Measurement Unit Description In this unit we will focus on the mathematical tools we use in science, especially chemistry the metric system and moles. We will also talk about how to gauge the accuracy and precision of our measurements. The Big Questions How do we measure things in chemistry? Why are units so important? How accurate and precise are my measurements and how can I show this in my calculations? How can I move between different measurement units? What the heck are moles and why are they important? Review Topics scientific notation and exponents metric system algebra density calculations dimensional analysis conversions temperature conversions New Topics accuracy vs. precision rounding in chemistry significant figures determining uncertainty of a measurement % error moles - 1 -
Accuracy and Precision Accuracy = how close one comes to the actual value (absolute error) Precision = the agreement of two or more measurements that have been made in the same way (reproducibility) Can you have accuracy without precision? Or precision without accuracy? Why or why not? What are significant figures and why do we use them? Measurements are dependent on the instruments we use. We round our measurements to reflect the level of precision of these instruments. These are significant figures. - 2 -
Rules for Recognizing Significant Figures 1. Non-zero numbers are always significant. 2. Zeros between non-zero numbers are always significant. captive zeros 3. All final zeros to the right of the decimal place are significant. trailing zeros with decimal 4. Zeros that act as placeholders are not significant. trailing zeros without decimal, leading zeros Convert quantities to scientific notation to remove the placeholder zeros. 5. Counting numbers and defined constants have an infinite/unlimited number of significant figures. Recognizing Sig Figs - Practice How many sig figs are in the following measurements? 1. 46 g 7. 0.04066 g 2. 406 g 8. 0.00406600 g 3. 460 g 9. 1.04066 g 4. 460. g 10. 100.040660 g 5. 460.0 g 11. 1000466 g 6. 40660 g 12. 100046600 g - 3 -
Rules for Rounding Numbers If the digit to the immediate right of the last significant figure is 1. < 5, do not change the last significant figure. 2. > 5, round up the last significant figure. 3. = 5, and is followed by a nonzero digit, round up the last significant figure. 4. = 5, and is not followed by a non-zero digit, look at the last significant figure. If it is an odd digit, round it up. If it is an even digit, do not round up. Rounding Practice: Round the following measurements to two sig figs: 13.4 g 13.5 g 13.51 g 14.5 g 14.51 g 14.500001 g 14.500000 g 10.5 g Significant Figures in Measurement consist of all parts of the measurement that you know for sure + one estimated digit e.g. metric ruler, thermometer What about electronic instruments? e.g. electronic balances, digital thermometers The electronics within the instrument estimate the last digit. - 4 -
Addition and Subtraction You cannot be more precise than your last uncertain number. If the mass of something weighed on a truck scale was added to the mass of an object weighed on one of our centigram balances, the sum would NOT be precise to 0.01 g. If you circle the uncertain number (which is significant), it can be seen that in additions and subtractions, you round off to the left-most uncertain number. e.g. 20.53 6.6 3.986 31.116 31.1 An answer is reported to ONE uncertain number. Therefore 31.116 is rounded off to 31.1. Multiplication and Division The product or quotient is precise to the number of significant figures contained in the least precise factor. e.g. 1: 63.2 cm x 5.1 cm = 322.3 cm 2 320 cm 2 (2 sfs) e.g. 2: 5.30 m x 0.006 m = 0.0318 m 2 0.03 m 2 (1 sf) - 5 -
Sig Fig Practice Addition/Subtraction and Multiplication/Division 1. Calculate and round to the correct number of sig figs. a) 4.53 x 0.01 x 700 = b) 2 x 4 x 50400 = c) _0.01_ = 0.0001 d) 3211 + 0.1590 + 3.2 = e) 45119.32 0.001530 = 2. (8.7 + 15.43 + 19)/(4.32 x 1.7) = More Sig Fig Practice Perform each of the following mathematical operations and express each result to the correct number of significant figures. 1. 9.5 ml + 4.1 ml + 2.8 ml + 3.175 ml = 4 (this is an averaging calculation) 2. (8.925 g 8.804 g) x 100% = 8.925 g 3. (9.025 g/ml 9.024 g/ml) x 100% = 9.025 g/ml - 6 -
Uncertainty in Measurement The last place of a measurement is always an estimate The size of the estimate is based on the reliability of the instrument range within which the measured value probably lies Report to only one sig fig. That digit should be in the same decimal place as the last sig fig of the measurement. Correct Incorrect 36.5 ± 0.5 m 36.5 ± 0.25 m 300.4 ± 0.2 g 300.4 ± 0.05 g Percent Error theoretical actual x 100% = % theoretical what you should have got what you got x 100% = % what you should have got - 7 -
Temperature Conversions o C K K o C 259 o C 375 K 15 o C 1462 K -5 o C 186 K -162 o C 5 K - 8 -