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Scientific Method, Calculations, and Values

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Accuracy Vs. Precision Measuring and obtaining data experimentally always comes with some degree of error. Human or method errors & limits of the instruments We want BOTH accuracy AND precision MEASUREMENTS AND CALCULATIONS IN CHEMISTRY

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Selecting the right piece of equipment is key Beaker, Graduated Cylinder, Buret? Measuring 1.5 grams with a balance that only reads to the nearest whole gram would introduce a very large error. EXPERIMENTAL ERROR

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So what is Accuracy? Accuracy of a measurement is how close the measurement is to the TRUE value “bull’s-eye” ACCURACY

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An experiment calls for 36.4 mL to be added Trial 1: delivers 36.1 mL Trial 2: delivers 36.6 mL Which is more accurate??? Trial 2 is closer to the actual value (bull’s-eye), therefore it is more accurate that the first delivery ACCURACY

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Now, what about Precision?? Precision is the exactness of a measurement. It refers to how closely several measurements of the same quantity made in the same way agree with one another. “grouping” PRECISION

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Significant Figures (SigFigs) of a measurement or a calculation consist of all the digits known with certainty as well as one estimated, or uncertain, digit SIGNIFICANT FIGURES

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1.Nonzero digits are always significant 2.Zeros between nonzero digits are significant 3.Zeros in front of nonzero digits are NOT significant 4.Zeros both at the end of a number and to the right of a decimal point ARE significant 5.Zeros at the end of a number but to the left of a decimal point may or may not be significant RULES FOR DETERMINING SIGFIGS

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5.Zeros at the end of a number but to the left of a decimal point may or may not be significant If a zero has not been measured or estimated, it is NOT significant. A decimal point placed after zeros indicates that the zeros are significant. i.e. 2000 m has one sigfig, 2000. m has four SIGFIGS

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How many sigfigs do the following values have? 46.3 lbs40.7 in.580 mi 87,009 km0.009587 m580. cm 0.0009 kg85.00 L580.0 cm 9.070000 cm400. L580.000 cm PRACTICE WITH SIGFIGS

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Calculators DO NOT present values in the proper number of sigfigs! Exact Values have unlimited sigfigs Counted values, conversion factors, constants CALC WARNING

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Multiplying / Dividing The answer cannot have more sigfigs than the value with the smallest number of original sigfigs ex:12.548 x 1.28 = 16.06144 CALCULATING WITH SIGFIGS This value only has 3 sigfis, therefore the final answer must ONLY have 3 sigfigs!

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Multiplying / Dividing The answer cannot have more sigfigs than the value with the smallest number of original sigfigs ex:12.548 x 1.28 = 16.06144 = 16.1 CALCULATING WITH SIGFIGS This value only has 3 sigfis, therefore the final answer must ONLY have 3 sigfigs!

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How many sigfigs with the following FINAL answers have? Do not calculate. 12.85 * 0.001254,005 * 4000 48.12 / 11.24000. / 4000.0 PRACTICE

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Adding / Subtracting The result can be NO MORE certain than the least certain number in the calculation (total number) ex: 12.4 18.387 + 254.0248 284.8118 CALCULATING WITH SIGFIGS The least certain number is only certain to the “tenths” place. Therefore, the final answer can only go out one past the decimal.

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Adding / Subtracting The result can be NO MORE certain than the least certain number in the calculation (total number) ex: 12.4 18.387 + 254.0248 284.8118 = 284.7 CALCULATING WITH SIGFIGS The least certain number is only certain to the “tenths” place. Therefore, the final answer can only go out one past the decimal. Least certain number (total number)

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Both addition / subtraction and multiplication / division Round using the rules after each operation. Ex: (12.8 + 10.148) * 2.2 = 22.9 * 2.2 = 50.38 = 50. CALCULATING WITH SIGFIGS

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Review: What is Specific Heat?? Cp depends on the identity of the material, the mass of the material, and the size of the temperature change. Δ = “Delta” means “change in” T 2 – T 1 = Δ T SPECIFIC HEAT

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Cp is usually measured under constant pressure conditions, which is important. Why? This “constant pressure” is indicated by the p in Cp CALCULATING C P

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Cp = q m * Δ T Cp = specific heat at a given pressure q = energy transferred as heat m = mass of the substance Δ T = the change in temperature CALCULATING C P

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A 4.0 g sample of glass was heated from 274 K to 314 K and was found to absorb 32 J of energy as heat. Calculate the specific heat of this glass. PRACTICE WITH C P

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A 4.0 g sample of glass was heated from 274 K to 314 K and was found to absorb 32 J of energy as heat. Calculate the specific heat of this glass. = 0.20 What are the units of Cp??? PRACTICE WITH C P

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A 4.0 g sample of glass was heated from 274 K to 314 K and was found to absorb 32 J of energy as heat. Calculate the specific heat of this glass. = 0.20 What are the units of Cp??? = 0.20 J/g*K PRACTICE WITH C P

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Review Scientific Notation SCIENTIFIC NOTATION

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Addition / Subtraction 6.2 x 10 4 + 7.2 x 10 3 SCIENTIFIC NOTATION

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Addition / Subtraction 6.2 x 10 4 + 7.2 x 10 3 First, make exponents the same 62 x 10 3 + 7.2 x 10 3 Do the math and put back in Scientific Notation SCIENTIFIC NOTATION

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Multiplication / Division 3.1 x 10 3 * 5.01 x 10 4 The “mantissas” are multiplied and the exponents are added. (3.1 * 5.01) x 10 3+4 16 x 10 7 = 1.6 x 10 8 Do the math and put back in Scientific Notation (with correct number of sigfigs) SCIENTIFIC NOTATION

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Homework: Page 53, #1, 2, 3 Page 62, #14, 15 Due Monday on a separate sheet of paper

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