CHAPTER 2. SCIENTIFIC MEASUREMENTS CHM130 GCC Chemistry Department

Read all sections of Ch. 2 These slide presentation are not online. The online NOTES contain basically the same information, just in an outline form so it takes less paper. You should print them out and bring to class You should take your OWN additional notes during lecture in the margins or back of pages of the online notes for anything not in the online notes. I’ll help you know what to write down. Examples are different between the online notes and slides to give you MORE examples. You should write down the examples we do in class, and then do the examples in the notes at home.

2.1 Measurements Measurement – number with unit We’ll mostly use metric units All measurements have uncertainty Sometimes you have to estimate a reading

Length Measured in meters (cm, mm, m) Measured with rulers Some rulers have more marks than others Which ruler is more accurate? Which ruler has more uncertainty?

Mass Measured in grams (mg, kg, g) Measured by a balance Always write down all the numbers on a digital balance in lab!

Mass vs. Weight Mass: the amount of matter in an object; mass is not affected by gravity. Weight: a measure of the force of gravity. Mass is same anywhere, but weight differs. Ex: An astronaut weighs 170 lbs on earth, but 29 lbs on the moon.

Volume: amount of space occupied. Volume is measured using beakers, flasks, graduated cylinders, syringes, burettes and pipettes. Units are liters (L, kL, mL)

Can you name these for fun?

cc What kind of unit do syringes have in hospitals? What does that stand for? Remember this: 1 mL = 1 cm3 = 1 cc Remember these from the English system? 1 gallon = 4 quarts, 1 quart = 2 pints 1 pint = 2 cups cc Cubic centimeter

2.2 Significant Digits or Significant Figures (Sig figs) Significant Figures: All digits (numbers) in a measurement that are known plus one more that is estimated - a guess. Ex: Bathroom scale vs. surgical scale – which is more accurate? Which has more sig fig?

What is the length of the candy?

Counting Significant Figures Numbers 1-9 always count. 4895.2 has 5 sig figs Zeroes in front never count. 0.0005454 has 4 sig figs Zeroes after decimal point AND a # count. 0.0880 has 3 sig figs 28500 has 3 sig figs Zeros between sig digits count. 3050 has 3 sig fig 0.002001 has 4 sig fig

As you will see, sig fig rules don’t apply to exact numbers. Exact Number: something counted or a definition, not something measured Exact: 14 people, 3 feet per yard, 100 cents per dollar, 5 ipods, 12 cans of beer Not exact: 7 inches, 200 pounds, 10 ounces As you will see, sig fig rules don’t apply to exact numbers.

How many sig figs in: 5.05 1200 0.02020 0.0005 50 50.00 123.45 8090 3 2 4 1 5

2.3 Rounding Rules for rounding numbers: < 5, don’t round up. Don't change the magnitude of the number. Holy crap what is magnitude? How big or small the number is. Is it in the thousands? Hundreds? Tenths? Billions? If a number is in the thousands, when you round it must STILL be in the thousands.

Round these numbers off to 3 significant figures. 1.84 $7160 NOT 716. Seven thousand dollars is not the same as seven hundred dollars!!! (Magnitude) 0.00131 24,900 1) 1.8374 2) $7162.32 3) 0.00131154 4) 24,925

2.4 Adding and Subtracting Addition and subtraction: Your final answer must have the same decimal places as the fewest decimal places. (Your answer can only be as accurate as the weakest link) 13.5478 - 11.20 2.3478  Final answer = 2.35 Rounded to 2.35 since 11.20 has two decimal places Focus on Decimal Places

2.5 Multiplication and Division Your final answer has the same # sig dig as the LEAST sig dig. 3.546 x 1.4 = 4.9644 = 5.0 2 sig fig cause 1.4 is 2 sig fig Focus on Sig Fig

2.6 and 2.7 Exponential Numbers and Scientific Notation Convenient method for expressing very large or very small numbers.

Writing Numbers in Scientific Notation: Left for large numbers Distance from the earth to the sun ~ 93,000,000 miles We need to move the decimal 7 places to the left = 9.3 x 107 miles We must have one digit before the decimal place only. 93 x 106 is wrong

Writing Numbers in Scientific Notation: Right for small numbers Radius of a carbon atom ~ 0.00000000017 meters We need to move the decimal 10 places to the right = 1.7 x 10-10 meters 21

Convert the following to scientific notation: 548.005 68,100,000 0.000400 2000 Note – Sci notation always shows sig fig’s. 5.48005 x 102 6.81 x 107 4.00 x 10-4 2 x 103

DO NOT type in “x10 ^”. The EE or EXP is in place of the x10^ The number 235,000,000 in scientific notation on your calculator: is 2.35 x 108 Punch in as 2.35 EE 8 DO NOT type in “x10 ^”. The EE or EXP is in place of the x10^

Calculator You must have your own scientific calculator Your instructor will show you examples You may not use graphing calculators on quizzes or exams – Department rules You may not use your phone as a calculator on quizzes or exams either!

Practice Problem Try this on your calculator – write in your notes 2.84 x 1023 / 7.24 x 1012 = ? 3.92 x 1010 If you got this wrong, you forgot to use your EE or EXP button correctly. You MUST be able to do problems like this on your calculator. Raise your hand if you need help or see me after class.

Making Sci notation show What if your calculator shows you a large number like 123456789? You don’t want to have to count to figure out the scientific notation. On most calculators push “2nd” “SCI” and then it shows 1.23456789 8 For other calculators you much put it into Scientific mode by pushing the “mode” button and selecting SCI then hitting enter. Get help with this after class or in tutoring.

2.8 Unit Equation and Unit Factor Unit equation : 10 dimes = 1 dollar Unit factor : Any equality (3 feet per 1 yard, 5 pennies per nickel, 12 inches per foot) can be written in fraction form for conversions. Remember definitions don’t count as sig fig in calculations. Examples to follow.

2.9 Unit Analysis Problem Solving What units need to be found? Always START with the given Multiply GIVEN by fractions so the units cancel until you get the final units Round to the correct # of sig fig SHOW ALL YOUR WORK IN THIS CLASS FOR FULL CREDIT

(Note that exact numbers in conversions do not limit sig figs) How many feet is 47.25 inches? 47.25 inches ( 1 foot / 12 inch) = 3.938 feet Can someone explain? Multiplying so focus on sig fig Least sig fig is 4! The 1 foot / 12 inch is EXACT which means infinite sig fig (1.000000000… / 12.000000000…) Definitions like 12 inches = 1 foot will not be “counted” in figuring out your sig fig. (12 inches is EXACTLY 1 foot)

Worksheets for each chapter http://web.gccaz.edu/~ksmith8/rev130.htm These types of problems are conversions, and we’ll do more in chapter 3. Start practicing NOW on them. Seriously. Also do all the practice problems in your online notes. Same web page. See we expect you to already know how to do conversions, so will not spend much time in class on them, so YOU MUST practice a lot of problems at home!

2.10 The Percent Concept Percent: Ratio of parts per 100 total parts. (e.g. 80% is 80 parts/100 total parts) To calculate Percent: % = Given the percent, you can find the part or whole.

75.3% = (part pure / 425 kg total) x 100 A chemistry class has 24 students. If 7 students are wearing red, what percent is wearing red? A coin collector has 5 silver dollars, 6 state quarters, and 3 Indian Head pennies. What percent is silver dollars? 29% or 29.2% 36 or 35.7% These problems ONLY have exact numbers, no measurements, so you can write how many sig figs you want. The next problem has measurements, so obey sig fig rules. A crime lab finds 425 kilograms of meth that is 75.3% pure? How many kilograms of pure meth are there? 75.3% = (part pure / 425 kg total) x 100 Part pure = 3.20 x 102 kg (not 320, why?) Need 3 sig fig

Page 39 self test Try problems 1 – 10, 14 – 18, 20 Answers in Appendix J

If time How many inches are in 3.95 yards? How many days is 7.94 x 109 seconds?