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## Unit 2

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**Unit 2**Scientific Method, Calculations, and Values**Measurements and Calculations in Chemistry**• 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**Experimental Error**• 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.**Accuracy**• So what is Accuracy? • Accuracy of a measurement is how close the measurement is to the TRUE value • “bull’s-eye”**Accuracy**• 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**Precision**• 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”**Error**• Maximizing Accuracy and Precision will help to Minimize ERROR • Error is a measure of all possible “mistakes” or imperfections in our lab data • As we discussed, they can be caused from us (human error), faulty instruments (instrumental error), or from simply selecting the wrong piece of equipment (methodical error)**Error**• Error can be calculated using an “Accepted Value” and comparing it to the “Experimental Value” • The Accepted Value is the correct value based on reliable resources (research, textbooks, peers, internet) • The Experimental Value is the value YOU measure in lab. It is not always going to match the Accepted value… Why not??**Error**• Error is measured as a percent, just as your grades on a test. • Percent Error = accepted – experimental x100% • accepted • This can be remembered as the “BLT” equation: • bigger minus littler over the true value **Significant Figures**• 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**Rules for Determining SigFigs**• Nonzero digits are always significant • Zeros between nonzero digits are significant • Zeros in front of nonzero digits are NOT significant • Zeros both at the end of a number and to the right of a decimal point ARE significant • Zeros at the end of a number but to the left of a decimal point may or may not be significant**SigFigs**• 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**Practice with Sigfigs**• How many sigfigs do the following values have? • 46.3 lbs 40.7 in. 580 mi • 87,009 km 0.009587 m 580. cm • 0.0009 kg 85.00 L 580.0 cm • 9.070000 cm 400. L 580.000 cm**Calc Warning**• Calculators DO NOT present values in the proper number of sigfigs! • Exact Values have unlimited sigfigs • Counted values, conversion factors, constants**Calculating with SigFigs**• 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 This value only has 3 sigfis, therefore the final answer must ONLY have 3 sigfigs!**Calculating with SigFigs**• 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 This value only has 3 sigfis, therefore the final answer must ONLY have 3 sigfigs!**Practice**• How many sigfigs with the following FINAL answers have? Do not calculate. • 12.85 * 0.00125 4,005 * 4000 • 48.12 / 11.2 4000. / 4000.0**Calculating with SigFigs**• 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 The least certain number is only certain to the “tenths” place. Therefore, the final answer can only go out one past the decimal.**Calculating with SigFigs**• 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 Least certain number (total number) The least certain number is only certain to the “tenths” place. Therefore, the final answer can only go out one past the decimal.**Calculating with SigFigs**• 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.**Specific Heat**• 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” • T2 – T1 = ΔT**Calculating Cp**• Cp is usually measured under constant pressure conditions, which is important. Why? • This “constant pressure” is indicated by the p in Cp**Calculating Cp**• Cp = q m * ΔT • Cp = specific heat at a given pressure • q = energy transferred as heat • m = mass of the substance • ΔT = the change in temperature**Practice with Cp**• 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 Cp**• 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 Cp**• 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**Scientific Notation**• Scientific Notation – a number written a the product of two values: • A number out front & • A x10 to a power • This notation allows us to easily work with very, very large numbers or very, very small numbers.**Scientific Notation**• The number out front MUST be written with ONLY one value prior to the decimal point • Examples: • a. 3.24x104g b. 2.5x107mL • = 32,400 grams = 250,000,000 mL**Scientific Notation**• The exponent (x104) value can have a power that is positive or negative, depending on if you are dealing with a SMALL number or a LARGE number • Examples: • a. 8.55x104g b. 4.67x10-5 L • = 85,500 grams = 0.000467 Liters**Scientific Notation**• Addition / Subtraction • 6.2 x 104 + 7.2 x 103**Scientific Notation**• Addition / Subtraction • 6.2 x 104 + 7.2 x 103 • First, make exponents the same • 62 x 103+ 7.2 x 103 • Do the math and put back in Scientific Notation**Scientific Notation**• Multiplication / Division • 3.1 x 103 * 5.01 x 104 • The “mantissas” are multiplied and the exponents are added. • (3.1 * 5.01) x 103+4 • 16 x 107 = 1.6 x 108 • Do the math and put back in Scientific Notation (with correct number of sigfigs)**Homework:**Page 53, #1, 2, 3 Page 62, #14, 15 Due Monday on a separate sheet of paper