1. Scientific Measurement 1.4 Properties that can be measured are called quantitative properties. A measured quantity must always include a unit. The English system has units such as the foot, gallon, pound, etc. The metric system includes units such as the meter, liter, kilogram, etc.

2. SI Base Units The revised metric system is called the International System of Units (abbreviated SI Units) and was designed for universal use by scientists. There are seven SI base units

3. SI Base Units The magnitude of a unit may be tailored to a particular application using prefixes.

4. Mass Mass is a measure of the amount of matter in an object or sample. Because gravity varies from location to location, the weight of an object varies depending on where it is measured. But mass doesn’t change. The SI base unit of mass is the kilogram (kg), but in chemistry the smaller gram (g) is often used. 1 kg = 1000 g = 1×10 3 g Atomic mass unit (amu) is used to express the masses of atoms and other similar sized objects. 1 amu = 1.6605378×10 -24 g

5. Temperature There are two temperature scales used in chemistry: The Celsius scale (°C)  Freezing point (pure water): 0°C  Boiling point (pure water):100°C The Kelvin scale (K)  The “absolute” scale  Lowest possible temperature:0 K (absolute zero) K = °C + 273.15

6. Normal human body temperature can range over the course of a day from about 36°C in the early morning to about 37°C in the afternoon. Express these two temperatures and the range that they span using the Kelvin scale. Worked Example 1.1 Worked Example 1.1 Strategy Use K = °C + 273.15 to convert temperatures from Celsius to Kelvin. Solution 36°C + 273 = 309 K 37°C + 273 = 310 K What range do they span? 310 K - 309 K = 1 K Depending on the precision required, the conversion from °C to K is often simply done by adding 273, rather than 273.15. Think About It Remember that converting a temperature from ° C to K is different from converting a range or difference in temperature from ° C to K.

7. The Fahrenheit scale is common in the United States.  Freezing point (pure water): 32°C  Boiling point (pure water):212°C There are 180 degrees between freezing and boiling in Fahrenheit (212°F-32°F) but only 100 degrees in Celsius (100°C-0°C).  The size of a degree on the Fahrenheit scale is of a degree on the Celsius scale. Temperature Temp in °F = ( × temp in °C ) + 32°F

8. Derived Units: Volume and Density A practical unit for volume is the liter (L).  1 dm 3 = 1 L  1 cm 3 = 1 mL

9. d = density m = mass V = volume SI-derived unit:kilogram per cubic meter (kg/m 3 ) Other common units:g/cm 3 (solids) g/mL (liquids) g/L (gases) Derived Units: Volume and Density The density of a substance is the ratio of mass to volume. https://phet.colorado.edu/en/simulation/density Activity: Which is more dense, ice or liquid water? Propose a hypothesis explaining why.

10. An empty container with a volume of 9.850 x 10 2 cm 3 is weighed and found to have a mass of 124.6 g. The container is filled with a gas and reweighed. The mass of the container and the gas is 126.5 g. Determine the density of the gas to the appropriate number of significant figures. Worked Example 1.6 Worked Example 1.6 Solution 126.5 g – 124.6 g mass of gas = 1.9 g density = Strategy This problem requires two steps: subtraction to determine the mass of the gas, and division to determine its density. Apply the corresponding rule regarding significant figures to each step. ← one place past the decimal point (two sig figs) 1.9 g 9.850 x 10 2 cm 3 ← round to 0.0019 g/cm 3 = 0.00193 g/cm 3 Think About It In this case, although each of the three numbers we started with has four significant figures, the solution only has two significant figures.

11. Uncertainty in Measurement There are two types of numbers used in chemistry: 1) Exact numbers: a)are those that have defined values  1 kg = 1000 g  1 dozen = 12 objects b)are those determined by counting  students in a class 2) Inexact numbers: a)measured by any method other than counting  length, mass, volume, time, speed, etc. Text Practice: 1.33 1.5

12. Uncertainty in Measurement An inexact number must be reported so as to indicate its uncertainty. Significant figures are the meaningful digits in a reported number. The last digit in a measured number is referred to as the uncertain digit. When using the top ruler to measure the memory card, we could estimate 2.5 cm. We are certain about the 2, but we are not certain about the 5. The uncertainty is generally considered to be + 1 in the last digit. 2.5 + 0.1 cm

13. Uncertainty in Measurement When using the bottom ruler to measure the memory card, we might record 2.45 cm. Again, we estimate one more digit than we are certain of. 2.45 + 0.01 cm

14. Significant Figures The number of significant figures can be determined using the following guidelines: 1)Any nonzero digit is significant. 2)Zeros between nonzero digits are significant. 3)Zeros to the left of the first nonzero digit are not significant. 112.14 significant figures 3053 significant figures 0.00232 significant figure 50.084 significant figures 0.0000011 significant figure

15. Significant Figures The number of significant figures can be determined using the following guidelines: 4) Zeros to the right of the last nonzero digit are significant if a decimal is present. 5) Zeros to the right of the last nonzero digit in a number that does not contain a decimal point may or may not be significant. 1.2004 significant figures 1001, 2, or 3 – ambiguous

16. Determine the number of significant figures in the following measurements: (a) 443 cm, (b) 15.03 g, (c) 0.0356 kg Worked Example 1.4 Worked Example 1.4 Strategy Zeros are significant between nonzero digits or after a nonzero digit with a decimal. Zeros may or may not be significant if they appear to the right of a nonzero digit without a decimal. Text Practice: 1.36

17. In addition and subtraction, the answer cannot have more digits to the right of the decimal point than any of the original numbers. 102.50 + 0.231 102.731 ← round to two digits after the decimal point, 102.73 ← two digits after the decimal point ← three digits after the decimal point Calculations with Measured Numbers What about 1.1x10 3 + 345?

18. In multiplication and division, the number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures. 1.4×8.011 = 11.2154 11.57/305.88 = 0.0378252 2 S.F. ←fewest significant figures is 2, so round to 11 4 S.F. ← fewest significant figures is 4, so round to 0.03783 4 S.F.5 S.F. Calculations with Measured Numbers

19. Exact numbers can be considered to have an infinite number of significant figures and do not limit the number of significant figures in a result.  Example: Three pennies each have a mass of 2.5 g. What is the total mass? 3×2.5 = 7.5 g Calculations with Measured Numbers Exact (counting number) Inexact (measurement)

20. In calculations with multiple steps, round at the end of the calculation to reduce any rounding errors.  Do not round after each step. Calculate the following: 3.66 x 8.45 x 2.11 Calculations with Measured Numbers 1) 3.66×8.45 = 30.9 2) 30.9×2.11 = 65.2 1) 3.66×8.45 = 30.93 2) 30.93×2.11 = 65.3 Rounding after each stepRounding at end In general, keep at least one extra digit until the end of a multistep calculation.

21. Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) 317.5 mL + 0.675 mL, (b) 47.80 L – 2.075 L, (c) 13.5 g ÷ 45.18 L, (d) 6.25 cm x 1.175 cm, (e) 5.46x10 2 g + 4.991x10 3 g Worked Example 1.5 Worked Example 1.5 Solution (a) 317.5 mL + 0.675 mL 318.175 mL (b) 47.80 L - 2.075 L 45.725 L Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. ← round to 318.2 mL ← round to 45.73 L

22. Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) 317.5 mL + 0.675 mL, (b) 47.80 L – 2.075 L, (c) 13.5 g ÷ 45.18 L, (d) 6.25 cm x 1.175 cm, (e) 5.46x10 2 g + 4.991x10 3 g Worked Example 1.5 (cont.) Worked Example 1.5 (cont.) Solution (c) 13.5 g 45.18 L (d) 6.25 cm×1.175 cm Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. ← round to 0.299 g/L= 0.298804781 g/L 3 S.F. 4 S.F. ← round to 7.34 cm 2 = 7.34375 cm 2 3 S.F.4 S.F.

23. Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) 317.5 mL + 0.675 mL, (b) 47.80 L – 2.075 L, (c) 13.5 g ÷ 45.18 L, (d) 6.25 cm x 1.175 cm, (e) 5.46x10 2 g + 4.991x10 3 g Worked Example 1.5 (cont.) Worked Example 1.5 (cont.) Solution (e) 5.46 x 10 2 g + 49.91 x 10 2 g 55.37 x 10 2 g Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. = 5.537 x 10 3 g Think About It Changing the answer to correct scientific notation doesn’t change the number of significant figures, but in this case it changes the number of places past the decimal place.

24. Accuracy and Precision Accuracy tells us how close a measurement is to the true value. Precision tells us how close a series of replicate measurements are to one another. Good accuracy and good precision Poor accuracy but good precision Poor accuracy and poor precision

25. Accuracy and Precision Three students were asked to find the mass of an aspirin tablet. The true mass of the tablet is 0.370 g. Student A: Results are precise but not accurate Student B: Results are neither precise nor accurate Student C: Results are both precise and accurate

26. Study Guide for sections 1.4-1.5 DAY 2, Terms to know: Sections 1.4-1.5 mass, atomic mass unit, temperature, volume, density, significant figures, meaningful digit, uncertain digit, accuracy, precision DAY 2, Specific outcomes and skills that may be tested on exam 1: Sections 1.4-1.5 Be able to convert temperature measurements from °C to K and vice versa Be able to explain how to get the correct number of sig figs from a measuring device Given a number that was measured, be able to determine how many sig figs the number has When adding or subtracting measured values, be able to determine the answer with correct sig figs When multiplying or dividing measured values, be able to determine the answer with correct sig figs Be able to recognize when numbers are exact and have infinite sig figs Given measurement(s) and a known value, be able to reasonably describe the accuracy of the measurement(s) Given multiple measurements, be able to reasonably describe the precision of the measurements

27. Extra Practice Problems for sections 1.4-1.5 Complete these problems outside of class until you are confident you have learned the SKILLS in this section outlined on the study guide and we will review some of them next class period. 1.29 1.37 1.39 1.41 1.43 1.49

28. Prepare for Day 3 Must Watch videos: http://www.youtube.com/watch?v=7tVebi3TSsghttp://www.youtube.com/watch?v=7tVebi3TSsg (Tyler DeWitt: density example) http://www.youtube.com/watch?v=Rb6MguN0Uj4http://www.youtube.com/watch?v=Rb6MguN0Uj4 (Tyler DeWitt: cathode ray experiment) http://www.youtube.com/watch?v=dNp-vP17asIhttp://www.youtube.com/watch?v=dNp-vP17asI (Tyler DeWitt: Gold foil experiment) https://www.youtube.com/watch?v=h6LPAwAmnCQ https://www.youtube.com/watch?v=h6LPAwAmnCQ (Tyler DeWitt: atomic structure) Other helpful videos: http://ps.uci.edu/content/chem-1p-preparation-general-chemistryhttp://ps.uci.edu/content/chem-1p-preparation-general-chemistry (UC-Irvine lectures 4 and 5) http://ocw.mit.edu/courses/chemistry/5-111-principles-of-chemical-science-fall-2008/video- lectures/lecture-2/http://ocw.mit.edu/courses/chemistry/5-111-principles-of-chemical-science-fall-2008/video- lectures/lecture-2/ (MIT) Read sections 1.6, 2.1-2.2