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Chapter 2 – Measurement and Calculations Taken from Modern Chemistry written by Davis, Metcalfe, Williams & Castka Scientific Method Section 1 - Objectives – Describe the purpose of the scientific method. – Distinguish between qualitative and quantitative observations. – Describe the differences between: – Hypotheses – theories – and models Section 2-1 The 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 in 3. Hypothesis that by eliminating something I will get a better nights sleep 4. Test the same 5. Come up with theory supported by data Section 2-1 (continued) Observing and Collecting Data Observing 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 Section 2-1 (continued) Formulating Hypothesis A hypothesis is a testable statement. “if...then” •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. Section 2-1 (continued) Testing Hypothesis Testing a hypothesis requires experimentation. •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.) Section 2-1 (continued) Theorizing A model in science is often used as an explanation of how phenomenon occur and how data or events are related. A theory is a broad generalization that explains a body of facts or phenomena. Section 2-1 (continued) Experimental Design – POGIL Units of Measurement Section 2 - Homework Notes on section 2.2 only pages 33-38. Units of Measurement Section 2 - Objectives – 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 2-2 Measurements represent quantities. A quantity is something that has a magnitude and a size or amount. My mass and height Section 2-2 (continued) SI Measurements 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. Section 2-2 (continued) SI Base Units - Mass Mass is a measure of the quantity of matter. SI Standard is the kilogram (kg). ~2.2 pounds The gram (g) which is 1/1000th of a kilogram is more commonly used for smaller objects. Section 2-2 (continued) SI Base Units – Mass (continued) Mass should not be confused with weight. Weight is a measure of the gravitational pull on matter Mass is measured with a balance. Weight is measured with a spring scale.. Section 2-2 (continued) SI Base Units – Length SI standard is the meter (m). 1 meter = 39.3701 inches To express longer distances the kilometer (km) is used, = 1000 meters Section 2-2 (continued) Derived SI units Combinations of SI base units form derived units. EXAMPLES 2 m = length x width Others are given there own name… kg/m∙s2 This is a pascal (Pa) and it is used to measure pressure. Section 2-2 (continued) Derived SI Units (continued) – Volume Volume is the amount of space occupied by an object. 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 Section 2-2 (continued) Derived SI Units (continued) – Density Density is the ratio of mass to volume, written as mass divided by volume.. D= m/ v Earth based reference The density of H2O @ 4 ° C = 1 g/cm3 Section 2-2 (continued) Derived SI Units– Density (continued) We are going to practice by finding the Section 2-2 (continued) Derived SI Units– Density (continued) Section 2-2 (continued) Conversion Factors 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 Section 2-2 (continued) Conversion Factors - Deriving Conversion Factors We can deriver a conversion factor when we know the relationship between the factors we have and the units we what. Section 2-2 (continued) Conversion Factors - Deriving Conversion Factors Practice HW / Classwork (depends) – Section review bottom of page 42 questions 2-5 all Section 2-2 (continued) Conversion Factors – Metrics (step method) The next slide will teach you about: King henry died by drinking chocolate milk under no pressure Kilo- (k) Decimal Moves to left 103 Hecto(h) Deka102 (da) Base 10 ________ Remember The decimal moves the way you are stepping ____ Liters Deci(d) Meters 10-1 Grams Larger Units Smaller Units Centi(c) 10-2 Milli(m) 10-3 Micro (µ) 10-6 nano- (n) Decimal Moves to right 10-9 pico (p) 10-12 Kilo- (k) Decimal Moves to left 103 Hecto(h) Deka102 (da) Base 10 ________ Remember The decimal moves the way you are stepping ____ Liters Deci(d) Meters 10-1 Grams Larger Units Smaller Units Centi(c) 10-2 Step Practice HW Milli(m) 10-3 Micro (µ) 10-6 nano- (n) Decimal Moves to right 10-9 pico (p) 10-12 Using Scientific Measurements Section 3 - Objectives HW Notes on this section with these objectives in mind – 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 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. Section 2-3 (continued) Accuracy and Precision (continued) – Percent Error ( VALUEACCEPTED – VALUEEXPERIMENTAL) Percent error = ----------------------------------------------------- x 100 VALUEACCEPTED % error is positive (+) when the VALUEACCEPTED is greater than VALUEEXPERIMENTAL % error is negative (-) when the VALUEACCEPTED is less than VALUEEXPERIMENTAL Section 2-3 (continued) Accuracy and Precision (continued) – Percent Error ( VALUEACCEPTED – VALUEEXPERIMENTAL) Percent error = ----------------------------------------------------- x 100 VALUEACCEPTED EXAMPLE 1 (time estimation) EXAMPLE 2 (penny density) Section 2-3 (continued) Accuracy and Precision (continued) – Error in Measurement Some error or uncertainty always exists in any measurement. Reasons Skill of measurer conditions (temperature, air pressure, humidity etc) Instruments themselves Section 2-3 (continued) Accuracy and Precision – Error in Measurement (continued) ONLY NEED TO COPY THE RED Ways to Improve Accuracy in Measurement 1. 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. Using Scientific Measurements Section 2.3 (second) - Objectives – Determine the number of significant figures in measurements. – Perform mathematical operations involving significant figures. HW Notes on this section with these objectives in mind Pgs 46-50 Section 2-2 (continued) Accuracy and Precision – POGIL Up to Problem # 22 Section 2-3 Significant figures (‘Sig 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 digits EXAMPLES 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. 12 eggs 2001 Dalmations 172.00 Kg 10000. L Section 2-3 Significant Figures – Determining the number of significant digits (continued) Number 48,923 3.967 900.06 0.0004 (= 4 E-4) 8.1000 501.040 3,000,000 (= 3 E+6) 10.0 (= 1.00 E+1) # Significant Figures 5 4 5 1 5 6 1 3 Rule(s) 1 1 1,2,4 1,4 1,3 1,2,3,4 1 1,3,4 Section 2-3 Significant Figures – 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 (continued) PRACTICE # 1 (only front side) PRACTICE # 2 (only front side) Section 2-3 Significant Figures (continued) – Addition or subtraction with Significant 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 with 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. Example Density = mass ÷ volume 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 & Significant 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 Break Practice break (the other sides & more) PRACTICE # 1 (only back side) PRACTICE # 2 (only back side) TONIGHT’S HW HW in advance: Notes to the end of the chapter for Friday Section 2-3 Scientific Notation In scientific 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 1.49e8 0.000181 m 1.81 x 10-4 m 1.81e-4 Section 2-3 Scientific Notation (continued) – Mathematical Operations using Scientific Notation – addition & subtraction To add or subtract you must make the exponents the same 1.49 x 104 km 1.81 x 103 OR EITHER Examples - adding km 14.9 x 103 km 1.49 x 104 km km 0.181 x 104 km 16.71 x 103 km 1.671 x 104 km 1.81 x 103 16.7 x 103 km Remember rounding 1.67 x 104 km Section 2-3 Scientific Notation (continued) – Mathematical Operations using Scientific Notation – addition & subtraction UNITS TOO (don’t get tripped up on this) Examples 1.49 x 105 km Becomes 1.49 x 108 m 5.02 x 104 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 using 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 using Scientific Notation – Division M factors are divided and ns are subtracted denominator from numerator Examples 7 g 5.44 x 10 _____________ 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 Break A 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 PRACTICE Adding & Subtracting Multiplying & Dividing PRACTICE Sig Figs Key to Sig Figs Section 2-2 (continued) Significant Figures – POGIL HW Chapter Review Key Section 2-3 Direct & Inverse Proportions Graphing Practice What the results should look like: Chapter Summary Questions HW – pages 60-61 27, 31, 34, 36, 43, 48 & 57 Supplemental Scientific Notation Material Back 27 Density = Mass / Volume 5.03 g / 3.24 mL = 1.552496...... g/mL Rounded = 1.55 g/mL 31 0.603 L x 1000 ml/L = 6.03 x 102 mL 34 ( VALUEACCEPTED – VALUEEXPERIMENTAL) Percent error = ----------------------------------------------------- x 100% VALUEACCEPTED ((1.54 g/cm3 – 1.25 g/cm3) / 1.54 g/cm3) x 100% = 18.8311.....% Rounded = 18.8 % 36 a) b) c) d) Four One Six Three 43 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 48 Density = Mass / Volume 57.6 g / 40.25 cm3 = 1.4310559....... g/cm3 Rounded = 1.43 g/cm3 57 a) 2 g fat = 15 calories 1g = 7.5 Cal 8 Cal/g a) 0.6 kg b) 2 x 105 μg c) One; the value 2 g limits the number of significant figures for these data. Supplemental Scientific Notation Adding (or substracting) 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 PRACTICE Adding & Subtracting Saturn is approximately 7.9 × 108 miles more from the sun than Earth is. Supplemental Scientific Notation Multiplying & Dividing PRACTICE Multiplying & Dividing