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Scientific & Chemical Fundamentals Measurement, Conversions & Calculations Dr. Ron Rusay Fall 2007 © Copyright 2003-2007 R.J. Rusay Measurement & Units SI units & common units in General Chemistry (Lab Manual pp. 139-142) 1 • Quantitative vs. Qualitative • MASS (Chem: gram; SI: kg) • LENGTH (Chem: cm & others; SI: m) • TEMPERATURE (Celsius & Kelvin; SI: K) • VOLUME (Chem: mL; SI: Liter) • CHEMICAL AMOUNT: Mole (mol) © Copyright 1998-2007 R.J. Rusay Units of Measure Units U.S. SI Chemistry Mass (weight) Pound (lb) Kilogram (kg) Volume Gallon (gal) u Liter (L) Temperature Fahrenheit (oF) Mile (mi), Feet(ft), Inches (in) Kelvin (K) “ Gram” (g, mg) “ Liter” (mL, L) K & Celsius (oC) Length Time Meter (m) “ Meter” (cm, mm, nm) Second (s) Second (s) Mole (mol) Mass and Volume Measurements: Refer to pp. 5-8 Mass Determination (Weighing Devices: Balances) Volumes of regular shapes V=s3 h V=lxwxh 01_05 1m3 Volume 1dm3= 1 L 1cm3= 1 mL 1 cm 1 cm Liquid Measurement Tools Numbers & Measurement The Importance of Units Measurement - quantitative observation consisting of 2 parts • Part 1 - number • Part 2 - unit Examples: • 20 grams • 6.63 joules / second Scale: Size & Comparison Macroscopic vs. Microscopic IBM financed Video: http://www.wordwizz.com/imagendx.htm How would you compare your lifespan?.. to that of a dog? ….to the age of the earth?…How about the age of mankind to that of all life?.. ..the age of industrialized mankind to the age of mankind? Graphic Comparisons Powers of Ten: Scale Language describes scale (prefixes) Shorthand Prefixes How many zeroes does yotta yotta yotta have? Commonly used prefixes in Chemistry These should be known from memory. Commonly used prefixes in Chemistry Attosecond spectroscopy = 10 -15 x 10 -3 seconds Science, 317, 765-775, (2007) “The Electron Stopwatch” QUESTION Conveniently, a U.S. nickel has a mass of approximately 5 grams. If you had one dollar’s worth of nickels what would be the mass of the nickels in milligrams? 1. 2. 3. 4. 100 milligrams 50 milligrams 1,000 milligrams 100,000 milligrams 1000 milligrams (mg) = 1 gram (g) Scientific Notation & Significant Digits Scientific Notation: A single digit followed by a decimal and a power of ten. Examples: 2,345 mL and 0.002340 g 2,345 mL = 2.345 x 10 3mL 0.002340 g = 2.340 x 10 -3 g Numbers 1 • Expressing a number correctly is determined by the method used in the measurement! • How many numbers should I include? Significant Digits (Figures) Consider: the exactness of the measured value • Short Hand expression translates the number: Scientific Notation © Copyright 1998-2007 R.J. Rusay What is the length of the rod? Different measurement tools give different numbers: Which ruler is better? ? cm 4.2 - 4.3cm ? cm 4.24 - 4.25cm What is the diameter of a circle? All measuring devices are not the same, and the values (numbers) that come from them indicate their limitations. Is there a better instrument to use other than a ruler? Buret 08 mL 0 10 22.2 mL 20 30 40 50 What does each line represent? 1 mL What can be estimated? O.1 mL Measurement Assignment http://chemconnections.llnl.gov/General/Chem120/volume1.htm Temperature Scales Relative to Water “Normal” Body Temperature QUESTION Dr. R. walks into class and claims, “It is very cold in here today. It feels like 242 K.” If that were the temperature, would you agree that you would feel cold? What would that be in Celsius degrees? 1. 2. 3. 4. I agree, that would be 31°C. I agree, that would be – 31°C. I do not agree, that would be 31°C. I agree, that would be –31.15°C. Temperature Reporting Numbers Rules for Significant Digits (Figures) Nonzero integers always count as significant figures. 3456 g has how many sig figs? 4 sig figs. • Expressed in scientific notation? 3.456 x 10 3 g Reporting Numbers Rules for Significant (Digits) Figures Exact numbers (unit, conversion or scale factors) can have an infinite number of significant figures. 1 liter = 1,000. ml, exactly 1 inch = 2.54 cm, exactly Zeros Leading zeros do not count as significant figures. 0.0486 mL has how many sig figs? 3 sig figs. • Number expressed in scientific notation? 4.86 x 10 -2 mL Zeros Captive zeros always count as significant figures. 16.07 cm has how many sig figs? 4 sig figs. Number expressed in scientific 1.607 x 10 1 cm notation? Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 kg has how many sig figs? 4 sig figs. • Number expressed in scientific 9.300 kg notation? QUESTION Which one of the following does NOT represent a result with four significant digits? 1. 2. 3. 4. 0.07100 0.7100 0.7010 0.0710 Mathematics & Arithmetic 1 • Relative to method(s) of measurement • Short Hand expression: Scientific Notation • Numbers : How many to include? Quantitative vs. Qualitative • Addition/Subtraction...... • Multiplication/Division..... • What is “significant”?.....Rounding Off • http:dbhs.wvusd.k12.ca.us/SigFigsFable.html © Copyright 1998-2007 R.J. Rusay Systematic Problem Solving Dimensional/Unit Analysis: Conversions Workshop pp. 145-149 How many mL of milk are in a1/2 gallon carton? 0.50 gal 1 gal = 4 qt ? mL 1 qt = 946 mL 0.50 gal | 1 qt | 946 mL = ? mL | 4 gal | 1 qt Complete the following Units & Conversions Number 13,000,000,000 yrs. Scientific Notation 10 yrs 1.3 x 10 ________________ 546 ___________ mL 5.46 X 10 2 mL ______________ 0.845 ____________ kg __8.45 x 10 -1 kg___ Named unit __? gigayears 13 Gyrs 0.546 Liters 0.546 L _? grams__ 845 g Computational Rules 1 • Addition/Subtraction: Answer expressed • to the least number of decimal places of the figures in the process Multiplication/Division: Answer expressed to the least number of significant figures © Copyright 1998-2007 R.J. Rusay Addition Four students were each asked to measure a piece of wire and provide a total length for the four pieces. Report the result correctly: 0.05 cm 12.01 cm 1.9 cm + 2.386 cm _______ 16.346 cm QUESTION If you were unloading a 23.50 kg box of books from your car and a “friend” added two more 482 gram chemistry books, how much in kg and using the rules for significant digits, would you be lifting? 1. 2. 3. 4. 23.98 kg 24.464 kg 24.46 kg 24.5 kg Mathematical Processes: Provide correct answers assuming each value (unit omitted) is written with the correct number of sig figs: 12.01 x 1.90 _______ ______________ = 9.56370 2.386 12.01 x 1.90 _______ ______________ + 0.05 = 9.61370 2.386 QUESTION The average mass of a certain brand of vitamin C tablets is 253 mg. What is the mass of three such tablets rounded to the proper number of significant digits? 1. 2. 3. 4. 0.760 grams 0.759 grams 0.7590 grams 0.253 grams Conversion Factor Method (Dimensional Analysis) 1 • Qualitative Descriptions vs. Quantitative • Use exact numbers / “scale factor” UNITS • A Bookkeeping Method: Example Short” 5 ft___in 5 ___ --------> ? m • (1 ft = 12 in; 2.54 cm = 1 in; 100 cm = 1 m) 5 5 • ___ft x 12 in/ft + ___in = 65 ___in 1.651 65 • ___in x 2.54 cm/in x 1 m/100cm = ___m © Copyright 1998-2007 R.J. Rusay