Chapter 3 - Measurements You ll learn it in the summer, If not, it ll be a bummer. You ll need to know conversions, For units, Euro version. Metrics are powers of ten, And you might cry when, You re forced to use sig figs, No one will do any jigs. You ll want to know about Kelvins, And Celsius degrees, Don t get frustrated with rate factors, Or calculations of density. - Ben Nichols Learning Targets : Students should understand and apply the law of conservation of mass. Students should be able to use and determine the accuracy and precision of measurements made by various measuring instruments. Students should be able to recognize and manipulate significant digits correctly when making measurements and using them in the lab. Students should be able to utilize scientific notation. Students should be able to perform metric conversions. Students should be able understand and calculate density. Students should be able to analyze experimental results to determine the amount of error. Honors Chemistry Ch 3 Measurements Page 1
Scientific notation 3.2 x 10 3 740900000000000 5.5 x 10-4 0.084 SI Units: Basic SI Units: length meter (m) mass time All other are derived units - kilogram (kg) - second (s) electric current - ampere (A) temperature - Kelvin (K) amount of a substance mole (mol) luminous intensity candela (cd) Quantity Quantity SI Unit SI Unit Symbol Abbreviation Derivation Area A Square meter m 2 length x width Volume V Cubic meter m 3 length x width x height Density D Kilograms per 3 cubic meter mass / volume Molar Mass M Kilograms per mole kg/mol mass / amount Energy (heat) E Joule J force x length Pressure P Pascal * Pa force / area Honors Chemistry Ch 3 Measurements Page 2
Metric prefixes Base units Mass: grams (g) Length: meter (m) Volume: liter (L) prefix giga mega kilo deka Base deci centi milli micro nano Pico symbol G M k Da - d c m n p 10^ 0 big # small unit = small # big unit Metric conversions Examples: 22.6 mm = m.61 kg = cg 78.5 ml = L 12.0 cm 2 = mm 2 24.1m 3 = dm 3 1 L = 1mL = 21 ml = cm 3 6.3 dm 3 = L 3.7 L = cm 3 4.89 dm 3 = ml Temperature: Scientists commonly use two equivalent units of temperature, the Celsius scale and the Kelvin scale. A change of 1 degree on the Celsius scale is equal to a change of one Kelvin on the Kelvin scale. Absolute zero is equal to K or o C. K = o C = Example: 25 o C = K 312 K = o C Honors Chemistry Ch 3 Measurements Page 3
Density calculations Mass is a measure of the amount of matter in an object. Essentially, how much stuff is inside an object. Weight is the force that mass has as a result of gravity. When the gravity changes, the weight will change, but the mass will remain constant Volume is the amount of space an object occupies. This remains constant for solids and liquids. Density is the amount of matter per the amount of space. It is calculated by dividing the mass by the volume. Density is an intensive property; it will remain the same no matter how much of the substance there is. The density of an object will determine if it will float or sink in another phase. If an object floats, it is less dense than the other substance. If it sinks, it is denser. The formula for density looks like a heart with a line through it: D m V Example: What is the volume of a substance with a mass of 75.8g and a density of 7.87 g/cm 3?. Honors Chemistry Ch 3 Measurements Page 4
Name: SIGNIFICANT FIGURES Every value is an estimation limited to our. Scientists try to obtain accurate and precise measurements. refers to how close a measurement approaches the true value. refers to obtaining a constant value. A significant figure is one which is known to be reasonably reliable. If you have a measurement to the nearest tenth of 15.7 cm, this means that is is between 15.65 and 15.75 cm. 1. Rules for recording data you measured The number of significant figures here is the number of digits you are able to read with certainty from the measuring device plus digit you estimate. EXCPTION: measuring devices record all the numbers displayed and do not add an estimated digit. 2. Rules for reading and interpreting data reported by others. 1. If YES, find the most end of the entire number and look to the until you reach the last "NONZERO" digit. This digit and all others to the left are significant. Ex. 12.050 L has sig figs 0.00050 ml has sig figs 12.24 g has sig figs 2. If NO, reverse the instructions from above (find the most end of the entire number and look to the until you reach the last non-zero digit. This digist and all others to the right are significant. Ex. 230 kg has sig figs 10000 ml has sig fig 1204 mg has sig figs 3. Rules for calculations Addition and subtraction In addition and subtraction we consider the significant figures on the right side of decimal point. This means that only as many digits are to be retained to the right side of decimal point as the number with fewest digits to the right of the decimal point. For example: 4.345 + 23.5 =27.845 (calculator answer) Answer after rounding off: Honors Chemistry Ch 5 Measurements Page 5
Name: Multiplication and Division In multiplication and division, the number obtained after calculation of two or more numbers must have no more significant figure than that number used in multiplication or division. For example: 4.3458 x 2.7 11.73366 (calculator answer) Answer after rounding off: (because 2.7 has only two significant figures Significant Figures are only limited for measurements. Counting numbers or defined quantities have an infinite number of significant figures. Ex: 12 students, 1 m = 100 cm. 4. Rounding If the number to be rounded is greater than 5 round. If the number to be rounded is less than 5 round. If the number to be rounded is equal to 5 o if it is followed by nonzero digit, round. o if not followed by a nonzero digit and is preceded by an odd digit, round up o if not followed by a nonzero digit and is preceded by an even digit keep the same Scientific notation Scientific notation is a way to indicate proper precision. All digits in scientific notation are significant. Example 2100 cm = 2.1 x 10 3 cm and has significant figures. Practice Problems 1. How many significant digits do the following measurements contain? a) 101 g b) 0.06 m c) 900. cm d) 40200 kg e) 0.92 ml f) 90 torr 2. Round the number 389.55 to a) 1 sig fig b) 2 sig figs c) 3 sig figs d) 4 sig figs 3. Convert the following to scientific notation keeping the same number of significant figures. a) 0.0048 c) 0.82 e) 9090 b) 60.0 d) 3000 f) 28050 4. 6.82 ml + 4.028 ml = 5. You live 3.562 miles away from school. It take you 5.37 minutes to go to school. What is your average speed? Honors Chemistry Ch 5 Measurements Page 6
Worksheet 1 - Scientific Notation/Metric Conversions 1. Express 205,000,000 mi in scientific notation. 2. Express 15,545,000 kg in scientific notation. 3. Express 0.001 s in scientific notation. 4. Convert 6.02 x 10-2 from scientific notation. 5. Convert 24.5 cm to m. 6. Convert 68.4 kg to Mg. 7. Convert 8.54 kg to cg. 8. Convert 68.4 g to kg. 9. 3.5 o C = K 10 59.9 K = o C 11. 82.4 m = Mm 12. 2100 cg = Mg 13. 2080 g = Dag 14. 4082 cm 3 = m 3 15. 947.0 km 2 = m 2 16. 21.94 L = cm 3 17. 80.0448 cm 3 = ml 18. 0.093 ml = dm 3 19. What does the following measure and is it base or derived? (Example: 34 cm 2 : area, derived unit) a) 12.3 km b) 14.0 pl c) 34.5 mol d) 890.3 mm 2 e) 438 in 3 f) 74 g/ml g) -53.4 C h) 320 Pa Honors Chemistry Ch 3 Measurements Page 7
1. Read the following ruler measurements. Worksheet 2 Significant Figures in the Lab a) b) 2. Read the following graduated cylinder measurements. a) b) c) d) 3. Read the following temperature measurements in degrees Celsius. a) b) c) d) Honors Chemistry Ch 3 Measurements Page 8
4. In an experiment, the mass of an evaporating dish was recorded. A sample of salt water was added to the dish, and the mass was recorded. Then, the dish was heated until all of the water evaporated, leaving the salt behind. The mass of the dish, and remaining salt, was recorded after the dish cooled. Data Obtained: Item Mass (g) Evaporating Dish 26.54 Evaporating Dish with salt water 33.98 Evaporating Dish with dried salt 29.28 a. Determine the mass of salt water in the evaporating dish. b. Determine the mass of dried salt remaining in the dish after evaporation. c. Determine the mass of water which was lost during evaporation. Honors Chemistry Ch 3 Measurements Page 9
Worksheet 3 Significant Figures Calculations 1. How many sig figs do the following measurements contain? a) 12.00 g b) 0.0024 cm c) 108.04 torr d) 3,000m e) 0.84 L f) 60 g g) 6020080 cm h) 0.050 ml i)1.0 x 10 4 s j) 0.3 X 10 6 atm k) 1.080 X10 3 atm 2. Round the number 682.55 to a) 1 sig fig b) 2 sig figs c) 3 sig figs d) 4 sig figs e) 5 sig figs 3. Convert the following to scientific notation keeping the same number of significant figures. a) 0.0048 b) 3000 c) 60.0 d) 8080 e) 0.82 f) 28050. 4. Round the following measurements to 3 significant figures a) 22.77 g b) 14.62 m c) 2108.4 L d) 99.999s 5. Compute the following. Show all your work and express each answer in the proper number of significant figures. Include units. a) If 12.00000 grams of carbon contain 6.02 x 10 23 atoms, what is the mass of one carbon atom in milligrams? b) If a glass marble has a mass of 1.275 grams, what will be the mass of a dozen identical marbles? What would be the mass (in kg) of a "dozen dozen" marbles? c) 82 cm x 3.00 cm x 10 cm d) 105 g/0.86 ml e) 1.054 x 10 4 km + 4.216xl0 2 km g) 40.821 L-0.86 L Honors Chemistry Ch 3 Measurements Page 10
Worksheet 4 Density 1. What is the relationship between mass and volume of a substance called? 2. Is density of a substance constant? Explain. 3. Draw particle diagrams of copper at 30 o C and copper at 80 o C. Use your diagrams to discuss the density of copper at both temperatures. 4. Draw a particle diagram of pure water. Draw another particle diagram of salt water. Use your diagrams to discuss the density of pure water vs. salt water. 5. Which has a larger density: table salt or lead? 6. Balloon A is filled with 1.0 x 10 22 particles of carbon dioxide. Balloon B is filled with 1.0 x 10 22 particles of helium. Both balloons have the same volume. Carbon dioxide is denser than air and balloon A will fall on the floor. Helium is less dense than air and balloon B will rise. If both balloons have the same volume and the same number of particles, how do you explain the difference in densities? 7. The density of copper is 8.3 g/cm 3. What is the mass of a bar of copper that has a volume of 3.0 cm 3. 8. What is the density of a solution that has a mass of 13.5 g and a volume of 22 ml? 9. What is the density of a substance that has a mass of 22 kg and a volume of 2.0 L? 10. What is the mass of a substance that has a density of 33.4 kg/gallon and a volume of 2.58 gallons. 11. A cube has a mass of 22.6 g and a density of 3.7 g/cm 3. What are the dimensions of the cube? 12. A block has a length of 2.45 cm and a width of 4.52 cm. What is the block s height if it has a mass of 78.4 g and a density of 3.54 g/cm 3? Honors Chemistry Ch 3 Measurements Page 11
Chapter 3 Sample Questions 1. How many significant figures are in each of the following numbers? a) 0.0087 b) 400 c) 20030 d) 45.5 x 10 8 e) 4.6 x 10 3 f) 30. 2. Round 399.65 to a) 1 sig. fig. b) 2 sig. figs. c) 3 sig. figs. d) 4 sig. figs. 3. Convert the following to scientific notation keeping the same number of sig. figs. a) 0.00022 b) 340000 4. Convert the following to long hand keeping the same number of significant figures. a) 3.20 x 10-8 b) 0.002 x 10 4 5. Perform the following conversions. a) 21 o C = K c) 38.6 ml = dm 3 b) 3400 Dam = dm d) 22.2 L = dm 3 6. Perform the following calculations. Make sure to express your answers with the correct number of significant figures. Show work and box your final answer. a) The mass of 6.02 x 10 23 molecule of oxygen gas is equal to 32.06 grams. What is the mass of 1 molecule of oxygen gas? b) What is the density of a ball that has a volume of 1.62 L and a mass of 3490 grams? c) What is the length of a cube that has a mass of 22.6 grams and a density of 2.825 g/cm 3? Answers 1. a) 2 b) 1 c) 4 d) 3 e) 2 f) 2 2. a) 400 b) 4.0 x10 2 c) 4.00 x10 2 d)399.6 3. a) 2.2 x10-4 b) 3.4 x10 5 4. a) 0.0000000320 b) 20 5. a) 294 K b) 340000 c) 0.0386 d) 22.2 6. a) 5.33x10-23 grams/molecule b) 2150 g/l c) 2.00 cm Honors Chemistry Ch 3 Measurements Page 12
Law of Conservation of mass: Mass Demos Demo 1 Prediction: Initial mass: Final mass: Change: Observations: Explanation: Particle diagrams Initial Final Demo 2 Prediction: Initial mass: Final mass: Change: Observations: Explanation: Particle diagrams Initial Final Demo 3 Prediction: Initial mass: Final mass: Change: Observations: Explanation: Particle diagrams Initial Final Honors Chemistry Ch 3 Measurements Page 13
Demo 4 Prediction: Initial mass: Final mass: Change: Observations: Explanation: Particle diagrams Initial Final Demo 5 Prediction: Initial mass: Final mass: Change: Observations: Explanation: Particle diagrams Initial Final Demo 6 Prediction: Initial mass: Final mass: Change: Observations: Explanation: Particle diagrams Initial Final Honors Chemistry Ch 3 Measurements Page 14
Density of Metals Lab You will use the mass-volume relationship to identify two metals. You will need to come up with your own procedure. Tips: You will need at least 3 data points for each metal. Remember that your sample sizes need to be large enough to make a significant difference in volume. Remember that your sample sizes need to be different so when you graph your data, the points are not all on top of each other or close together. Please place the wet metals on the proper labeled paper towel on the back counter. DO NOT PUT THE WET METALS BACK IN YOUR BEAKERS. Here is a list of the possible metals: Silicon 2.33 g/ml Aluminum 2.70 g/ml Tin 6.99 g/ml Zinc 7.13 g/ml Copper 8.96 g/ml Lead 11.34 g/ml You will need a formal lab report. Remember it needs to be in past tense and passive voice. Use your syllabus packet and follow the lab report rules. You will need: Heading Purpose Procedure (past tense and passive voice) Data Table (don t forget the units) Results Here you should include: o Graph for both metals of mass vs. volume (don t forget to label axes and title your graph) o Line of best fit (don t connect the dots) o Slope of the line. (show your calculation or indicate if you didn t on excel) o Densities of both metals (the slopes) and the identity of the metals. Conclusion (see lab report rules) Honors Chemistry Ch 3 Measurements Page 15
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Measurement Stations Station # Measuring Equipment Smallest Increment Measurement # Sig. Figs. 1 2 3 4 5 6 7 8 9 10 11 12 Honors Chemistry Ch 3 Measurements Page 17