*STUDENT* *STUDENT* Regents Chemistry NOTE PACKET Unit 1: Measurement 1 Co py ri g ht 2015 Tim Dol g os
*STUDENT* *STUDENT* Name: Date: Period: Unit 1: Measurement Unit Vocabulary: 1. S.I. unit 9. Significant Figures 2. Meter 10. Precision 3. Liter 11. Accuracy 4. Gram 12. Scientific Notation 5. Mass 6. Weight 7. Volume 8. Density Unit Objectives: When you complete this unit you will be able to do the following 1) Convert between units of measurements 2) Differentiate between accuracy and precision 3) Write numbers in scientific notation 4) State rules to determine significant figures 5) Count significant figures 6) Understand the importance of significant figures 7) Calculate the volume and density of an object 2
SCIENTIFIC NOTATION method for expressing very large or small numbers easily (Example: ) For example, the number 1,000,000 is in standard formation format. The scientific notation of this number is 1.0 x 10 6 We always move the decimal place to make the (the number out in front) between We then arrange the (the number up to the right of the ten) Now, if you were to take the 1.0 and move the decimal place 6 places to the right (since it is a positive number), you would get the original number (1,000,000) Example: 123000000000 Guided Practice Write the following numbers in scientific notation (remember the mantissa rule!) 1. 34000000 = 2. 0.0000067 = 3. 25,864 = Now, write the following scientific notations in standard (normal) notation form: 4. 5.7 x 10 8 = 5. 6.34 x 10-11 = Calculator Practice: First, let s enter the number 2.3 x 10-5 in scientific notation: 1. Type 2 2. Type the decimal point 3. Type 3 4. Then press the ee EXP or key(s) 5. Press the +/- key (NOT the or subtract key) 6. Type 5 Next, let s multiply that number by 1 mole, or 6.02 x 10 23. What do you get for your answer? 3
Measurements and the Metric System In chemistry we measure matter using units. This is an abbreviation for. SI BASE UNITS (AKA Base Units): **If you forget, use Table D in your Reference Tables! 4
SI Metric Prefixes Numerical (Multiply Root Word Prefix Symbol by)* Exponential tera T 1,000,000,000,000 10 12 giga G 1,000,000,000 10 9 mega M 1,000,000 10 6 kilo k 1,000 10 3 hecto h 100 10 2 deca da 10 10 1 no prefix: 1 10 0 deci d 0.1 10 1 centi c 0.01 10 2 milli m 0.001 10 3 micro 0.000001 10 6 nano n 0.000000001 10 9 pico p 0.000000000001 10 12 femto f 0.000000000000001 10 15 atto a 0.000000000000000001 10 18 *Example: In the word kilometer, the root word (base unit) is meter and the prefix is kilo. Kilo means multiply the root word by 1000. Therefore, one kilometer is 1000 meters (1 km = 1000 m). 5
Conversion Factors a mathematical expression that relates two units that measure the same type of quantity Examples: - *Rest Assured! For the Regents, the most you will have to convert will be between the milli-/kilo- /base unit (g, L, etc.). This is always a matter of. You must also make sure you move the decimal the (right or left, which depends on whether you are converting from small to big or vice versa). TRICK: kilo hecto deca base unit deci centi milli k h d base unit d c m Let s practice! 1. A car travels 845 km. How many meters is this? 2. Convert 0.0290 L to milliliters. 3. Convert 2500mL to liters. 4. 3 g = kg 5. 1 km = m 6. 1 kg = g 7. 1 L = ml 8. 7 m = mm 9. 12 ml = L Compare by placing a <, >, or = on the line provided: 10. 56 cm 6 m 11. 7 g 698 mg Once you get your answer, check it! Does it make sense? 6
Dimensional Analysis Often you will be required to solve a problem with mixed units, or to convert from one set of units to another. Dimensional analysis is a simple method to accomplish this task. Example: How many minutes are there in 15 days? Solution A: STEP 1: Figure out the units that you have and the steps to get to the units that you need. HAVE (What s missing?) NEED Days (d) Minutes (min) STEP 2: Make a math problem and plug in the numbers to make your first conversion. The number/units you HAVE goes in the top left, the number/units you NEED go in the top right, and the conversion factor goes in the bottom right. Have 15 d 24 h 1 d Need Conversion Factor STEP 3: Cancel like terms. Then, multiply the top numbers (the numerators) together and divide the result by the bottom number (the denominator). 15 d 24 h 1 d = 360 h minutes Since 24 hours and 1 day are equivalent, you are actually multiplying 15 days by a factor of 1. This means that the magnitude of your number stays the same and only the units change. In other words, 15 days = 360 hours STEP 4: Now, use your answer from Step 3 as the new HAVE and repeat the process using the conversion factor 60 minutes = 1 hour Have 360 h 7 60 min 1 h = 21600 min Conversion Factor Need minutes Now you try on: How many minutes are there in the month of October?
ACCURACY VS. PRECISION Accuracy Example: Hitting bulls eye when you are aiming for it *For most experiments, means from the expected value - Precision *For an experiment with +/- 5% as the margin for accuracy, that means the difference between the highest and lowest percent error cannot exceed a Example: If the highest percent error for an experiment is +7.6%, and the lowest is - 5.4% that range is 13.0%, which means that experiment was not precise Practice: Cheryl, Cynthia, Carmen, and Casey take target practice in PE. Assuming that they were all aiming at the bulls eye, match each target with the proper description. (a) Accurate and precise (b) Not precise, but one piece of data accurate (c) Precise but not accurate (d) Neither precise nor accurate Practice: The following data was collected during a lab experiment. The density of the cube should be 10.8 g/ml. Is this data is accurate, precise, both, or neither? Justify your answer. Trial Number Density of Cube 1 6.2 g/ml 2 6.3 g/ml 3 6.5 g/ml 8
SIGNIFICANT FIGURES - also known as Sig Figs (SF) A method for handling in all measurements This arises due to the fact that we have different equipment with different degrees of Significant figures are associated with do when determining sig figs o Ex: Atomic masses on periodic table Conversions (1in = 2.54 cm) Examples: 1. Reading a ruler We know for sure that the object is more than, but less than We know for sure that the object is more than, but less than This ruler allows us to estimate the length to 2. Reading a graduated cylinder: Measurements are read from the bottom of the Which gives a volume reading of 9
The Atlantic/Pacific Method - another way to determine the # sig figs in a number 1) Determine if a decimal point is present. If a decimal is present, think of P for present. If there is no decimal, think of A for Absent. P stands for the Pacific coast and A stands for the Atlantic Coast. 2) Imagine the number you are looking at is a map of the USA. Begin counting from the correct side of the number (Atlantic/right side or Pacific/left side) based on what you determined in step 1. Consider the first nonzero number you land on the start of your count. Consider each digit from here on out significant as well until you reach the other end of the number. Pacific Coast 3. Atlantic Coast Decimal is Present 1. Start @ 1 st NONZERO 2.Count all the way to the Atlantic NO EXCEPTIONS Decimal is Absent 1. Start @ 1 st NONZERO 2. Count all the way to the Pacific NO EXCEPTIONS Determine the number of significant numbers in each of the following: 1) 357 2) 3570 3) 3570. 4) 0.357 5) 0.0357 6) 3.570 x 10 3 7) 0.3570 10
Rules for Determining Number of Significant Figures in a Given Number Rule Example 1. All nonzero numbers (ex: 1 9) are always significant 123456789 m 1.23 x 10 2 2. Zeros located between nonzero numbers are significant 40.7 L 87,009 km 3. For numbers less than one, all zeros to the left of the 1 st nonzero number are NOT significant 4. Zeros at the end of a number and to the right of a decimal point are significant 5. Zeros at the end of a whole number may be significant or not. If there is a decimal after the last zero, they are significant. If there is not a decimal point after the end zeros, they are NOT significant 0.009587 m 0.0009 kg 85.00 g 9.070000000 L 2000 m 2000. m 6. Exact numbers have an infinite number of significant figures 1 ft = 12 inch PRACTICE: Measurement Number of Significant Figures Rule(s) Applied 1020 ml 1200 m 1200. L 1200.00 mm 0.001 km 10.00 L 12000 m 00.100 cl 22.101 mm 101,000 km 11
Rules for Using Sig Figs in Calculations General Rule Final answer must be expressed in the lowest amount of significant figures that were originally given to you (you can t create accuracy when you didn t have it to start with!) Operation Rule Examples Multiplication/Division Perform operation as normal & express answer in least # sigfigs that were given to you 12.257 x 1.162 = Addition/Subtraction Line decimal points up; round final answer to lowest decimal place (least accurate) value given 3.95 2.879 + 213.6 Examples: 5.1456 2.31 = 69.25/45.8 = Rules for Calculations with Numbers in Scientific Notation: Rule Addition/Subtraction All values must have the same exponent. Result is the sum or difference of the mantissas, multiplied by the same exponent of 10 Multiplication mantissas are multiplied and exponents of 10 are added Example 4.5 x 10 6-2.3 x 10 5 (3.1 x 10 3 ) (5.01 x 10 4 ) Division mantissas are divided and exponents are subtracted 7.63 x 10 3 / 8.6203 x 10 4 12
MEASURING MATTER 1. Mass vs. Weight MASS WEIGH T *We really only work with in chemistry class! ** We have the same whether we are on earth or on the moon. The different forces of gravity on each cause us to weigh more on earth than on the moon though (this is why we float on the moon!) 2. Volume - amount of an object takes up Techniques: Liquids Regular Solids Irregular Solids 3. Density: amount of mass in a given space; of mass to volume Formula (Table T): BOX A BOX B Which box has a higher density? Explain your answer. 13
Density Problems Show all work! *Note: the density of water is 1) What is the density of an object with a mass of 60 g and a volume of 2 cm 3? 2) If you have a gold brick that is 2.0 cm x 3.0 cm x 4.0 cm and has a mass of 48.0 g, what is its density? 3) If a block of wood has a density of 0.6 g/ cm 3 and a mass of 120 g, what is its volume? 4) What is the mass of an object that has a volume of 34 cm 3 and a density of 6.0 g/cm 3? 5) Which is heavier, a ton of feathers or a ton of bowling balls? 14
Percent Error Measurement of the % that the measured value is off from accepted value Measured value = Accepted value = Formula is found in Table T (back page 12) of your Reference Tables: If negative, your measured value is the accepted value If positive, your measured value is the accepted value *It is very important that you put the given values into the proper place in the formula! Sample Problem: In a lab experiment, you are told by your teacher that the actual (or accepted) amount of sugar in a can of Coke is 39 g. You experimentally determine it to be 40 g based on your own data and calculations. What is your percent error? Express answer in the proper amount of significant figures. 15
HOMEWORK: Scientific Notation and SigFigs Name: Date: Period: Show the work for each problem. No credit will be given for answers only. Section A: The Definition of the Notation (Decimal => Scientific) Write the following numbers in scientific notation. 1. 1001 6. 0.13592 2. 53 7. -0.0038 3. 6,926,300,000 8. 0.00000013 4. -392 9. -0.567 5. 0.00361 Section B: Converting Back (Scientific => Decimal) 1. 1.92 x 10 3 6. 1.03 x 10-2 2. 3.051x10 1 7. 8.862 x 10-1 3. -4.29 x 10 2 8. 9.512 x 10-8 4. 6.251 x 10 9 9. -6.5 x 10-3 5. 8.317 x 10 6 10. 3.159 x 10 2 Section C: Multiplication, Division and... with Scientific Notation Use Scientific Notation (and only the scientific notation!) to find the answer to the following multiplictions, divisions, additions. 1. 4.1357 x 10-15. 5.4 x 10 2 =? 2. 1.695 x 10 4 1.395 x 10 15 =? 3. 4.367 x 10 5. 1.96 x 10 11 =? 4. 6.97 x 10 3. 2.34 x 10-6 + 3.2 x 10-2 =? 5. 5.16 x 10-4 8.65 x 10-8 + 9.68 x 10 4 =? Section D: Significant Figures For the following, write each with the correct number of significant figures. 1. 38617954 x 10-1 * 1.15197705 x 10 6 2. 3.0001 * 5 3. 1.12 x 10 5 * 6.06 x 10 5 4. 2.27513 x 10 3 * 1.9376 x 10 2 5. 2 x 10 1 * 3.0 x 10 1 6. 5.567 x 10 8 / 2.215 x 10 8 7. 2.775 x 10-4 * 4.775 x 10 4 8. 5 / 8.14 x 10 2 9. 4.7192 x 10 2 / 3.862 x 10-4 16
Homework: Dimensional Analysis You must show your work using dimensional analysis to receive credit. Name: Date: Period: Length Mass 1 nautical mile = 6076.1 feet 1 league = 5 280 yards 1 cable = 120 fathoms 1 fathom = 6 feet 1 degree = 69.047 miles 1 mile = 5280 feet 1 hand = 4 inches 3 feet = 1 yard 1 gram = 15.432 grains Area 1 township = 36 square miles Volume 4 gills = 1 pint 2 pints = 1 quart 1 liter = 1.0567 quarts 1 bushel = 4 pecks = 32 quarts 1 gallon = 4 quarts 1 mile = 1.61 kilometers 1 meter = 3.28 feet 1. How many seconds old are you? 2. A person s weight is 154 pounds. Convert this to kilograms. (1 lbs. = 0.454 kilograms) 3. An aspirin tablet contains 325 mg of acetaminophen (Tylenol). How many grains is this equivalent to? 4. You pour yourself a glass of 500 ml of water. How many gallons is this? 5. Your best friend, Pluto, has just built a Spongebob Squarepants piñata that it 10 feet tall. How many meters is this? 6. A human has a density of 1.08 g/ml. Using dimensional analysis, what is the person s density in kg/l? 7. After eating 20 hot chili peppers, you race at 20 miles per hour to find a glass of water. How fast were you travelling in feet per second? 17
Homework: PERCENT ERROR ACCURACY AND PRECISION Name: Date: Period: PERCENT ERROR The accepted value is the true or correct value (what you SHOULD have gotten). The measured value is what YOU measured or calculated yourself. Notice that the numerator is in absolute value form. You should not have any negative percent error values. 1. A student buys a rope at the store. The label on the packaging says that the rope is 2.15 meters in length. The student measures the rope as 1.85m. What is the student s percent error? 2. A 250.0 gram block is placed on a balance. The balance measures the mass of the block as 243.9 grams. What is the percent error of the block? 3. A teacher calculates the molar mass of sodium hydroxide as 37 g/mol. The true molar mass of sodium hydroxide is 40 g/mol. Find the teacher s percent error. 4. There are 34 questions on a test. John answers 22 of them correctly. What is John s percent error? 5. You bought a new car and estimated that your monthly payment would be $312. However, your actual payment amount is $325. How much error was in your estimate? ACCURACY AND PRECISION If a value is ACCURATE, that means that it is CORRECT. (You re right!!) If a value is NOT ACCURATE, that means that it is INCORRECT. (You re wrong.) If your values are PRECISE, that means that they are very close to each other, whether or not they are correct (accurate). If your values are NOT PRECISE, that means that they are not very close to each other, whether or not they are correct (accurate) 1. For each of the following, label the accuracy and precision as either high or low. 18
accuracy accuracy accuracy precision precision precision 2. Using X s or dots to represent the location that arrows have struck a target, draw the following. Three arrows that have been thrown with high precision and high accuracy. Three arrows that have been thrown with high precision and low accuracy. Three arrows that have been thrown with low precision and high accuracy. Three arrows that have been thrown with low precision and low accuracy. 3. For each of the following, label the accuracy and precision of the temperature sensor measurements as either high or low. A. Suppose a lab refrigerator holds a constant temperature of 38.0 F A temperature sensor is tested 5 times in the refrigerator. The temperatures from the test yield are given in the table. Accuracy Precision Temperatures gained from sensor testing, degrees F 39.4 48.2 28.1 46.3 34.5 B. Suppose a lab refrigerator holds a constant temperature of 38.0 F. A temperature sensor is tested 5 times in the refrigerator. The temperatures from the test yield are given in the table. Accuracy Precision Temperatures gained from sensor testing, degrees F 37.8 38.3 38.1 37.4 38.0 C. Suppose a lab refrigerator holds a constant temperature of 38.0 F. A temperature sensor is tested 5 times in the refrigerator. The temperatures from the test yield are given in the table. Accuracy Precision 4. A measurement was taken three times. The correct measurement 19 Temperatures gained from sensor testing, degrees F 49.6 49.5 49.7 49.9 49.9
was 68.1 ml. Circle whether the set of measurements is accurate, precise, both, or neither. a. 78.1 ml, 43.9 ml, 2.0 ml accurate precise both neither b. 68.1 ml, 68.2 ml, 68.0 ml accurate precise both neither c. 98.0 ml, 98.2 ml, 97.9 ml accurate precise both neither 5. A student is given a rock that is known to have a mass of 436.8 grams. She measures the mass of the rock three different times with the following results: 460.9 g, 461.4g, 459.0 g. What can be said about her precision and accuracy? 4. A student is given a cube of metal that is known to have a mass of 125.0 grams. She measures the mass of the metal three different times with the following results: 125.1 g, 124.8 g, 125.3 g. What can be said about her precision and accuracy? 5. Label each of the following as PRECISE, ACCURATE, NEITHER, OR BOTH. 20
Homework: Density Practice Problems Name: Date: Period: Directions: Use the density formula below to derive two additional formulas, one for calculating mass and one for calculating volume. You can approach this as if you were solving for an unknown in math class or you can use the density triangle. Once you have all three formulas, use them to solve questions 1-6. For Density D = m/v For Mass m = For Volume V = You must show all work! 1) What is the mass of a 350 cm 3 sample of pure silicon (Si) with a density of 2.336 g/cm 3? 2) A student finds a rock on the way to school. In the laboratory he determines that the volume of the rock is 22.7 cm 3, and the mass is 39.943 g. What is the density of the rock? 3) The density of lead (Pb) is 11.342 g/cm 3. What would be the volume of a 200.0 g sample of this metal? 4) The density of silver (Ag) is 10.49 g/cm 3. If a sample of pure silver has a volume of 12.993 cm 3, what would the mass be? 5) If 30.943 g of a liquid occupy a space of 35.0 ml, what is the density of the liquid in g/cm 3? 6) Pure gold (Au) has a density of 19.32 g/cm 3. How large would a piece of gold be if it had a mass of 318.97 g? 21