2 Steps in the Scientific Method 1. Pose problem; Make Observations- quantitative (numerical) Ex: length, height, mass. Benefits: non-biased- qualitative (descriptive) Ex: color, smell, taste. Drawback: biased (opinion)2. Formulating hypotheses- possible explanation for the observation3. Performing experiments- gathering new information to decidewhether the hypothesis is valid
3 Outcomes Over the Long-Term Theory (Model)- A set of tested hypotheses that give an overall explanation of some natural phenomenon.Natural Law- The same observation applies to many different systems
4 A law summarizes what happens Law vs. TheoryA law summarizes what happensA theory (model) is an attempt to explain why it happens.Einstein's theory of gravity describes gravitational forces in terms of the curvature of spacetime caused by the presence of mass
5 Nature of Measurement Part 2 - scale (unit) A measurement is a quantitative observation consisting of 2 parts:Part 1 - numberPart 2 - scale (unit)Examples:20 grams6.63 x Joule·seconds
6 The Fundamental SI Units (le Système International, SI)
8 Derived UnitsA derived unit is calculated by doing some mathematical operation. For Example:Volume = L x w x h Ex: m3 or cm3Volume is a 3-dimensional measurement that measures how much space an object occupiesA common volume measurement used in Chemistry is the Liter (L) and/or the milliliter (ml)Area = L x w Ex: m2
11 Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.Measurements are performed withinstrumentsNo instrument can read to an infinite number of decimal places
12 Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value.Precision refers to the degree of agreement among several measurements made in the same manner.Neither accurate nor precisePrecise but not accuratePrecise AND accurate
13 Types of Error Percent Error: The percent error indicates how far off an observed result (collected data) is from the actual value. If a mass of 15.4 is obtained from a lab scale and the actual value should have been 20.0g, the percent error is calculated as:%error = /observed – expected/ x or /15.4 g – 20.0g/ x 100 = 23%expected gAbsolute Error or “Error Digit” Every measurement in the laboratory comes with some uncertainty. The uncertain digit is always the rightmost digit, or the last digit in the measurement. When using a device such as a graduated cylinder or metric ruler, the actual measurement may fall between two graduation marks on the device. Therefore, the last number is estimated and is “uncertain.” The measurement lies between the graduations and is written as +/- the distance of the graduated unit. For Example:The reading on thegraduated cylinder below The reading in this beakerwould be recorded as: is 48 ml +/- 10 ml ml +/- 1 ml where the 8 is estimatedThe 2 is estimated
14 Examples of Absolute Error in readings that come from a measuring device such as a scale, graduated cylinder or ruler.A scale that gave the reading: g.The error is +/ g (the smallest reading on the scaleA reading from a graduated cylinder that reads 45.67ml has a error of +/ ml, or the smallest reading from the device.A length measurement from a device that reads m has an error of +/ m, or the smallest reading from the device.
15 Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures.3456 has4 sig figs.
16 Rules for Counting Significant Figures - Details Zeros- Leading zeros do not count as significant figures.has3 sig figs.
17 Rules for Counting Significant Figures - Details Zeros- Captive zeros always count as significant figures.16.07 has4 sig figs.
18 Rules for Counting Significant Figures - Details ZerosTrailing zeros are significant only if the number contains a decimal point.9.300 has4 sig figs.
19 Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures.1 inch = cm, exactly
20 Sig Fig Practice #1 1.0070 m 5 sig figs 17.10 kg 4 sig figs How many significant figures in each of the following?m 5 sig figs17.10 kg 4 sig figs100,890 L 5 sig figs3.29 x 103 s 3 sig figscm 2 sig figs3,200,000 2 sig figs
21 Rules for Significant Figures in Mathematical Operations Multiplication and Division:# sig figs in the result equals the number in the least precise measurement used in the calculation.6.38 x 2.0 =12.76 13 (2 sig figs)
22 Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 100.0 g ÷ 23.7 cm3g/cm34.22 g/cm30.02 cm x cmcm20.05 cm2710 m ÷ 3.0 sm/s240 m/slb x 3.23 ftlb·ft5870 lb·ft1.030 g ÷ 2.87 mLg/mL2.96 g/mL
23 Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.= 18.7 (3 sig figs)
24 Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 100.0 g g76.27 g76.3 g0.02 cm cm2.391 cm2.39 cm713.1 L LL709.2 Llb lblblb2.030 mL mL0.16 mL0.160 mL