1-1 MEASUREMENT AND SIG FIGS

1-2 The number of significant figures in a measurement depends upon the measuring device. Figure 1.9A C C

1-3 Rules for Determining Which Digits are Significant All digits are significant Make sure that the measured quantity has a decimal point. Start at the left of the number and move right until you reach the first nonzero digit. Count that digit and every digit to it’s right as significant. 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! except zeros that are used only to position the decimal point. Zeros that end a number and lie either after or before the decimal point are significant; thus ml has four significant figures, and L has four significant figures also.

1-4 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) g(a) L(c) 53,069 mL (e) 57,600. s(d) m (f) cm 3

1-5 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 mL = mL Example: subtracting two volumes mL = mL mL mL Example: adding two volumes83.5 mL mL

1-6 = cm 3 = 23 cm cm x 6.8 cm x 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:

1-7 Rules for Rounding Off Numbers 1. If the digit removed is more than 5, the preceding number increases by 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 rounds to if three significant figures are retained and to 0.24 if two significant figures are retained. 3.If the digit removed is 5, the preceding number increases by 1 if it is odd and remains unchanged if it is even rounds to 17.8, but rounds to If the 5 is followed only by zeros, rule 3 is followed; if the 5 is followed by nonzeros, rule 1 is followed: rounds to 17.6, but rounds to Be sure to carry two or more additional significant figures through a multistep calculation and round off only the final answer.

1-8 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

1-9 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.

1-10 Figure 1.10 precise and accurate precise but not accurate Precision and accuracy in the laboratory.

1-11 systematic error random error Precision and accuracy in the laboratory. Figure 1.10 continued

1-12 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

1-13 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

1-14 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 g g g Law of Mass Conservation:

1-15 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

1-16 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 = = 1.33 = g O g C = g O/g C in II 1.33 g O/g C in I 2 1 = Law of Multiple Proportions: