Chapter 3: Scientific Measurement

1. 3.1 Chapter 3: Scientific Measurement A measurement is a quantity that has both a number and a unit. Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.

2. Scientific Notation How important is a change in the power of 10? Diameter of Earth’s orbit around the sun ≈ 100,000,000,000 m = 1.0*1011 m Diameter of an atom ≈ 0.0000000001 = 1.0*10-10 m

3. Writing in scientific notation • Move the decimal point in the original number so that it is located to the right of the first nonzero digit. • Multiply the new number by 10 raised to the proper power that is equal to the number of places the decimal moved. • If the decimal point moves: • To the left, the power of 10 is positive. • To the right, the power of 10 is negative.

4. 3.1 Accuracy, Precision, and Error Accuracy is a measure of how close a measurement comes to the actual, true, or accepted value of whatever is measured. Precision is a measure of how close a series of measurements are to one another. • How closely individual measurements compare with each other • The “fineness” of a measurement To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

5. Accurate or Precise? • What is the temperature at which water boils? • Measurements: 95.0°C, 95.1°C, 95.3°C • True value: 100°C Precise! (but not accurate)

6. Accurate or Precise? • What is the temperature at which water freezes? • Measurements: 1.0°C, 1.2°C, -5.0°C • True value: 0.0°C Accurate! (it’s hard to be accurate without being precise)

7. Accurate or Precise? • What is the atmospheric pressure at sea level? • Measurements: 10.01 atm, 0.25 atm, 234.5 atm • True value: 1.00 atm Not Accurate & Not Precise (don’t quit your day job)

8. Accurate or Precise? • What is the mass of one Liter of water? • Measurements: 1.000 kg, 0.999 kg, 1.002 kg • True value: 1.000 kg Accurate & Precise (it’s time to go pro)

9. A graduated cylinder: 41.2 mL (3 sig figs = very precise) 41.0 50 mL Graduated cylinder 100 mL Beaker A beaker: 40. mL (2 sig figs = not as precise) 50

10. Accuracy or Precision? When deciding on accuracy, precision, both, or neither….it is quantitative data (numerical), not qualitative (descriptive) • The recipe calls for 25 chocolate chips per cookie. The cookies analyzed have 34, 35, and 32 chips respectively. • The percent NaCl is 99%, 99%, and 98%. • The number of grams of KF required is 0.04 g. The amounts used were 0.038, 0.039, 0.041, and 0.040 g. • To win, Henry must earn 500 points. In his three trials, he earned 400, 480, and 395 points.

11. 3.1 Accuracy, Precision, and Error Determining Error The accepted value is the correct value based on reliable references. The experimental value is the value measured in the lab. The difference between the experimental value and the accepted value is called the error. • The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.

12. 3.1 Accuracy, Precision, and Error Ex. Find the percent error if your data shows 1.23 g Mg and the true answer is 1.40 g Mg.

13. 3.1 Accuracy, Precision, and Error Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.

14. Significant Figures Every measurement has some degree of uncertainty. • Significant figures (“sig figs”): the digits in a measurement that are reliable (or precise). The greater the number of sig figs, the more precise that measurement is. A more precise instrument will give more sig. figs. in its measurements. The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. Ex. Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to be 2.46 lb. The first two digits (2 and 4) are known. The last digit (6) is an estimate and involves some uncertainty. All three digits convey useful information, however, and are called significant figures.

15. Uncertainty examples: • To measure the time for a pencil to fall…compare a stopwatch and a wall clock. • To measure the volume of a liquid…compare a graduated cylinder and a beaker. The stopwatch & graduated cylinder are more precise instruments…so the readings they produce will have more sig figs.

16. 3.1 Significant Figures in Measurements

17. a. 3 d. unlimited b. 5 e. 4 c. 5 f. 2

18. 3.1 Significant Figures in Calculations In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. The calculated value must be rounded to make it consistent with the measurements from which it was calculated. To round a number, you must first decide how many significant figures your answer should have. The answer depends on the given measurements and on the mathematical process used to arrive at the answer.

19. PACIFIC PACIFIC The “Atlantic-Pacific” Rule “PACIFIC” Decimal point is PRESENT. Count digits from left side, starting with the first nonzero digit. 40603.23 ft2 = 7 sig figs 0.01586 mL = 4 sig figs

20. ATLANTIC ATLANTIC When are digits “significant”? “ATLANTIC” Decimal point is ABSENT. Count digits from right side, starting with the first nonzero digit. 3 sig figs = 40600 ft2 1 sig fig = 1000 mL

21. Examples • 0.00932 Decimal point present → “Pacific” → count digits from left, starting with first nonzero digit = 3 sig figs • 4035 Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit = 4 sig figs • 27510 Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit = 4 sig figs

22. Practice problems Write the following measurements in scientific notation, then record the number of sig figs. • 789 g • 96,875 mL • 0.0000133 J • 8.915 atm • 0.94°C 3 sig figs 7.89*102 g 5 sig figs 9.6875*104 mL 3 sig figs 1.33*10-5 J 4 sig figs 8.915 atm or 8.915 x 100 2 sig figs 9.4*10-1 °C

24. Sig. Figs. In Calculations And Scientific Notation • In this class, we will not follow the sig. fig. rules for operations (see text if interested) • In this class, use scientific notation for all numbers greater than 1000 and smaller than 0.001 • In this class, we will carry all digits in our calculations and then round the final answer to 3 significant digits Exception…in very large or very small numbers, you may use 4 digits in intermediate steps (i.e. 0.0034567432 can be rounded to 0.003457)

25. 3.1 Section Quiz 1. In which of the following expressions is the number on the left NOT equal to the number on the right? a) 0.00456  10–8 = 4.56  10–11 b) 454  10–8 = 4.54  10–6 c) 842.6  104 = 8.426  106 d) 0.00452  106 = 4.52  109

26. 3.1 Section Quiz 2. Which set of measurements of a 2.00-g standard is the most precise? a) 2.00 g, 2.01 g, 1.98 g b) 2.10 g, 2.00 g, 2.20 g c) 2.02 g, 2.03 g, 2.04 g d) 1.50 g, 2.00 g, 2.50 g

27. 3.1 Section Quiz 3. A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement? a) 2 b) 3 c) 4 d) 5

28. 3.2 3.2 The International System of Units In the signs shown here, the distances are listed as numbers with no units attached. Without the units, it is impossible to communicate the measurement to others. When you make a measurement, you must assign the correct units to the numerical value.

29. 3.2 Measuring with SI Units All measurements depend on units that serve as reference standards. The standards of measurement used in science are those of the metric system. The International System of Units (abbreviated SI, after the French name, Le Système International d’Unités) is a revised version of the metric system.

30. 3.2 Measuring with SI Units The five SI base units commonly used by chemists are the meter, the kilogram, the kelvin, the second, and the mole.

31. 3.2 Units and Quantities Units of Length In SI, the basic unit of length, or linear measure, is the meter (m). For very large or and very small lengths, it may be more convenient to use a unit of length that has a prefix.

32. History of SI • The metric system or Système International d'Unités (S.I.), was first organized in Paris as part of the French Revolution and adopted by France in 1795. At that time, the meter and kilogram were standardized. • Why was it organized? It is simple, being based on powers of 10. (like our number system) • Every country in the world uses the metric system except the USA, Myanmar, and Liberia. • By 2009, all products sold in Europe must use the metric system. No dual-labelling will be permitted. • Visit U.S. Metric Association (USMA), Inc. for more info.

33. 3.2 Units and Quantities Common metric units of length include the centimeter, meter, and kilometer.

34. 3.2 Units and Quantities Units of Volume • The SI unit of volume is the amount of space occupied by a cube that is 1 m along each edge. This volume is the cubic meter (m)3. A more convenient unit of volume for everyday use is the liter, a non-SI unit. • A liter (L) is the volume of a cube that is 10 centimeters (10 cm) along each edge (10 cm  10 cm  10 cm = 1000 cm3 = 1 L). • Common metric units of volume include the liter, milliliter, cubic centimeter, and microliter.

35. 3.2 Units and Quantities • A sugar cube has a volume of 1 cm3. 1 mL is the same as 1 cm3. The volume of 20 drops of liquid from a medicine dropper is approximately 1 mL.

36. 3.2 Units and Quantities Units of Mass • The mass of an object is measured in comparison to a standard mass of 1 kilogram (kg), which is the basic SI unit of mass. • A gram (g) is 1/1000 of a kilogram; the mass of 1 cm3 of water at 4°C is 1 g. • Common metric units of mass include kilogram, gram, milligram, and microgram.

37. 3.2 Units and Quantities Weight is a force that measures the pull on a given mass by gravity. The astronaut shown on the surface of the moon weighs one sixth of what he weighs on Earth.

38. 3.2 Units and Quantities Units of Temperature • Temperature is a measure of how hot or cold an object is. • Thermometers are used to measure temperature.

39. 3.2 Units and Quantities • Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin. • On the Celsius scale, the freezing point of water is 0°C and the boiling point is 100°C. • On the Kelvin scale, the freezing point of water is 273.15 kelvins (K), and the boiling point is 373.15 K. • The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to 273.15 °C. • °F = (1.8 * °C) + 32 • °C = (°F-32) 1.8

40. 3.2 Units and Quantities Units of Energy Energy is the capacity to do work or to produce heat. • The joule (J) is the SI unit of energy. • One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1°C. • One Calorie (Cal) equals 1000 calories

41. 3.2 Section Quiz. 1. Which of the following is not a base SI unit? a) meter b) gram c) second d) mole

42. 3.2 Section Quiz. 2. If you measured both the mass and weight of an object on Earth and on the moon, you would find that a) both the mass and the weight do not change. b) both the mass and the weight change. c) the mass remains the same, but the weight changes. d) the mass changes, but the weight remains the same.

43. 3.2 Section Quiz. 3. A temperature of 30 degrees Celsius is equivalent to a) 303 K. b) 300 K. c) 243 K. d) 247 K.

44. 3.33 3.3 Conversion Problems Because each country’s currency compares differently with the U.S. dollar, knowing how to convert currency units correctly is very important. Conversion problems are readily solved by a problem-solving approach called dimensional analysis.

45. Practice Problems before moving on 1) Round to 3 sig. fig. A) 21.8704 B) 0.0021504 C) 6,299,7432) Write answers to #1 in scientific notation 3) Convert 8 km to inches. Use railroad tracks, write in scientific notation, round to 3 digits!

46. 3.3 Conversion Factors A conversion factor is a ratio of equivalent measurements. The ratios 100 cm/1 m and 1 m/100 cm are examples of conversion factors.

47. 3.3 Conversion Factors When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same. The scale of the micrograph is in nanometers. Using the relationship 109 nm = 1 m, you can write the following conversion factors.

48. 3.3 Dimensional Analysis Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements. Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis. Otherwise known as factor label method

49. Dimensional Analysis Use “railroad tracks” Show units Box answer or write answer in statement unless part of a larger problem YOU MUST DO IT MY WAY AND SHOW WORK IF YOU WANT CREDIT Ex. Convert 140,500,000 mL to kL 140,500,000 mL L kL = 140.5 kL (141 kL) 1000 mL 1000L

50. Practice problems • 1) Convert 55°F to °C and K • 2) How many seconds in a year? • 3) Convert 1.23 km to m and then to um • 4) Convert 42.8 kg to oz.