General Chemistry Unit 8 Measurement (2017-2018) Significant Figures Scientific Notation Unit Analysis Unit of Measure Accuracy and Precision Density Percent Error 1
Adding Numbers: Add numbers as you would a normal addition problem. To determine the number of digits in your answer: Look at the number of places after the decimal in each of the original numbers. The answer will match the value that has the fewest places after the decimal. Example: 44.223 + 11.55 55.773 (From the calculator) the answer is 55.773, but 11.55 only has 2 places after the decimal so the answer must be reported to 2 places after the decimal (55.77). From the previous example if the 3 in thousandths place had been a 5 or higher, the answer would have been reported as 55.78. So before reporting places after the decimal, you must look at one place past the correct answer to see if that digit is 5 or more. If it is, the last reported digit must be rounded up by one. Example: 28.218 + 1.55 29.768 Since 1.55 only has 2 places after the decimal, the answer would be 29.76 BUT since an 8 is in the place after the 6, the answer is reported as 29.77. Examples: Subtracting Numbers: Follow the same rules as Addition: Look at the places after the decimal. The answer must match the number with the fewest places. Examples: 2
Significant Figures To determine how many significant figures a number has: Atlantic Pacific Rule: P = Pacific = Present decimal = Start on Left A = Atlantic = Absent decimal = Start on Right Pass over any zeroes until you come to a non-zero digit. Count every digit starting with that digit. They are all considered significant starting from the non-zero digit. Examples: 3
Multiplying Sig Figs: Multiply the numbers as you normally would. To determine the number of digits to report, calculate the number of significant figures for each of the numbers being multiplied (decimal present or absent). The answer will have the same number of significant figures as the number being multiplied with the lowest number of sig figs. Example: x 33.874 (left : 5 sig figs) 11.24 (left : 4 sig figs) 380.74376 (From the calculator), the answer is 380.74376 BUT 11.24 only has 4 sig figs, so the answer can only contain 4 sig figs. Start counting from the left: 380.74 123 4 Look at the digit in the 5 th place to see if it is a 5 or higher. If it is a 5 or higher, the 4 th digit would be rounded up by one. In this example, it is a four so no rounding will take place. The correct answer is 380.7. Examples: Dividing Sig Figs: Follow the same rules for multiplication. Examples: 4
General Chemistry Worksheet "Significant Figures" Part 1. Determine the number of significant figures in each of the following measurements and write your answer in the space provided. 1) 8 675 309 g 4) 30 200 s 2) 0.035 6 m 5) 0.080 20 g 3) 801.50 ml 6) 1000 K Part 2: Round the following quantity to the specified number of significant figures. 7) 650,000 ml to one sig fig. 8) 0.001 342 94 g to four sig figs. 9) 49 203.03 g to three sig figs. 10) 48 412 g to two sig figs. 11) 0.000 823 938 0 g to five sig figs. 12) 7600 g to one sig fig, Part 3: Perform each of the following calculations and express the answer to the correct number of significant figures. 13) 69.24 cm + 14.2 cm = 14) 13.5 mg 8 mg = 15) 45.90 dam x 5.41 dam = 16) 34.9 km / 11.169 hr = 17) 0.0023 Mg x 787 Mg = 18) 22.0 m + 5.28 m + 15.554 m = 19) 13.75 mm x 10.1 mm x 0.91 mm = 5
Scientific Notation When writing a number in scientific notation, there are two parts: 1. a number equal to or greater than 1 and less than 10 1 n < 10 2. a power of 10 Example: 2.37 x 10 5 Writing a number in scientific notation Example: # of electrons in a circuit: 6,250,000,000,000,000,000 Step 1: If original # is larger than 1, the power is going to be POSITIVE! Step 2: Put imaginary decimal point at the end of the number. 6,250,000,000,000,000,000. Step 3: Put another imaginary decimal point in the position where the number is between 1 and 10 6.250 000 000 000 000 000. Step 4: Move the decimal at the end of the number until it is on top of the decimal in the 6.25 position. Count the positions as you move. Step 5: The number of times you move is equal to the power value. Step 6: Write the value that is now 1 n < 10 followed by x 10 and The number of times the decimal moved should be written as a superscript on the 10. Add units to the answer Answer: 6.25 x 10 18 electrons/sec To undo the scientific notation, move the decimal 18 times to the right (since the power is positive, the new value will be larger than 10) 6
Adding / Subtracting with Scientific Notation: You will use your calculator to add and subtract with scientific notation. You will learn to use the EE button on your calculator to make the math easier Multiplying and Dividing with scientific notation: Multiplying: The numbers in front multiply like a regular math problem and the exponents ADD. Dividing: The numbers in front divide like a regular math problem and the exponents SUBTRACT. 7
Take these measurements out of scientific notation and put them into standard notation: 17.) 8.4356 x 10-4 g = 18.) 6.574839 x 10 3 g = 19.) 4.21 x 10 6 m = 20.) 9.21 x 10-7 m = Carry out the following calculations. For addition and subtraction, write everything the calculator gives you. For multiplication and division you must use sig figs on your answer. Use units! 21.) 2.48 x 10 2 kg + 9.17 x10 3 kg + 7.2 x 10 1 kg = 22.) 4.07 x10-5 mg + 3.966 x 10-4 mg + 7.1 x 10-2 mg = 23.) 3.890 x 10 8 km / 1.97 x 10 3 s = 24.) 1.111 1 x 10 5 cm x 5.82 x 10 4 cm = Without using a calculator, solve the following problems: 25.) 2.000 x 10 120 ml x 3.0 x 10 44 ml = 26.) 5.000 x 10 341 g / 5.00 x 10 141 ml = 8
General Chemistry Worksheet "Scientific Notation" Change the following numbers to proper scientific notation: 1. 65.7 g 2. 0.005 45 g 3. 22 450 000 g 4. 3 450 678 001 g 5. 679.3 g 6. 0.0803 g Change the following numbers to standard notation: 7. 6.5 x 10-2 g 8. 9.75 x 10 6 g 9. 3.4009 x 10-5 g 10. 1.847 x 10 2 g 11. 8.85 x 10-1 g Addition / Subtraction Problems: 12. 2.367 x 10-3 ml + 5.4 x 10-2 ml 13. 6.50 x 10 1 ml + 4.321 x 10 2 ml 14. 4.89 x 10-3 ml + 2.17 x 10-6 ml 15. 9.875 x 10 2 ml - 2.343x10 1 ml 9
Multiplication Problems (Put the answer in scientific notation form with the correct number of sig figs): 16. (2.87 x 10 5 ml) x (3.514 x 10 9 ml) 17. (5.0 x 10-2 ml) x (7.85 x 10 4 ml) 18. (1.042 x 10-1 ml) x (4.002 x 10-5 ml ) 19. (2.21 x 10 5 ml) x (1.807 x 10-7 ml) Division Problems (Put the answer is in scientific notation form and with the orrect number of sig figs): 20. (9.4 x 10 7 ml) / (1.24 x 10 5 ml) 21. (2.4 x 10 6 ml) / 5.49 x 10 9 ml) 22. (1.92 x 10-2 ml) / (2.3 x 10 6 ml) 23. (9.2 x 10-3 ml) / (6.3 x 10-5 ml) 10
Name General Chemistry Worksheet "Significant Figures and Scientific Notation" Part 1: Determine the number of significant figures in each of the following measurements and write your answer in the space provided. 1) 8 675 309 g 4) 30200 s 2) 0.0356 m 5) 0.080 20 g 3) 801.50 ml 6) 1 000 000 K Part 2: Round the following quantity to the specified number of significant figures. Standard Notation Scientific Notation 7) 695,900 ml to three sig. figs. 8) 0.001 342 94 g to four sig. figs. 9) 49 203.03 g to three sig. figs. 10) 0.000 000 775 2 mg to two sig. figs. 11) 0.000 293 749 0 in to four sig. figs. 12) 3400 kg to one sig. fig. Part 3: Perform each of the following calculations and express the answer to the correct number of significant figures. Standard Notation Scientific Notation 9) 69.24 dm + 144. 2 dm = 10) 13.5 mg 8 mg = 11) 245.90 dam x 9.41 dam = 12) 34 g / 1581.169 m = 13) 0.0023 Mg x 77 Mg = 14) 5.44 cm x 31 cm x 0.0984 cm = 15) 0.043 km / 452.1 s = 16) 300 ft x 9.7600 ft = 11
Factor Label Method (Notes on how to convert using conversion factors) I. Conversion Factor: a ratio that can be used to convert from one unit to another. The numerator and the denominator are equal to each other The denominator s unit should be the same as the given numbers unit The numerator s unit will be the unit you want to convert to Example of a conversion factor: 4 quarters or 12 eggs 1 dollar 1 dozen II. III. Factor Label Method Procedure: 1. Write the given number and unit 2. Set up a conversion factor (fraction used to convert one unit to another) 3. Place the given unit as denominator of conversion factor 4. Place desired unit as numerator 5. Cancel units 6. Solve Problem Factor Label Method Procedure (Metric to Metric): 1. Write the given number and unit 2. Set up a conversion factor (fraction used to convert one unit to another) 3. Place the given unit as denominator of conversion factor 4. Place desired unit as numerator 5. Place a 1 in front of the larger unit 6. Determine the number of smaller units needed to make 1 of the larger unit 7. Cancel units 8. Solve Problem 12
Set up is very important for factor label or unit analysis. To get a unit to cancel it is on the top of one frame but on the bottom of the next frame. You only have one equal sign per problem so it could take multiple frames to solve a problem. Examples: 462 eggs =? dozen 462 eggs ( ---------------- ) = dozen 8457 inch ( --------------- ) = feet 5.75 hours =? sec 5.75 hours 13
Factor Label Problems 1 mile = 1.61 km 2.54 centimeters (cm) = 1 inch 1 cup = 236.59 milliliters (ml) 5280 feet = 1 mile 1) 1254.50 inches =? feet 2) 400. minutes =? hours 3) 3.0 miles =? inches 4) 9.000 weeks =? minutes 5) 4590 seconds =? days 6) 42 hours =? days 14
7) 15.8 miles =? kilometers 8) 62.88 inches =? cm (centimeters) 9) 459.75 ml =? cups 10) 43.0 ft =? km 11) 65 miles/hour =? kilometers/sec 12) 80.50 kilometers /year =? miles/min 15
Metric System Units (Number of base units needed to make one) Grand Giga G 1,000,000,000 Master Mega M 1,000,000 King Kilo k 1,000 Henry Hecto h 100 Died Deka da 10 By Base Unit Liter, Meter, Gram (Number needed to make one base unit) Drinking Deci d 10 Chocolate Centi c 100 Milk Milli m 1,000 Monday Micro μ 1,000,000 Night Nano n 1,000,000,000 Other Important Conversions: 12 in. = 1ft 3 ft = 1 yd 5280 ft = 1 mi 1760 ft = 1 mi 2 pt = 1 qt 4 qt = 1 gal 1 qt = 0.946 L 1 qt = 32 fl oz 1 lb = 454 g 1 lb = 16 oz 1 metric ton = 2200 lb 1 in = 2.54 cm 1 m = 39 in 1 mi = 1.61 Km 16
Metric Conversions Practice Worksheet Complete the following problems using UNIT ANALYSIS (must show work). Remember to have your answer to the proper number of significant figures. (b = base and units are grams or liters or meters) G M k h da b d c m μ n 1. 550.0 millimeters (mm) =? meters (m) 2. 9.50 dekaseconds (das) =? deciseconds (ds) 3. 2500 centigrams (cg) =? kilograms (kg) 4. 5.30 centimeters (cm) =? millimeters (mm) 5. 462.55 Gigaliters (GL) =? hectoliters (hl) 17
G M k h da b d c m μ n 6. 77.1 micrograms (μg) =? grams (g) 7. 21000 millimeters (mm) =? kilometers (km) 8. 500.88 Megaliters (ML) =? kiloliters (kl) 9. 442.6 decimeters (dm) =? nanometers (nm) 10. 34.5 Gigagrams (Gg) =? nanograms (ng) 18
Unit Analysis Practice You must show all of your work. Your answer should be reported to the correct number of sig figs. 1) Convert 62 km to centimeters G M k h da b d c m μ n Must memorize 1 inch = 2.54 cm 2) Convert 198.50 micrograms to dekagrams 3) Convert 15.00 ft to meters 4) 5.00 meters to inches (you should have a hint memorized!!) 5) Change 64 hours to seconds 19
6) Change 1,314,000 minutes to years 7) Convert 3.0 liters to quarts (hints: 1 gallon = 4 qts, 1 liter = 1.0567 qts) 20
Unit of Measure Qualitative: Quantative: 21
Accuracy and Precision: Accuracy and Precision Activity Lab Equipment Burette Your Reading Volume Reading #1 Volume Reading #2 Average Reading Precision Prediction 1 5 1 = best Actual Precision Ranking Actual Accuracy Ranking 50 ml Graduated Cylinder 250 ml Beaker 250 ml Graduated Cylinder 250 ml Erlenmeyer Flask Actual Reading Burette 50 ml Grad Cylinder 250 ml Beaker 250 ml Grad Cylinder 250 ml Erlenmeyer Flask 1. Predict how precise each piece of lab equipment is by ranking them from 1-5. 1 being most precise to 5 being least precise. Put your predictions in column 5. 2. Read the volume of water in each type of lab equipment. 3. Record your answer in column 1. 4. Record the answers of two classmates in column 2 and column 3. 5. Find the average reading for each piece of lab equipment. Record your answer in column 4. 6. Obtain the actual volume of water in each piece of equipment. 7. Determine the actual ranking of precision of each piece of equipment by comparing the actual reading to your average reading. Record the actual precision ranking in column 6. 22
Accuracy Precision 23
Reading Lab Equipment Correctly Must always report one digit past what is given on the scale of that piece of equipment. This last digit is called the uncertainty digit you are estimating it as best as you can. 24
What is the volume of liquid in each graduated cylinder? What is the length (in cm) of the lines below? 25
What is the length (in mm) of the lines below? 26
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Measurement Lab Activity There are eight lab stations set up and each will ask you to answer a question related to measurement. Please record your values (a complete value requires UNITS AND UNCERTAINTY!!!) and answer the follow-up question in a complete sentence. Station 1: Temperature of beaker A: Temperature of Beaker B: Convert both temperatures into the appropriate SI unit, which for temperature is:. Temperature A: Temperature B: What is the accuracy of the scale on the thermometer? This means that you should read your measurement and estimate a value in the place. When measuring the temperature of a liquid, what procedural error must you avoid? Explain. Station 2: Determine which graduated cylinder would be most accurate for measuring the following: a) A volume of 13 ml b) A volume of 31 ml When reading the graduated cylinder, you must remember to read the of the. What is the accuracy of the scale on each graduated cylinder? 10 ml 25 ml 50 ml 100 ml This means that you should read your measurement and estimate a value in what place? 10 ml 25 ml 50 ml 100 ml Station 3: Determine the accuracy of the 10 ml mark on the beaker. If it is not accurate, state whether it is over or under and by how much. Should you use a beaker or a graduated cylinder to measure volumes? Why? 28
Station 4: Determine the accuracy of the 50 ml and the 75 ml marks on the Erlenmeyer flask are accurate. If they are not accurate, state whether it is over or under and by how much. Should you use a graduated cylinder or an Erlenmeyer flask to measure volumes? Why? Station 5: If this buret was originally filled to the 0 ml mark, how much liquid has been removed? What is the accuracy of the scale on the buret? This means that you should read your measurement and estimate a value in the place. Based on the design on the buret, what is its purpose? Be clear about your answer. Station 6: What is the length of each of the pieces of string? Short Long What is the accuracy of the scale on the meter stick and ruler? This means that you should read your measurement and estimate a value in the place. Station 7: What is the mass of each of these samples? A: B: C: What is the accuracy of the balance you used? Can you estimate a final digit on the electronic balances? Station 8: Use the equipment provided to determine the density of the irregular object. Show your density calculations and explain how each value was determined. 29
Answer the following questions on density and experimental error. Put your answers on the lines provided. 1. Cerium sulfate has a density of 3.17 grams per cubic centimeter. What is the volume of.54 grams of this substance? 2. Cerium sulfate has a density of 3.17 grams per cubic centimeter. What is the volume of 1.25 grams of this substance? 3. What is the mass of a piece of aluminum having a volume of 15.12 cubic centimeters and a density of 2.70 grams per cubic centimeter. 4. What is the density of a gold nugget having a volume of 2.39 cubic centimeters and a mass of 45.58 grams? Your answer must have the correct number of significant digits. 5 What is the density of a brick if 51.21 g occupy 31.32 cubic centimeters? 30
6. What is the density of a cardboard if 6.2 g occupy 8.56 cubic centimeters? 7. Tin has a density of 7.28 grams per cubic centimeter. What is the volume of 11.2 grams of this substance? Density and Experimental Error: 1a. Your measurement of the volume of tap water is 9.6 ml, 9.52 ml and 9.553 ml using 3 different graduates. What is the average volume of the tap water? 1b. The average mass of this tap water is 9.2 g, what is the density? 2. The standard density of water is 1.00 g /ml, what is your experimental error for the problem above? 31
Lab: Graphing and Density Name: Purpose: -Determine the density of a liquid from a graph of mass and volume. -Determine the layering order of three liquids if poured together into a graduated cylinder. Problem: Are density and the layering order of liquids in a graduated cylinder related? Hypothesis: (If,then ) Experiment: Materials: 25mL graduated cylinder water balance dropper rubbing alcohol calculator Procedure: 1) Determine the mass of 5mL of water and record this in the data table. a. Place the empty graduated cylinder on the balance and record this mass below: i. Mass of empty cylinder: g b. Place the 5mL of water in the cylinder and carefully place it on the balance. c. Subtract the mass of the empty cylinder. d. Record the mass in the data table. 2) Repeat step 1 for 15mL and 25mL of water. 3) Repeat step 1 for 5mL, 15mL, and 25mL of rubbing alcohol. a. Use the beaker of rubbing alcohol that is at your table. Return the alcohol to the beaker when finished for the next class to use!! 4) We will not be measuring the values for silicone oil because it is too messy. The data has already been given to you in the data table. 5) Graph the data on the provided graph under the data table. a. Use a different colored pencil for each line. b. Provide a key to identify each color. c. Make a title for the graph. d. Make a best-fit line for each color. The line must go through 0,0. e. Determine the slope of each line and show your work. Data: Volume (ml) Water (g) Rubbing Alcohol (g) Silicone Oil (g) 5.0 4.60 15.0 13.70 25.0 23.10 32
Use slope determination of each line to calculate the density of each liquid: (You MUST show your work! Remember to put units with your work and answer.) Circle your answer. Water: Rubbing alcohol: Silicone oil: Given your results, how will the liquids be layered if poured carefully into a graduated cylinder? Make sketch show which liquid would form the bottom will be in the middle, and will be on top. 33
Density Graphing Pre-test Activity 1. Graph the following data on a sheet of graph paper. What variable goes on the x-axis? What variable goes on the y-axis? 2. Make sure to include all graph features Volume, ml Mass, g 0.0 0.00 2.0 5.40 5.0 12.50 10.0 27.30 15.0 40.50 3. Determine the slope of your line DO NOT use (0,0) as one of your data points. Please show all of your work below: 4. How are the slope of the line from the graph and density related? Explain. 5. Based on the density you calculated and the table below determine the name of the substance represented in the graph! Unknown Substance = Substance Density (g/ml) Methanol 0.97 Glycerin 1.26 Carbon Tetrachloride 1.58 Aluminum 2.70 Lead 11.3 34