Chapter 2 Measurements and Solving Problems

Transcription

1 History of Measurement Chapter 2 Measurements and Solving Problems Humans once used handy items as standards or reference tools for measurement. Ex: foot, cubit, hand, yard. English System the one we use. Feet, inches, yards, miles, pounds, gallons, etc. Uses a variety of conversions (12 inches = 1 foot, 3 feet = 1 yard, 8 pints = 1 gallon, 16 ounces = 1 pound, etc.) 1960 Scientists around the world adopted the SI System Systeme International) (what we sometimes call the metric system). I. Fundamental SI Units -SI measurement names come from base units with prefixes used to modify the size of the base unit. - Important prefixes for chemistry: kilo = 1000 x centi =1/100 th x milli = 1/1000 th x 1

2 1. Length - base unit is the meter (m) 1 meter is slightly longer than 1 yard - 1 centimeter (cm) = 1/100 th of a meter 1 cm =1/2 inch 100 cm = 1 m - 1 millimeter (mm) = 1/1000 th of a meter 1 mm = thickness of a dime 1000 mm = 1m 2. Mass - base unit is the kilogram (kg) 1 kilogram is heavier than 1 pound ( lbs.) 1 gram (g) = mass of 1 paper clip 1 milligram (mg) = 1/1000 th of a gram (very small mass) 1000 mg = 1 g 3. Volume a. solids -base unit is a cubic centimeter (cc or cm 3 ) (a small cube 1 cm on each side) 2

3 b. liquids and gases - base unit is the liter (L) slightly larger than a quart we will generally use milliliters (ml) 1 ml = 1/1000 th of a liter also, 1 ml = 1 cm 3 4. Time measured in seconds (s) 1000 ml = 1000 cm 3 = 1 L (a 10 cm x 10 cm x 10 cm cube) 3

4 II. Use of Measurements in Calculations How many inches in 10 feet? How did you find that? Factor-Label Method **Extremely useful calculation method, based on simple algebra. 1. Write down the given from the problem (including units). 2. Multiply by a conversion factor - on the bottom, put the units you are given - on the top put the units you are trying to find. 3. Insert the necessary numbers into the conversion factor. 4. Cancel units that appear on both top and bottom (if units don t cancel to give the desired unit, it is probably set up incorrectly). 5. Multiply/divide as needed to get answer (include units). Ex: How many inches in 10 feet? 10 ft. x 12 inches = 120 inches 1 ft. **Always include units!! Without units it is wrong!! Ex: = 1 Do you agree? 36 weeks + 16 weeks = 1 year Units matter!! Ex: Using factor-label method, find the # of quarters in 75 dollars. 75 dollars x 4 quarters = 300 quarters 1 dollars Ex: How many seconds in one week? 1 week x 7 days x 24 hours x 60 mins x 60 sec = 604,800 sec 1 week 1 days 1 hrs 1 min 4

5 III. Density - a measure of how tightly the atoms of a substance are packed together. Density = mass volume d = m V normal density units are g/ml or g/cm 3 **Since temperature affects how tightly molecules are packed, temp. affects density! Ex: warm air rises, cold water sinks, etc. 5

6 Calculating with Density: Ex: Find the density of a piece of Al with a volume of 4.0 cm 3 and a mass of 10.8 grams. D = m D = 10.8 g D = 2.7 g/cm 3 V 4.0 cm 3 Ex: What is the density of a block of marble with a mass of 594 g and a volume of 216 cm 3? D = m = 594 g = 2.75 g/cm 3 V 216 cm 3 Ex: A 40.0 cm 3 sample of quartz has a density of 2.65 g/cm 3. What is the mass of the quartz sample? D = m V m = DV (2.65 g/cm 3 )(40.0 cm 3 ) m = 106 g 6

7 IV. Heat and Temperature 1. Temperature a measure of the average kinetic energy of the particles in a sample of matter. As T, KE (particles are moving faster), and as T, KE (particles are moving slower). If you have a beaker of water at 50 C, then pour off half of the water, is the T still 50 C? Yes So, T is an intensive physical property. (intensive/extensive) 2. Heat also called heat energy. The total of the kinetic energies ofall of the particles in the sample of matter. If you pour off half of the 50 C water, do you have the same amount of heat? No so, heat is an extensive physical property. If you put 10 ml of boiling water on one ice cube, and 100 ml of boiling water on another ice cube, will both have the same effect? Explain. 3. Heat Flow heat energy transferred between two systems at different temps. Heat always flows from higher T lower T. Once the temps are equal, no more energy will flow. 7

8 (Our hands are reliable heat flow indicators, but not reliable temp. indicators!) 4. Temperature Scales how do thermometers work? 1. Fahrenheit ( F) Invented with the mercury thermometer in 1714 by Gabriel Fahrenheit (Holland). 2. Celsius ( C) Developed in the early-mid 1700 s by Anders Celsius (Sweden). 3. Kelvin (K) Developed in mid-late 1800 s by William Thomson, Lord Kelvin (England). **Official SI unit for temp. Comparisons: F C K (rounded) Boiling Pt. of water Body temp of humans Freezing pt. of water Absolute zero (coldest poss. temp) Conversions K = C C = K F = [t( C) x 1.8] + 32 C = t( F)

9 V. Using Scientific Measurements A. Accuracy and Precision 1. Accuracy how close a measurement is to the true or accepted value. 2. Precision when several measurements of the same thing are very close together. A set of measurements can be very precise, but not accurate. B. Significant Figures (sig figs) when scientists report a measurement, they want to give as much information as possible, but only dependable info. They do this using sig figs. Sig figs all digits known with certainty, plus one estimated digit. People tend to report measurements this way naturally when they are doing the measuring. However, you have to be careful when calculating (especially with a calculator) that you don t offer too many digits in an answer. RULES FOR COUNTING THE NUMBER OF SIG FIGS 1. If there is no decimal point: any ending zeros are nonsignificant; all other digits are significant. 2. If there is a decimal point: any beginning zeros are non-significant; all other digits are significant. Note: Non-significant zeros are still important (they are place holder ). They are called non-significant because they are uncertain. Examples: #of sig figs 7500 C 2 9

10 kg L ml 4 Do sig fig work sheet top half C. Rounding if you calculate an answer and the calculator gives you too many digits (you ll learn the rules for this in the next section), you will need to round off the number. Rounding Summary If the digit(s) you are discarding start with: 4 or below: drop them, without changing any numbers. 5 or above: drop them, and increase the last remaining digit by one (round up) Ex: Round the following to 4 sig figs If the digits you are discarding come after a decimal point, they can just be dropped. However, if you need to discard digits that come before a decimal point, they must be kept but changed to zeros (they are place holders ). Practice: Round g to: 3 sig figs 49.9 ** Sig Figs Worksheet, bottom half. 4 sig figs sig figs sig figs sig figs 50 10

11 D. Calculating with Sig Figs 1. Multiplication and Division - the answer needs the same # of sig figs as the original figure with the fewest sig figs. Ex: 12.0 cm x 4.3 cm = 51.6 cm 2, rounded to 52 cm 2 (3 sf) (2 sf) (2 sf) Ex: 96 g = _ g, rounded to _14 g 7.0 g Ex: 96 g = _ g, rounded to 10 g 7 g Note: In a factor-label calculation, exact conversion factors are often used (ex: 60 sec/1 min, or 4 quarters/ 1 dollar). These conversion factors are exact, so they have an unlimited # of sig figs. Ex: How many milliliters are in 8.32 L? 8.32 L x 1000 ml = 8320 ml 1 L 2. Addition and Subtraction in these problems, it is not the total # of sig figs that is important, but the number of decimal places. The answer can have only as many decimal places as the original number with the fewest decimal places. Ex: L 65 L = L, rounded to 42 L 6.43 ml ml = ml, rounded to _118 ml **Sig Fig Worksheet #2 11

12 VI. Scientific Notation Two very important numbers in chemistry: Avogadro s number: (602,200,000,000,000,000,000,000) Mass of electron: kg Scientific notation: a shorthand for numbers. In Sci. Not., numbers are written as: M x 10 n M must be between 1 and 10 (1 M < 10) n is an integer To convert from long form numbers into S.N.: Move the decimal as needed until only one non-zero digit is to the left of the decimal. (Could go right or left). Count the number of places you have to move it. This number is n (the exponent). Ex: Avogadro s number: x (The positive exponent tells you that the long form number is very large, and is found by multiplying the short number by 10, 23 times.) Ex: kg Mass of e - : x (The negative exponent tells you that the long form number is very Small, and is found by dividing the short number by 10, 31 times.) In scientific notation, sig figs are easy to indicate. Sig figs are shown in the M part of the number. Ex: (a) put into scientific notation Orig # has 2 sig figs, so S.N. # must have 2 sig figs 12

13 S.N.: 8.5 x 10 7 _ (b) put into S.N. 9 x 10-4 Practice: 74, x 10 4 To convert from S.N. to long form _5 x x _8.64 X _6.02 x x x 10 8 Start with the M part Start with the M part of the S.N. number, and move the decimal the number of places indicated by the exponent. If the exp. Is Positive, move the decimal right. If the exp. Is negative, move the decimal left. Always put a zero left of an empty decimal. (be careful to have the same # of sig figs in the answer as the orig. # had). Ex: 7 x 10 4 kg x 10-7 L Calculating with Sci. Not. (entering on calculator) For these notes, determine which rules apply to your calculator, then write down only those rules. Find a key that is labeled: This key stands for x10 EE or EXP So, to enter a number like 6.02 x 10 23, press: 6.02 EE EXP x10 n 23 13

14 To enter negative numbers, be careful not to use the subtraction key. Find a key that is labeled +/- or (-) (This is called the sign change key) Ex: To enter x 10-7 press EE (sign change) 7 Calculating practice: x x = (Watch sig figs). On answers, be sure to convert the calculator answer as you see it on the screen back into correct scientific notation. (Don t write or 3.75E 14 ) 2. 3 x x 10 6 = 3. (4.5 x 10 8 ) x (3.17 x 10 5 ) = 4. (4.3 x 10 8 ) x (2.51 x ) = x 10 7 = 2.0 x x 10 5 = 3.0 x