Figure 1.9A The number of significant figures in a measurement depends upon the measuring device. 32.330C 32.30C

Rules for Determining Which Digits are Significant All nonzero digits are significant Zeros in between two nonzero digits are significant Zeros to the left of any nonzero digit are NOT significant Zeros to the right of nonzero digits are significant if the number has a decimal point Zeros that end a number and lie either after or before the decimal point are significant; thus 1.030 ml has four significant figures, and 5300. L has four significant figures also. Numbers such as 5300 L are assumed to only have 2 significant figures. A terminal decimal point is often used to clarify the situation, but scientific notation is the best!

Sample Problem 1.7 Determining the Number of Significant Figures PROBLEM: For each of the following quantities, underline the zeros that are significant figures(sig figs), and determine the number of significant figures in each quantity. For (d) to (f), express each in exponential notation first. (a) 0.0030 L (b) 0.1044 g (c) 53,069 mL (d) 0.00004715 m (e) 57,600. s (f) 0.0000007160 cm3

Rules for Significant Figures in Answers 1. For addition and subtraction. The answer has the same number of decimal places as there are in the measurement with the fewest decimal places. Example: adding two volumes 83.5 mL + 23.28 mL 106.78 mL = 106.8 mL Example: subtracting two volumes 865.9 mL - 2.8121 mL 863.0879 mL = 863.1 mL

Multiply the following numbers: Rules for Significant Figures in Answers 2. For multiplication and division. The number with the least certainty limits the certainty of the result. Therefore, the answer contains the same number of significant figures as there are in the measurement with the fewest significant figures. Multiply the following numbers: 9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm3 = 23 cm3

Rules for Rounding Off Numbers 1. If the digit removed is more than 5, the preceding number increases by 1. 5.379 rounds to 5.38 if three significant figures are retained and to 5.4 if two significant figures are retained. 2. If the digit removed is less than 5, the preceding number is unchanged. 0.2413 rounds to 0.241 if three significant figures are retained and to 0.24 if two significant figures are retained. 3. Be sure to carry two or more additional significant figures through a multistep calculation and round off only the final answer.

Issues Concerning Significant Figures Electronic Calculators be sure to correlate with the problem FIX function on some calculators Choice of Measuring Device graduated cylinder < buret ≤ pipet Exact Numbers 60 min = 1 hr numbers with no uncertainty 1000 mg = 1 g These have as many significant digits as the calculation requires.

Precision and Accuracy Errors in Scientific Measurements Refers to reproducibility or how close the measurements are to each other. Accuracy - Refers to how close a measurement is to the real value. Systematic Error - Values that are either all higher or all lower than the actual value. Random Error - In the absence of systematic error, some values that are higher and some that are lower than the actual value.

Precision and accuracy in the laboratory. Figure 1.10 Precision and accuracy in the laboratory. precise and accurate precise but not accurate

Precision and accuracy in the laboratory. Figure 1.10 continued random error systematic error

Definitions for Components of Matter Element - the simplest type of substance with unique physical and chemical properties. An element consists of only one type of atom. It cannot be broken down into any simpler substances by physical or chemical means. Molecule - a structure that consists of two or more atoms that are chemically bound together and thus behaves as an independent unit. Figure 2.1

Definitions for Components of Matter Compound - a substance composed of two or more elements which are chemically combined. Figure 2.1 Mixture - a group of two or more elements and/or compounds that are physically intermingled.

Law of Mass Conservation: The total mass of substances does not change during a chemical reaction. total mass total mass reactant 1 + reactant 2 product = calcium oxide + carbon dioxide calcium carbonate CaO + CO2 CaCO3 56.08g + 44.00g 100.08g

Law of Definite (or Constant) Composition: Figure 2.2 Law of Definite (or Constant) Composition: No matter the source, a particular compound is composed of the same elements in the same parts (fractions) by mass. Calcium carbonate Analysis by Mass (grams/20.0g) Mass Fraction (parts/1.00 part) Percent by Mass (parts/100 parts) 8.0 g calcium 2.4 g carbon 9.6 g oxygen 20.0 g 0.40 calcium 0.12 carbon 0.48 oxygen 1.00 part by mass 40% calcium 12% carbon 48% oxygen 100% by mass

Law of Multiple Proportions: If elements A and B react to form two compounds, the different masses of B that combine with a fixed mass of A can be expressed as a ratio of small whole numbers. Example: Carbon Oxides A & B Carbon Oxide I : 57.1% oxygen and 42.9% carbon Carbon Oxide II : 72.7% oxygen and 27.3% carbon Assume that you have 100g of each compound. In 100 g of each compound: g O = 57.1 g for oxide I & 72.7 g for oxide II g C = 42.9 g for oxide I & 27.3 g for oxide II g O g C = 57.1 42.9 = 1.33 g O g C 72.7 27.3 = = 2.66 2.66 g O/g C in II 1.33 g O/g C in I 2 1 =