# Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 The number of significant figures in a measurement depends.

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Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 The number of significant figures in a measurement depends upon the measuring device. Figure 1.9A 32.3 0 C32.33 0 C

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-2 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 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! 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.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-3 Sample Problem 1.7Determining 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. (b) 0.1044 g(a) 0.0030 L(c) 53,069 mL (e) 57,600. s(d) 0.00004715 m (f) 0.0000007160 cm 3

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-4 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. 106.78 mL = 106.8 mL Example: subtracting two volumes 863.0879 mL = 863.1 mL 865.9 mL - 2.8121 mL Example: adding two volumes83.5 mL + 23.28 mL

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-5 = 23.4225 cm 3 = 23 cm 3 9.2 cm x 6.8 cm x 0.3744 cm 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. Rules for Significant Figures in Answers Multiply the following numbers:

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-6 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.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-7 Issues Concerning Significant Figures graduated cylinder < buret ≤ pipet numbers with no uncertainty 1000 mg = 1 g 60 min = 1 hr These have as many significant digits as the calculation requires. be sure to correlate with the problem FIX function on some calculators Electronic Calculators Choice of Measuring Device Exact Numbers

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-8 Precision and Accuracy Errors in Scientific Measurements Random Error - In the absence of systematic error, some values that are higher and some that are lower than the actual value. Precision - 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.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-9 Figure 1.10 precise and accurate precise but not accurate Precision and accuracy in the laboratory.

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-10 systematic error random error Precision and accuracy in the laboratory. Figure 1.10 continued

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-11 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

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-12 Compound - a substance composed of two or more elements which are chemically combined. Mixture - a group of two or more elements and/or compounds that are physically intermingled. Definitions for Components of Matter Figure 2.1

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-13 The total mass of substances does not change during a chemical reaction. reactant 1 + reactant 2product total mass = calcium oxide + carbon dioxidecalcium carbonate CaO + CO 2 CaCO 3 56.08g + 44.00g 100.08g Law of Mass Conservation:

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-14 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 40% calcium 12% carbon 48% oxygen 100% by mass 0.40 calcium 0.12 carbon 0.48 oxygen 1.00 part by mass Law of Definite (or Constant) Composition: Figure 2.2

Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-15 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 = Law of Multiple Proportions:

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