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Unit 1: Basic Chemical Math

Learn about types of observations, SI units, and accuracy in measurements with examples and practice questions for mastering chemical math concepts. Understand significant figures, precision, and important measurement tools.

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Unit 1: Basic Chemical Math

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  1. Unit 1: Basic Chemical Math

  2. Scientific Method • Observation • Question • Hypothesis • Method • Results • Conclusion

  3. Types of Observations and Measurements • A qualitative measurement is something that cannot be measured in numbers. • Usually referred to as an observation • Ex: odor, texture, color • Quantitative measurements are those which involve the collection of numbers. • Ex: temperature, mass, volume • In chemistry SI units are used (International System of Units) — based on the metric system • Ex: Grams, meters, liters • As opposed to U.S customary units • Ex: Pounds, feet, gallons

  4. UNITS OF MEASUREMENT Use SI units — based on the metric system Length Mass Volume Time Temperature Meter, m Gram, g Liter, L Seconds, s Celsius degrees, ˚C kelvins, K

  5. Standards of Measurement • At one time the standard for length was the king’s foot. What are some problems with this standard? • When we measure, we use a measuring tool to compare some dimension of an object to a standard. • We need a standard so we have a common understanding and can communicate, visualize, and compare measurements.

  6. Chemistry In Action On 9/23/99, $125,000,000 Mars Climate Orbiter was launched by NASA to study the climate of Mars. The Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat. This miscalculation was due to the computer software using non-SI units instead of the SI units NASA expected. All of this money was lost because of a miscommunication of units. “This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

  7. Stating a Measurement In every measurement there is a • Number followed by a • Unit from a measuring device

  8. Some Tools for Measurement Which tool(s) would you use to measure: A. temperature B. volume C. time D. mass

  9. Learning Check Match L) length M) mass V) volume ____ 1. A bag of tomatoes is 4.6 kg. ____ 2. A person is 2.0 m tall. ____ 3. A medication contains 0.50 g Aspirin. ____ 4. A bottle contains 1.5 L of water. M L M V

  10. Accuracy and Precision Three targets with three arrows each to shoot. How do they compare? Both accurate and precise Precise but not accurate Neither accurate nor precise Can you define accuracy and precision? Accuracy refers to the correctness and precision refers to consistency of measurements

  11. Significant Figures and Measurements • Significant figures (also called Sig Figs) of a number are digits that carry meaning contributing to the measurements accuracy. • More significant figures in a measurement means a more accurate measurement. • For example: If someone asks you how much money is in your bank account you might say $50, but your banking app would say $51.37. Which is a more accurate measurement? • Counting is a common type of measurement. The measurement is EXACT and can be expressed without error. • Ex: 26 students in a classroom, then there are truly 26 students in a classroom at that given time. Not 25 or 26.5, exactly 26. • Exact numbers have infinite significant figures. They are 100% accurate. • Exact numbers: counting and numbers from defined relationships (1 foot = 12 inches; 1 L = 1000 mL)

  12. Significant Figures • In other situations, measurement possesses some degree of error or uncertainty. In other words they are NOT EXACT. • Ex: measuring the width of a desk or reading the temperature from a thermometer • Measurements can only be as accurate as the device used to measure. • In science, measurements should only have ONE degree of uncertainty (or only one estimated digit). • Significant Figures come from the certain digits and the one estimated digit of a measurement. • The number of significant figures will tell us the accuracy of the measurement.

  13. Reading a Measurement- Example 1 . l2. . . . I . . . . I3 . . . .I . . . . I4. . cm Measure the blue line. First digit (known) = 2 2.?? cm Second digit (known) = 0.7 2.7? cm Third digit (estimated) between 0.05- 0.07 Length reported = 2.75 cm or 2.74 cm or 2.76 cm

  14. Known + Estimated Digits In 2.76 cm… • Known digits2and7are 100% certainThe third digit 6 is estimated (uncertain) • In the reported length, all three digits (2.76 cm) are significant including the estimated one • This measurement has 3 sig figs.

  15. Measuring • The certain digits come from the markings on the measuring tool • For example: If the device has markings that represent 1 mL, then the ones place is certain and you would estimate the tenths place (the first decimal) • For example: If the device has markings that represent 0.1 cm, then the tenths place is certain and you would estimate the hundredths place (the second decimal) • Always measure one place value past what the device measures • What is the measuring tool has markings that represent 100 mL, what place value would you estimate?

  16. Example 2: . l8. . . . I . . . . I9. . . .I . . . . I10. . cm What is the length of the line? 1) 9.6 cm 2) 9.60 cm 3) 9.600 cm • How many sig figs does this measurement have?

  17. Zero as a Measured Number- Example 3 . l3. . . . I . . . . I4 . . . . I . . . . I5. . cm What is the length of the line? First digit 5.?? cm Second digit 5.0? cm Last (estimated) digit is 5.00 cm

  18. Example 4 • If you are measuring the temperature of the room and you had the two thermometers below, which would give you a measurement with more accurate measurement and why? • Take the measurement using both thermometers. Remember you can only estimate 1 digit. How many significant figures are in each measurement?

  19. Always estimate ONE digit! Example 5: Example 6: mL mL • Measure volume from the bottom of the meniscus • Meniscus= the curved upper surface of a liquid in a tube.

  20. Digital Devices • Tools that take measurements digitally include the estimated digit in the measurement • For example… • If a piece of iron is measured on an electron balance and the balance reads 5.68g • The 5 and 6 are certain where the 8 is estimated by the scale

  21. 5 Rules for determining Significant Figures in a measurement • All digits 1-9 are significant • Zeros between significant digits are always significant. • Ex. 2007 has 4 sig figs • Trailing zeros in a number are significant ONLY if the number contains a decimal point. • Example: 100.0 has 4 sig figs 100 only has 1 sig fig. • Zeros in the beginning of a number that only serve as a placeholder are NOT significant. • Ex. 0.0025 only has 2 sig figs • Zeros following a decimal significant figure are significant. • Ex. 0.00470 has 3 sig figs

  22. Sig Figs • The “Cheat-Sheet” Version of determining if a number is significant or not is called the Atlantic-Pacific Rule for Sig Figs. • If there is a decimal point PRESENT, count from the PACIFIC side of the number, beginning with the first non-zero digit. • If the decimal point is ABSENT, count from the ATLANTIC side of the number, beginning with the first non-zero digit.

  23. Atlantic = decimal absent. Travel until you meet the first non-zero digit. It and everything after is significant. Pacific = decimal present. Travel until you meet the first non-zero digit. It and everything after is significant. * With scientific notation the x 10n is ignored when counting sig figs

  24. Learning Check 1) Which answers contain 3 significant figures? A) 0.4760 B) 0.00476 C) 4760 2) All the zeros are significant in A) 0.00307 B) 25.300 C) 2.050 x 103 3) 534,675 rounded to 3 significant figures is A) 535 B) 535,000 C) 5.35 x 105

  25. Learning Check 4) In which set(s) do both numbers contain the same number of significant figures? A) 22.0 and 22.00 B) 400.0 and 40 C) 0.000015 and 150,000

  26. Learning Check State the number of significant figures in each of the following: 5.) 0.030 m 6.) 4.050 L 7.) 1.200 x 10-34 mg 8.) 5 x 109 kJ 9.) 300. m 10.) 2,080,000 bees

  27. Significant Numbers in Calculations • A calculated answer cannot be more accurate than the measuring tool. • A calculated answer must match the least accurate measurement. • Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing • When rounding, if the digit used to round is 5 or above round up • Example: 8.450090983 rounded to 2 sig figs would be 8.5

  28. Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34two decimal places 26.54 answer 26.5 one decimal place

  29. Learning Check In each calculation, round the answer to the correct number of significant figures. 1. 235.05 + 19.6 + 2.1 = 2. 58.925 - 18.2 =

  30. Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. 15.7 x 0.63 = 3 sf x 2 sf = 2 sf

  31. Learning Check 1. 2.19 X 4.2 = 2. 4.311 ÷ 0.07 = 3. 2.54 X 0.0028 = 0.0105 X 0.060

  32. What is Scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • Best used for very large and very small numbers, scientific notation is more concise.

  33. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x *When you divide by a number that is in scientific notation, use parenthesis around the denominator *To determine the number of sig figs in a number written in scientific notation, ignore the x 10x part of the number

  34. To change standard form to scientific notation… • Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. • If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

  35. Examples • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer: 2.898 x 108 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer: 5.67 x 10-4

  36. To change scientific notation to standard form… • Simply move the decimal point to the right for positive exponent 10. • Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

  37. Example • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right) • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)

  38. Learning Check • Express these numbers in Scientific Notation: • 405789 • 0.003872 • 3000000000 • 2 • 0.478260

  39. Examples 2.898 x 108 x 5.67 x 10-4 = 1.64 x 105 2.898 x 108 / 5.67 x 10-4 = 5.11 x 1011

  40. Metric Units • The base units for the metric system are • Grams (g) • Liters (L) • Meters (m) • Prefixes are used with these base units to represent a factor of the base unit

  41. Metric Prefixes *Example: 1 m= 10−3 km *Because all of these numbers all equal 1 base unit, they also equal each other *Example: 10−2 hg = 103 mg *You need to know the conversion factors from Mega to Micro

  42. Metric Prefixes

  43. Learning Check Select the unit you would use to measure 1. Your height a) millimeters b) meters c) kilometers 2. Your mass a) milligrams b) grams c) kilograms 3. The distance between two cities a) millimeters b) meters c) kilometers 4. The width of an artery a) millimeters b) meters c) kilometers

  44. Dimensional Analysis • Dimensional Analysis is a method used to convert a quantity in one unit into a different unit • Conversion Factor: Fractions in which the numerator and denominator are EQUAL quantities expressed in different units. • Conversion factors ALWAYS equal 1 (anything divided by itself is 1); • When you multiply by a conversion factor, you are not changing the number (because you are multiplying by 1), but you are changing the unit. • Conversion Factors always have infinite sig figs. Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

  45. Learning Check Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Micrometers and kilometers

  46. How many minutes are in 2.5 hours? Conversion factor 2.5 hr x 60 min = 150 min 1 hr cancel To solve, multiple numbers in the numerator, and divide by any numbers in the denominator. By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers! Remember your answer should have proper sig figs and include a unit.

  47. Steps to Problem Solving • Write down the given amount. Don’t forget the units! • Multiply by a conversion factor in the form of a fraction. Remember to cancel a unit, it must be on the opposite side of the fraction. • If you do not know a direct conversion factor (like how many seconds are in a year), use multiple conversion factors (like seconds to minutes, minutes to days, and days to years). • Multiply numbers in the numerator and divide by the numbers in the denominator. • Write your answer with a unit and in proper sig figs. Remember conversion factors have infinity sig figs.

  48. Sample Problem • You have $7.25 in your pocket in quarters. How many quarters do you have? 7.25 dollars 4 quarters 1 dollar = 29.0 quarters X

  49. You Try This One! If Jacob runs 2.50 miles, how many meters did he run? 1 mile = 1.609 km 1 mile= 5280 ft 1 inch = 2.54 cm 1 qt = 0.9463 L 1 gal = 4 qt 1 lb = 453.6 g 1 cm3 = 1 mL 1 mile= 5280 ft 946 mL = 1 qt 3 ft = 1 yd

  50. Learning Check • 1000 Km = ___mm 4. 0.00125 μg = ___ kg 5. 0.56 L = ___cL 6. 0.099 m = ___ dm

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