used by different chemical companies.