Significant Figures, Precision and Accuracy, and Dimensional Analysis

Transcription

1 Significant Figures, Precision and Accuracy, and Dimensional Analysis 1 I. SIGNIFICANT FIGURES - In chemistry, when do we need to worry about the digits reported in a number? 1. Significant Figure Rules (Other Peoples Numbers) - non-zero digits are always considered to be significant 1. Zeros between nonzero digits Significant Figures Rule! 2. Zeros before nonzero digits are

2 3. Zeros that fall both at the end of a number and after the decimal point 2 4. Zeros at the end of a number without a decimal point 5. Exact numbers can viewed as having

3 2. Guidelines for Calculations Rounding Off and When to Round Off In all work keep two extra non-significant digits until the end, then simplify 3 # to right of last sig fig is 0,1,2,3,4 keep # as is g g (3 s.f.) 5,6,7,8,9 round up g g (3 s.f.) Dashed Line - Use a dashed line to show where significant figures end for intermediate and unrounded values Calculations (Multiplication and Division) 1. When multiplying and dividing, the final answer should contain the same number of sig. fig. as the number in the equation with the fewest sig. figs. (# number of sig figs)

4 Uncertainty - Magnitude of error in last digit of measurement or calc. (i.e. last sig. fig.) - Reported as +/- # e.g /- 0.2 cm Range of values cm No # given assume +/- 1 in last sig digit 4 Absolute Uncertainty (a.u.) - Absolute value of uncertainty Calculations (Addition and Subtraction) 2. When adding and subtracting, the final answer should have the same absolute uncertainty as the number in the equation with the largest absolute uncertainty. (location of last sig fig)

5 Calculations (Averages) 3. When calculating an average, follow the same rules for addition and subtraction. (location of last sig fig) 5 More Notation and Terms Relative Uncertainty (ru) absolute uncertainty (au) ru measured value - evaluates how good your measurement is (smaller the better) e.g. 1 cm au for a measurement of 10. cm 1 cm au for a measurement of cm

6 B. Significant Figures (Measurements Made by You Using a Linear Scale) 6 1. Find the value of the increment 2. Determine the family of the scale

7 3. Determine the absolute uncertainty of the scale 7 4. Make Measurement - To estimate the last digit in the measurement, divide the spaces between the increments into equal spaces 2 s Family 2 spaces 5 s Family 5 spaces 10 s Family 10 spaces

8 II. PRECISION AND ACCURACY PAY ATTENTION TO UNITS AND SIG FIGS Precision- A measure of how close each trial is to the others 8 Accuracy- A measure of the closeness of a measured or average value to the true or acceptable value

9 III. Dimensional Analysis How many cm in a furlong? 9 - A method for solving mathematical problems using conversion factors Conversion Factor ratio used to convert one number with a set of units into another number with a different set of units Example Problems 1. How many femtometers in 2.34x10-3 in?

10 2. I recently purchased ml of fresh squeezed OJ at COSTCO. What is the volume in m 3? 10

11 3. While digging in my backyard over the break, I found a shiny kg rock. I determined the rock was composed of only one type of element. Curious as to its identity, I chipped off a 16.4 g piece of the rock, measured its volume, and calculated its density. a.) If the volume of the sample was 7.645x10 8 pl, what density (in g/ml) did I calculate? b.) What is the rock composed of? Should I quit my day job at OCC and excavate my backyard? 11

12 3. Cont d While digging in my backyard over the break, I found a shiny kg rock. I determined the rock was composed of only one type of element. Curious as to its identity, I chipped off a 16.4 g piece of the rock, measured its volume, and calculated its density. a.) If the volume of the sample was 7.645x10 8 pl, what density (in g/ml) did I calculate? b.) What is the rock composed of? Should I quit my day job at OCC and excavate my backyard? 12

13 4. A solution containing a 12.0% sodium hydroxide by mass has a density of g/ml. What volume of this solution, in liters, must be used in an application requiring kg of sodium hydroxide? 13

14 Blood alcohol content (BAC) is sometimes reported in weight-volume percent and, when it is, a BAC of 0.10% corresponds to 0.10 g ethyl alcohol per 100 ml of blood. In many jurisdictions, a person is considered legally intoxicated if his or her BAC is 0.10%. Suppose that a 68 kg person has a total blood volume of 5.4 L and breaks down ethyl alcohol at a rate of 10.0 grams per hour. (*The rate at which ethyl alcohol is broken down varies dramatically from person to person. The value given here for the rate is a realistic, but not necessarily accurate, value.) How many 145 ml glasses of wine, consumed over three hours, will produce a BAC of 0.10% in this 68 kg person? Assume the wine has a density of 1.01 g/ml and is 11.5% ethyl alcohol by mass. 14