Unit 0: Observation, Measurement and Calculations Cartoon courtesy of NearingZero.net

Steps in the Scientific Method 1.Observations1.Observations - quantitative - qualitative 2.Formulating hypotheses2.Formulating hypotheses - possible explanation for the observation 3.Performing experiments3.Performing experiments - gathering new information to decide whether the hypothesis is valid

Outcomes Over the Long-Term Theory (Model)Theory (Model) - A set of tested hypotheses that give an overall explanation of some natural phenomenon. Natural LawNatural Law - The same observation applies to many different systems - Example - Law of Conservation of Mass

Law vs. Theory A law summarizes what happens  A law summarizes what happens  A theory (model) is an attempt to explain why it happens.

Nature of Measurement Part 1 – number Part 2 - scale (unit) Examples: 20 grams20 grams 6.63 x Joule seconds6.63 x Joule seconds Measurement - quantitative observation consisting of 2 parts consisting of 2 parts

The Fundamental SI Units (le Système International, SI)

SI Prefixes Common to Chemistry

Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Why Is there Uncertainty?  Measurements are performed with instruments  No instrument can read to an infinite number of decimal places

Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value.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.Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate

Types of Error Random Error (Indeterminate Error) - measurement has an equal probability of being high or low.Random Error (Indeterminate Error) - measurement has an equal probability of being high or low. Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.

Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures.Nonzero integers always count as significant figures has 4 sig figs.

Rules for Counting Significant Figures - Details ZerosZeros - Leading zeros do not count as significant figures has 3 sig figs.

Rules for Counting Significant Figures - Details ZerosZeros - Captive zeros always count as significant figures has 4 sig figs.

Rules for Counting Significant Figures - Details ZerosZeros -Trailing zeros are significant only if the number contains a decimal point has 4 sig figs.

Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures.Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm, exactly

Sig Fig Practice #1 How many significant figures in each of the following? m  5 sig figs kg  4 sig figs 100,890 L  5 sig figs 3.29 x 10 3 s  3 sig figs cm  2 sig figs 3,200,000  2 sig figs

Why Sig-Figs in Science? Significant figures indicate the precision of the measured value Math classes don’t deal with measured values so all numbers are considered to be infinitely precise.

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.Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation x 2.0 =  13 (2 sig figs)

Sig Fig Practice # m x 7.0 m CalculationCalculator says:Answer m 2 23 m g ÷ 23.7 cm g/cm g/cm cm x cm cm cm m ÷ 3.0 s m/s240 m/s lb x 3.23 ft lb·ft 5870 lb·ft g ÷ 2.87 mL g/mL2.96 g/mL

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.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)

Sig Fig Practice # m m CalculationCalculator says:Answer m 10.2 m g g g 76.3 g 0.02 cm cm cm 2.39 cm L L L709.2 L lb lb lb lb mL mL 0.16 mL mL

In science, we deal with some very LARGE numbers: 1 mole = In science, we deal with some very SMALL numbers: Mass of an electron = kg Scientific Notation

Imagine the difficulty of calculating the mass of 1 mole of electrons! kg x x ???????????????????????????????????

Scientific Notation: A method of representing very large or very small numbers in the form: M x 10 n M x 10 n  M is a number between 1 and 10  n is an integer

Step #1: Insert an understood decimal point. Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n

2.5 x 10 9 The exponent is the number of places we moved the decimal.

Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n 12345

5.79 x The exponent is negative because the number we started with was less than 1.

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

Review: Scientific notation expresses a number in the form: M x 10 n 1  M  10 n is an integer

4 x x 10 6 IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 7 x 10 6

4 x x 10 6 The same holds true for subtraction in scientific notation. 1 x 10 6

4 x x 10 5 If the exponents are NOT the same, we must move a decimal to make them the same.

4.00 x x 10 5 Student A 40.0 x x 10 5  Is this good scientific notation? NO! = x 10 6 To avoid this problem, move the decimal on the smaller number!

4.00 x x 10 5 Student B.30 x x 10 6  Is this good scientific notation? YES!

A Problem for you… 2.37 x x 10 -4

2.37 x x Solution… x x x 10 -4

Scientific Notation Multiplication 1.Multiply N 1 and N 2 2.Add exponents n 1 and n 2 (4.0 x ) x (7.0 x 10 3 ) = (4.0 x 7.0) x ( ) = 28 x = 2.8 x Division 1.Divide N 1 and N 2 2.Subtract exponents n 1 and n x 10 4 ÷ 5.0 x 10 9 = (8.5 ÷ 5.0) x = 1.7 x 10 -5