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Unit 1 Lab Safety Notes . • _________________________ should be worn at all times when in the lab. • __________________________ can never be worn in the lab. All shoes must have ___________________________________________________. • If your lab partner is on fire, you should _____________________________ _____________________________________________________________. • If you get chemicals in your eyes (because you are a bad student so you did not wear your goggles in the lab area), you should use the eye wash station for _______ minutes. • The _____________________________________ is used to remove noxious fumes and vapors. • If you spill a large amount of chemical on you, you should ______________ ____________________________________________________________. • When heating a test tube, you should always ________________________ ____________________________________________________________. • Wafting is a method of smelling chemicals by ________________________ ____________________________________________________________. • You should never ______________ or ________________ in the lab. • You must complete the __________________________ if you want to participate in the lab. You MUST read the _________________ before you enter the lab. Unit 1 Scientific Notation Scientists often work with very large or very small numbers, which are more easily expressed in exponential form or scientific notation. You write a very large number in scientific notation by moving the decimal point to the left until only one digit remains to the left. The number of moves of the decimal point gives you the exponent. Formally, scientific notation is also known as standard index notation. For example: 3,454,000 = 3.454 x 106 For very small numbers, you move the decimal point to the right until only one digit remains to the left of the decimal point. The number of moves to the right gives you a negative exponent: For example: 0.0000005234 = 5.234 x 10-7 Practice Problems 0.000 000 000 000 615 g 98 000 000 000 m 0.000 104 s 407 302 000 000 000 Pa 4.38 x 10-7 km 1.89 x 104 L Addition Example Using Scientific Notation When adding and subtracting problems written in Scientific Notation the exponents must be the same. 1. The first part of the numbers are added or subtracted and the exponent portion is unchanged. 2. If necessary rewrite the problem in Standard Form for your final answer. (1.1 x 103) + (2.1 x 103) = 3.2 x 103 Subtraction Example Using Scientific Notation (5.3 x 10-4) - (2.2 x 10-4) = 3.1 x 10-4 Multiplication Example Using Scientific Notation You do not have to write numbers to be multiplied and divided so that they have the same exponents. You can multiply the first numbers in each expression and add the exponents of 10 for multiplication problems. (2.3 x 105)(5.0 x 10-12) = When you multiply 2.3 and 5.3 you get 11.5. When you add the exponents you get 10-7. At this point your answer is: 11.5 x 10-7 You want to express your answer in scientific notation, which has only one digit to the left of the decimal point, so the answer should be rewritten as: 1.15 x 10-6 Division Example Using Scientific Notation In division, you subtract the exponents of 10. (2.1 x 10-2) / (7.0 x 10-3) = 0.3 x 101 = Unit 1 Percent Error Notes Accuracy, Precision, and Error ____________ value. - accuracy can be determined by _______)____ measurement Accuracy – is how close the measurement is to the Precision – describes the closeness, or _____________, of a set of measurements taken under the ____________ conditions - precision is determined by _________________measurements Accepted (or theoretical) value – a quantity used by general agreement of the scientific community Experimental (or actual) value – a quantitative value measured during an experiment Error is the difference between the_ ___________ value and the_ ____________ _ value Formula % error = (|Your Result - Accepted Value| / Accepted Value) x 100 | | Example: Peter measured the volume of a 2.00 liter bottle of soda. The actual volume of the soda was 1.87 Liters. What is the percent error of the volume of soda? % error = (|Your Result - Accepted Value| / Accepted Value) x 100 % error = |1.87 L — 2.00 L| X 100 2.00 L % error = |- 0.13L| X 100 2.00 L % error = 0.13L X 100 2.00 L % error = 0.065 X 100 % error = 6.5% Significant Figures Pacific – Atlantic Rule • It's for determining the number of significant figures. Think of the U.S. in a map. The Atlantic Ocean is to the right. Pacific Ocean to left. • If a decimal is present, start counting from the "Pacific" (left). • If absent, starting count from "Atlantic" (right). • So, what are we counting? We count the first nonzero digit we encounter; and all subsequent digits If the decimal is PRESENT, start on the PACIFIC side or _____ __________. 14.020 0.00235 1.04 * 105 If the decimal is ABSENT, start on the ATLANTIC side or _____ t ___________. 7300200 1200 839 Significant Figures are all exact digits of a measurement plus one estimated digit. Brief determination of the number of significant digits Rule #1: All non-zero numbers are significant 732 g Rule #2: Any zero’s between non-zero numbers are significant 301 cm Rule #3: If there is a decimal point, any zero’s to the right of the last non-zero are significant a. 320. kg b. 320 kg c. 0.70 m d. 0.070 m Rule #4: Any number that is used to count things or is a direct conversion has infinite significant figures. a. 45 desks b. 60 s = 1 minute c. 10 pennies = 1 dime d. 4 beakers Remember If the value ___ _____ decimal point, then go to the__ ____ end of the value, moving right, find the first non-zero number; count it and every number to the right. ⟶0.0012040 If the value does not ____ ______ decimal point, go to the __ ____end of the value, moving to the left find the first non-zero number; count it and every number to the left. 7201000 ⟵ Significant Figures and Scientific Notation Practice Underline the significant figures in the following measurements and put the number in scientific notation: 1. 0.00325 m Round the following measurements to the requested number of significant figures and put the number in scientific notation: Put the following measurements in scientific notation and put the number in scientific notation: 1. 0.000000586 m 1. 0.003256 m 2 sig. figs. 2. 12500 s 2. 5620000 g 2. 564025000 g 3 sig. figs. 3. 304.00 g 3. 85000 L 3. 78265 ns 1 sig. fig. 4. 0.00256 kg 4. 0.00236 km 4. 0.236578 Pa 4 sig. figs. 5. 0.0030600 J 25640000000 Pa 5. 0.008596 ng 3 sig. figs. Perform the following calculations and write the answer with the appropriate number of sig figs AND in scientific notation. 1. 6.23 x 106 kL + 5.3 x 106 kL 2. 7.525 x 105 kg - 5.43 x 102 kg 3. 4.8 x 105 km x 2.02 x 103 km 4. 8.45 x 102 g ÷ 7.901 x 103 cm3 5. 2.45 x 10-15 J ÷ 3.4 x 10-19 J 6. 20.05 x 10343 – 15.9 x 10341 Rounding off numbers (Using Significant Figures) Rule #1: If the number after the number to be rounded is less than 5, round down. Rule #2: If the number after the number to be rounded is greater than or equal to 5, round up. In a series of calculations, carry extra digits through to the final result and then round off. This means that you should carry all of the digits that show on your calculator (or most of them) until you arrive at your final answer and then round off. Note: Don’t forget significant zeros when writing in scientific notation (ex: 20.0 is 2.00 x 10). Do not write INsignificant zeros when writing in scientific notation (ex: 6 000 000 is 6 x 106, not 6.000 000 x 106 – this number would have 7 sig figs). Addition and Subtraction Rule: Complete the desired calculation and then round off the answer to the number of decimal places as the value from the problem with the _______ NUMBER OF DIGITS ___ THE DECIMAL. a) 12.72 34.1 + 0.463 47.283 47.3 all numbers are significant to b) c) 370 + 101.037 the tenths place. All numbers are significant to the ______________ place. 900 790. 330 + 54.8 All numbers are significant to the ______________ place. Multiplication and Division Rule: Complete the desired mathematical calculation and then round off the answer to the same number of significant figures as the value from the problem with the ____________ NUMBER OF SIGNIFICANT FIGURES. 34.91 x 0.0053 = 0.185023 Rounds to 0.19 four sig figs two sig figs two sig figs Because 0.0053 has only two significant figures, it limits the answer to two significant figures. 3. 102 ÷ 0.0097 = Rounds to Combination of operations Complete mathematical calculations in correct order and use correct number of significant figures after each step. Example: (5.2 – 0.2) x 7.00 x 1.00 = 35.00 The difference of 5.2 and 0.2 is 5.0 which is precise to the nearest tenth and has 2 sig. figs. Since 7.00 and 1.00 have 3 sig. figs. The least number of sig figs in the multiplication operation is 2 from the 5.0 difference. The final answer has 2 sig figs. Answer = 35 7 DIMENSIONAL ANALYSIS NOTES: Metric and English Units Conversions This page features tables for converting between metric system units and corresponding English units commonly used in the United States. Here you will find convenient conversion tables for length, area, volume, weight, pressure, energy and temperature units. Conversion table calculations show approximately three (3) significant figures. Length Conversion Metric length units include the meter, the kilometer (1,000 meters), the decimeter (0.1 meters), the centimeter (0.01 meters), the millimeter (0.001 meters), the micron (0.000001 meters), the nanometer (0.000000001 or 1e-9 meters), and the angstrom (0.0000000001 or 1e-10 meters). British and American length units include the foot, the yard (3 feet), the furlong (660 feet), the mile (5,280 feet), the league (15,840 feet), and the inch (1/12th foot). Length Conversion Table Metric Units English Units Kilometers Meters Millimeters Inches Feet Yards 1 1,000 1,000,000 39,370 3,281 1,094 0.001 1 1,000 39.37 3.281 1.094 0.000001 0.001 1 0.03937 0.003281 0.001094 Miles 0.6214 0.0006214 6.214e-7 0.0000254 0.0003048 0.0009144 1.609 0.00001578 0.0001894 0.0005682 1 0.0254 0.3048 0.9144 1,609 25.4 304.8 914.4 1,609,000 1 12 36 63,360 0.08333 1 3 5,280 0.02778 0.3333 1 1,760 Scientists generally work in metric units. Common prefixes used are the following: Prefix megakilohectordeka g/m/l deci centimillimicronano- Abbreviation M k h da Meaning 106 103 102 101 Example 1 megameter (Mm) = 1 x 106 m 1 kilogram (kg) = 1 x 103 g 1 hectometer (hm) = 1 x 102 m 1 dekameter (dam) = 1 x 101 m d c m 10-1 10-2 10-3 10-6 10-9 1 decimeter (dm) = 1 x 10-1 m 1 centimeter (cm) = 1 x 10-2 m 1 milligram (mg) = 1 x 10-3 g 1 micrometer ( g) = 1 x 10-6 g 1 nanogram (ng) = 1 x 10-9 g n 8 The Principle behind Dimensional Analysis The guiding principle of dimensional analysis is that you can multiply anything by “1” without changing the meaning. An equality set into a fraction formation = 1. For example, if x = y, then x/y = 1 and y/x=1. Therefore, the equalities can be set into fractions and multiplied to convert units. Another concept necessary to understanding dimensional analysis is that units that are on the top and bottom of an expression cancel out. Example Let's focus on the first example: Convert 2.50 µg to picograms STEP ONE: Write the value (and its unit) from the problem, then in order write: 1) a multiplication sign, 2) a fraction bar, 3) an equals sign, and 4) the unit in the answer. Put a gap between 3 and 4. All that looks like this: The fraction bar will have the conversion factor. There will be a number and a unit in the numerator and the denominator. STEP TWO: Write the unit from the problem in the denominator of the conversion factor, like this: STEP THREE: Write the unit expected in the answer in the numerator of the conversion factor. STEP FOUR: Examine the two prefixes in the conversion factor. In front of the LARGER one, put a one. There is a reason for this. I'll get to it in a second. STEP FIVE: Determine the absolute distance between the two prefixes in the conversion unit. Write it as a positive exponent in front of the other prefix. Now, multiply and put into proper scientific notation format. Don't forget to write the new unit. 9 Practice Problems 1. 0.75 kg to milligrams Answer = ___________ mg 2. 1500 millimeters to km Answer = ___________ km 3. 2390 g to kg Answer = ___________ kg 10 4. 0.52 km to meters Answer = ___________ m 5. 65 kg to g Answer = ___________ g Website Dimensional Analysis Example: http://www.khanacademy.org/math/arithmetic/basic-ratios-proportions/v/conversion-between-metricunits?playlist=Developmental%20Math#channel=f275d6f01f13244&origin=http%3A%2F%2Fwww.khanacademy .org&channel_path=%2Fmath%2Farithmetic%2Fbasic-ratios-proportions%2Fv%2Fconversion-between-metricunits%3Fplaylist%3DDevelopmental%2520Math%26fb_xd_fragment%23xd_sig%3Df398c9ff7e273ce%26 11 Practice SI Unit Conversions (Single Unit Conversion) 1. Convert 0.0036 g to mg 1000 mg 0.0036 g x 1g 2. Convert 8.9 x 10-8 s to min = 3.600 g (remember sig figs!) 3. Convert 8200000nPa to MPa 4. Convert 3.26 L to cm3 5. Convert 0.0012 cm3 to mL 6. Convert 6500 dm3 to cm3 7. Convert 0.29 L to cm3 8. Convert 2.96 x 1014 nL to kL 12 SI Unit Conversions Practice Multiple Unit Conversion Example Sample 1: If light from the sun takes 8.11 minutes to get to the Earth, how far away is the sun in km? (speed of light is 3.0x108m/s and there are 1000 m in one km). 1. Identify the values in the problem, include units. 8.11 minutes km away from the earth Speed of light is 3.0x108m/s 2. Start with the value with only one unit. 8.11 minutes 3. Put that starting unit into the denominator to cancel units out. 8.11 minutes X 60 seconds 1 1 minute = 4. Find the value OR conversion to a given value with the same unit and place it into the problem. 8.11 minutes X 60 seconds 1 1 minute = 486.6 seconds 5. Repeat until you get to the desired units, cross out units which cancel. 3.0 x108 m 1 seconds 486.6 seconds X 1 = 14.598 x1010 m = 1.4598 x1011 m 6. Solve and put into correct scientific notation (multiply numerator and divide denominator). 1.4598 x1011 m 1 X 1 km 1000 m = 1.4598 x108 km 13 DIMENSIONAL ANALYSIS PRACTICE PROBLEM: If you live 3.2 miles from your best friend and the speed limit is 25 miles/hour, how many seconds will it take you to drive from your house to your friend’s house? You want to earn $600 to buy a new bicycle. You have a job that pays $6.75/hour, but you can work only 3 hours/ day. How many days before you will have enough to buy the bike? Someone that never learned dimensional analysis went off to work at a fast food restaurant for the past 35 years wrapping hamburgers. Each hour you wrap 184 hamburgers. You work 8 hours per day. You work 5 days a week. You get paid every 2 weeks with a salary of $840.34. How many hamburgers will you have to wrap to make your first one million dollars? In 1973 the Emergency Highway Energy Conservation Act instituted a National Maximum Speed Law of 55 mph. How many minutes would it take to travel 16 kilometers? (1 mile = 1.6093 km)? 14