Measurement, Error, & Uncertainty Overview Units in chemistry Graphs Scientific notation & Orders of Magnitude Error and Significant Figures

Units Metric system: SI = Système Internationale Length: meters (m) centimeters (cm) 100 cm = 1 m Millimeters (mm) 1000 mm = 1 m Kilometers (km) 1000 m = 1 km Temperature: Kelvin (K) = oC + 273.15

Units Mass Grams (g) Milligrams (mg) 1000 mg = 1 g Kilograms (kg) 1000 g = 1 kg Volume Liters (L) Milliliters (mL) 1000 mL = 1 L Time Sec (s)

Problem 1 Express the following in the units indicated: 558 m in km 0.00894 g in mg 116,322 mL in L 0.00889 kg in g, in mg

Problem 1 1000 km·m = 558 m·x km 558 m in km 1000 m = 1 km 558. m b) 0.00894 g in mg 1000 mg = 1 g = 8.94 mg

Problem 1 c) 116,322 mL in L 1000 mL = 1 L 116,322 mL = 116.322 L d) 0.00889 kg in g, in mg 1000 g = 1 kg 0.00889 kg = 8.89 g = 0.00889 mg

Graphs Reading graphs

Reading Graphs

Ozone Levels Problem 2 What time of day are ozone levels at their lowest? What time of day are ozone levels at their highest? If levels > 84 ppb are considered harmful, what percentage of the day has levels above “harmful”?

Rationale for Graphing Mass (g) Volume (mL) 2.334 1.63 5.743 4.02 9.944 6.96 7.002 4.90 Power of the visual depiction of data to understand relationships

Scientific Notation Used to express very large or very small numbers: 55,800,000 km from earth to sun: 5.58 x 107 km Mass of a H atom: 0.00000000000000000000000168 g 1.68 x 10–24 g

Problem 3 Put the following numbers into scientific notation 346,000,000,000 0.00049100 0.000000005664 340

Problem 3 346,000,000,000 = 3.46 x 1011 0.00049100 = 4.9100 x 10–4 0.000000005664 = 5.664 x 10–9 340 = 3.4 x 102

Significant Figures and Error E.g. Density calculation: 22 g has volume of 19 mL Density = 1.157894737 g/mL Not truthful value Precision vs. Accuracy

Precision vs. Accuracy Precision: depends upon the detection limit or “sensitivity” of the instrument used Accuracy: Difference between the “true value” and the average of a series of measurements True values rarely known: need multiple, repetitive measurements

Precision vs. Accuracy

Types of “Error” Every scientific measurement has error associated with it Error implies mistake: uncertainty better way to look at it Random (indeterminate) error: result from large number of minute variations in materials, conditions, equipment, etc.; completely unavoidable. Can be (never eliminated) mitigated by improving precision, calibration Systematic (determinate) error: result of inaccurate calibration, sampling or procedural bias, operator error, etc. Measurements are systematically low or high. Only error that we can eliminate

Precision vs. Accuracy bias bias

Back to Significant Figures Place holders: not significant Actual values or illustrating precision: significant E.g.: 45,600 vs. 45,600.0 0.0067 vs. 0.006700 Scientific notation solves issue 2.34 x 10–4 compared to 2.3400 x 10–4

Full Disclosure Significant figures: crude approach Standard deviation (statistics) more appropriate Error values (error bars on graphs) 3.44 mL  0.04 mL implies range 3.40 – 3.48 mL If error were  0.1, could only report 3.4  0.1

Error Bars