Lap 3 Chapter 3 Scientific Measurement Essential Question: How do measurements affect how scientists study matter in the world around us? 3.1 Measurements and Uncertainty A. Using and Writing Measurements 1. Measurement: quantity with number and unit Important to scientific experiments Ex: Mars planet orbiter crashed because of wrong units Calcium Carbide demo: 5 extra grams prevents top from popping Insulin for diabetics needs to be measured exactly Recipes rely upon measured ingredients 2. Scientists Use International System of Measurements (SI Units) 3. Scientific notation Way to write a very large or tiny number Number is written as product of 2 numbers - Coefficient and a number raised to power of 10 Example: 6.02 x 1023 602000000000000000000000 = number of atoms in 1 gram of H Example: 3.27 x 1022 0.000000000000000000000327 grams = mass of 1 atom of Au Examples of Scientific Notation 5.5 x 105 Power of +5: move 5 spots to the right (make larger) 5.5 5 5 0 0 0 0 . = 550000 7.8 x 10-3 Power of -3: move 3 spots to the left (make smaller) 7.8 0 . 0 0 7 8 = 0.0078 B. Accuracy and Precision Measurements should be both correct and reproducible. Accuracy: how close your measurement is to the actual value Must compare one measured value to true value Precision: how close a set of measurements are to each other Compare two or more repeated measurements Example: Given these sets of data: A. 80o C, 79o C, 82o C B. 77o C, 65o C, 73o C C. 76o C, 76o C, 75o C Which is the most precise? C: all within 1 degree Which is the most accurate if the liquid's known boiling point is 81o C? A: average is closest to known value C. Determining Error Error: absolute value of the difference between the accepted or known value and the experimental value Error = experimental value - accepted value Percent error = Experimental value – Accepted value 100% Known value Example: You conduct an experiment and find the boiling point of water to be 98oC. What is percent error? Experimental value = 98℃ Accepted value for boiling point of water =100℃ Solve: l 98℃ - 100℃ l 100% 100℃ = .02 x 100% = 2% D. Determining Significant Figures (Sig figs) Different tools measure with different certainty Significant figures tell how "good" your tool is Def: measurement that includes all of the known digits plus one estimated digit Must always record in correct significant digits or figures to indicate how precise the measurement was Example: Ruler marked in meter will give a measurement with less significant figures than a ruler marked with centimeters E. Rules for significant figures 1. Every nonzero number is significant. 56 m = 2 sig figs 45978 mm = 5 sig figs 2. Zeroes between nonzero digits are significant. 305 K= 3 sig figs 230098 L = 6 sig figs 3. Final zeroes after a decimal point are significant. 6.70 mg = 3 sig figs 11.00 km = 4 sig figs 4. Final or trailing zeros without a decimal point are NOT significant. 900 g = 1 sig fig 150 ms = 2 sig figs 70000 g = 1 sig fig 5. Leftmost or leading zeros appearing in front of nonzero digits are NOT significant. 0.008 g = 1 sig fig 0.78 ms = 2 sig figs 0.00000006 cm = 1 sig fig 6. These rules do not apply to: counting numbers 12 people (there can't be 12.3 people) unlimited number of sig figs: 12.00000000..... people to infinity conversion factors 1 m = 100 cm (these are exactly defined quantities, not measured) Examples: 123 m 3 sig figs Reason: 3 nonzero 9.800 x 105 s 4 sig figs Reason: 2 nonzero + 2 final zeroes after decimal (ignore 105 power: is never included in sig figs) 0.0708 g 3 sig figs Reason: 2 nonzero + 1 zero between nonzero F. Rules for significant figures in Calculations A calculated answer cannot be more precise than the least precise measurement from which it was calculated. Calculated answer must be rounded to the correct number of sig figs Rounding rules: If the last insignificant number is 4 or less, round down Example: 4.52 rounds to 4.5 Example: 0.0081 rounds to 0.008 If the last insignificant number is 5 or more, round up Example: 4.56 rounds to 4.6 Example: 0.0087 rounds to 0.009 Sample Problem Round off 314.721 meters to four significant figures and write the answer in scientific notation. 314.721 m = 314.7 m = 3.147 x 102 Rule for addition and subtraction: Answer should be rounded to the same number of decimal places as the least number of decimal places Example: 12.5 m + 4.35 m + 1.005 m Find the number with the least number of decimal places after the decimal point 12.5 has only 1 place after the decimal point, this is the least Answer should be rounded to 1 place after the decimal point Answer on calculator 17.855 m Answer should be rounded to 17.9 m Another example: 51.78 cm + 2.000 cm + 13.00008 cm 51.78 has least number of places after decimal point: 2 Answer will be rounded to 2 places after decimal point Answer on calculator 66.78008 cm Answer rounded is 66.78 cm Rule for multiplication and division Answer should be rounded to same number of sig figs as the least number of sig figs Example: 78.9 mm x 100 mm = 78.9 mm is 3 sig figs and 100 mm is 1 sig fig Answer should be round to only 1 sig fig Answer on calculator 78900 mm Answer rounded to 80000 mm Another example: 2.10 km X 0.70 km = 2.10 has 3 sig figs and 0.70 has 2 sig figs Answer should be rounded to 2 sig figs Answer on calculator: 1.47 Answer rounded to 1.5 km How many sig figs in: 45.79 cm 300 km 0.04 mm 10.042 nm 15,000 km 34100 mL 0.000902 mL 6.02 x 1023 1.7 x 10-3 3.00 x 10-24 How many sig figs in the answer to this problem? 1.2 g x 3.45 g 1200 g ÷ 7.43 g 10.0 + 2.00 75.4523 - 3.231 (5.6 x 103) x (3.21 x 105) (7.932 x 104) + (2.3 x 104) 3.1 Section Assessment 1. How are accuracy and precision evaluated? 2. How does the precision of a calculated answer compare to the precision of the measurements used to obtain it? 3. A technician experimentally determined the boiling point of octane to be 124.1 0C. The actual boiling point of octane is 125.7 0C. Calculate the error and the percent error. 4. Determine the number of significant figures in each of the following: a. 11 soccer players b. 0.070020 meter c. 10,800 meters d. 5.00 cubic meters 5. Solve the following and express each answer in scientific notation and to the correct number of significant figures. a. (5.3 x 104) + (1.3 x 104) b. (7.2 x 10-4) (1.8 x 103) c. 104 x 10-3 x 106 d. (9.12 x 10-1) - (4.7 x 10-2) e. (5.4 x 104) x (3.5 x 109) 3.2 SI Units (Le Systeme International d'Unites) A. Common SI units in Chemistry Length Mass Temperature Time Amount of substance Metric prefixes for large or small units – most commonly used: Prefix Meaning 1,000 times larger than the unit it precedes 100 times smaller than the unit it precedes 1,000 times smaller than the unit it precedes B. Units of Length Meter is base unit 1 kilometer = 1000 m 100 cm = 1 m 1000 mm = 1 m 1 meter = height of doorknob from the floor 1 kilometer = length of about five city blocks 1 centimeter = width of a shirt button 1 millimeter = thickness of a dime C. Units of Volume Volume = amount of space occupied by a sample of matter Found by length x width x height SI unit is m3 Liter is more commonly used 1 L = 1000 cm3 1 mL = 1 cm3 liter = quart of milk milliliter = 20 drops of water cubic centimeter = cube of sugar D. Units of Mass Mass = quantity of matter Kilogram is standard mass unit Previously based on mass of 1 liter of H2O Now based on mass of cylinder of platinum and irridium 1000 g = 1kg Factor 1000 mg = 1 g Weight is force of gravity on an object’s mass Weight can vary by location, but mass is constant (on the moon 1/6 of weight) E. Units of Temperature Temperature = measure of how hot or cold object is Object's temp determines direction of heat transfer Hold a glass of hot water - heat transfers to your hand Hold an ice cube - heat transfers from hand to ice cube Almost all substances expand when temp increases and contract when temp decreases, except water Celsius scale: set at 0 degrees C for freezing water and 100 degrees C for boiling water Kelvin or absolute scale: Does not use degrees freezing point of water is 273.15 K boiling point of water is 373.15 K 0 K is called absolute zero Lowest possible temperature; nothing could be colder and no heat energy remains K = C +273 C = K -273 Example of conversion 5 K = _____ degrees C 5 K - 273 = -268 degrees C F. Units of Energy Energy = capacity to do work or produce heat SI unit for energy is Joule (J) Also use calorie (cal) Definition for calorie = amount of heat needed to raise 1 gram of water 1 degree C A food Calorie is actually a kilocalorie or 1000 “little c” calories Conversion: 1 cal = 4.184 J 3.2 Section Assessment 1. Which five SI base units are commonly used in chemistry? 2. Which metric units are commonly used to measure length? volume? mass? temperature? energy? 3. What is the symbol and meaning of each prefix? kilocentimilli- 4. What is the volume of a paperback book 21 cm tall, 12 cm wide, and 3.5 cm thick? 5. State the difference between mass and weight. 6. Surgical instruments may be sterilized by heating at 1700C for 1.5 hours. Convert 1700C to kelvins.