CHEM161: Chapter 1 – Independent Review page 1 of 12 Chapter 1: Chemical Foundations (Topics to Review) 1.7 THE SCIENTIFIC METHOD The Scientific Method and Scientific Models 1. Perform experiments and record observations on the system studied. 2. Analyze the data, and propose a hypothesis to explain the observations. 3. Conduct additional experiments to test hypothesis. If initial hypothesis holds up to extensive testing, the hypothesis becomes a theory. theory (or model): a tested explanation of a basic natural phenomenon If all or part of the hypothesis does not hold up to testing, then it is adjusted or a new hypothesis is proposed to explain the observations. natural law: a simple statement or equation summarizing observations Note: A natural law summarizes what happens; a theory explains why it happens. 1.8 MAKING MEASUREMENTS AND EXPRESSING THE RESULTS Consider the three rulers below: Ruler ARuler B0 1 2 3 4 50 1 2 3 4 5Ruler C4.1 4.2 4.3 4.4 A B C Measurement # of sig figsCHEM161: Chapter 1 – Independent Review page 2 of 12 Thus, when a measurement is recorded, all the numbers known with certainty are given along with the last number, which is estimated. All the digits are significant because removing any of the digits changes the measurement's uncertainty. Guidelines for Sig Figs (if measurement is given): Count the number of digits in a measurement from left to right: 1. When there is a decimal point: – For measurements greater than 1, count all the digits (even zeros). – 62.4 cm has 3 sig figs, 5.0 m has 2 sig figs, 186.000 g has 6 s.f. – For measurements less than 1, start with the first nonzero digit and count all digits (even zeros) after it. – 0.011 mL and 0.00022 kg each have 2 sig figs 2. When there is no decimal point: – Count all non-zero digits and zeros between non-zero digits – 125 g has 3 sig figs, 107 mL has 3 sig figs – Placeholder zeros may or may not be significant – 1000 may have 1, 2, 3 or 4 sig figs SCIENTIFIC NOTATION Some numbers are very large or very small → difficult to express. For example, Avogadro’s number = 602,200,000,000,000,000,000,000 → 6.022×1023 an electron’s mass = 0.000 000 000 000 000 000 000 000 000 91 kg → 9.1×10-27 kg Also, it's not clear how many sig figs there are in some measurements, so expressing the final answer in scientific notation can eliminate the ambiguity. For example, Express 100.0 g to 3 sig figs: ______________________ Express 100.0 g to 2 sig figs: ______________________ Express 100.0 g to 1 sig fig: ______________________CHEM161: Chapter 1 – Independent Review page 3 of 12 UNBIASED ROUNDING (or ROUND-TO-EVEN METHOD) How do we eliminate nonsignificant digits? • If first nonsignificant digit < 5, just drop the nonsignificant digits • If first nonsignificant digit ≥ 6, raise the last sig digit by 1 and drop nonsignificant digits • If first nonsignificant digit =5 and – nonzero digits follow 5, raise the last sig digit by 1 and drop nonsignificant digits – e.g. 3.14501 ⎯⎯⎯→⎯s.f. 3 to 3.15 (since nonsig figs are “501” in 3.14501) – no digits or only zeros follow the 5, leave it alone or raise the last sig digit to get an even number and drop nonsignificant zeros – e.g. 3.145 or 3.145000 ⎯⎯⎯→⎯s.f. 3 to 3.14 (to get last sig fig to be an even number) – e.g. 3.175 or 3.175000 ⎯⎯⎯→⎯s.f. 3 to 3.18 (to get last sig fig to be an even number) Express each of the following with the number of sig figs indicated: a. 648.75 ⎯⎯⎯→⎯f. s. 3 to ___________________ d. 0.00123456 ⎯⎯⎯→⎯f. s. 3 to _______________ b. 23.6500 ⎯⎯⎯→⎯f. s. 3 to __________________ e. 1,234,567 ⎯⎯⎯→⎯f. s. 5 to _______________ c. 64.35 ⎯⎯⎯→⎯f. s. 3 to ___________________ f. 1975 ⎯⎯⎯→⎯s.f. 2 to _______________ Instead of using placeholder zeros (e.g. 100 s, 35000 ft.), express measurements in scientific notation (e.g. 1×102 s, 3.5×105 ft) to clarify the number of sig figs in the measurement. ADDING/SUBTRACTING MEASUREMENTS When adding and subtracting measurements, your final value is limited by the measurement with the largest uncertainty—i.e. the measurement with the fewest decimal places. MULTIPLYING/DIVIDING MEASUREMENTS When multiplying or dividing measurements, the final value is limited by the measurement with the least number of significant figures. Ex. 1: 7.4333 g + 8.25 g + 10.781 g = ______________________ Ex. 2: 13.55 cm × 7.95 cm × 4.00 cm = ______________________ Ex. 3: 9.75 mL − 7.35 mL = ______________________ Ex. 4: cm 8.50 cm 10.25 cm 25.75g 101.755 ××= ______________________CHEM161: Chapter 1 – Independent Review page 4 of 12 MULTIPLYING/DIVIDING WITH EXPONENTIAL NUMBERS: When multiplying or dividing measurements with exponents, use the digit term (N in “N×10n”) to determine number of sig figs. Ex. 1: (6.02×1023) (4.155×109) = 2.50131×1033 How do you calculate this using your scientific calculator? Step 1. Enter “6.02 × 1023” by pressing: 6.02 then EE or EXP (which corresponds to “×10”) then 23 → Your calculator display should be as follows: Step 2. Multiply by pressing: × Step 3. Enter “4.155×109” by pressing: 4.155 then EE or EXP then 9 → Your calculator should now read Step 4. Get the answer by pressing: = → Your calculator should now read: or something similar indicating 2.50131×1033 Thus, the answer with the correct sig figs is 2.50×1033 Be sure you can do exponential calculations with your calculator. Many calculations we do in chemistry involve numbers in scientific notation. Ex. 2: (3.75×1015) (8.6×104) = 3.225×1020 ⎯⎯⎯⎯⎯⎯→⎯figs sig of #correct to ___________________ Ex. 3: 415108.605103.75××= 4.357931435×1010 ⎯⎯⎯⎯⎯⎯→⎯figs sig of #correct to ___________________ EXACT NUMBERS Although measurements can never be exact, we can count an exact number of items. For example, we can count exactly how many students are present in a classroom, how many M&Ms are in a bowl, how many apples in a barrel. We say that exact numbers of objects have an infinite number of significant figures. 6.02 ×1023 4.155 ×1009 2.501313 ×1033CHEM161: