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# Unit 2

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1. Unit 2 Scientific Method, Calculations, and Values

2. 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

3. 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.

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

5. 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

6. 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”

7. 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)

8. 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??

9. 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 

10. Practice with Error

11. 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

12. 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

13. 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

14. 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

15. Calc Warning • Calculators DO NOT present values in the proper number of sigfigs! • Exact Values have unlimited sigfigs • Counted values, conversion factors, constants

16. 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!

17. 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!

18. 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

19. 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.

20. 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.

21. 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.

22. 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

23. Calculating Cp • Cp is usually measured under constant pressure conditions, which is important. Why? • This “constant pressure” is indicated by the p in Cp

24. 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

25. 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.

26. 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???

27. 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

28. 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.

29. 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

30. 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

31. Scientific Notation • Addition / Subtraction • 6.2 x 104 + 7.2 x 103

32. 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

33. 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)

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