Chapter 2 Measurement and Calculations GHS R. Krum

Scientific Method A way of solving problems or answering questions. Starts with observation- noting an recording facts Hypothesis- an educated guess as to the cause of the problem or answer to the question.

Scientific Method Experiment- designed to test the hypothesis only two possible answers – hypothesis is right – hypothesis is wrong Generates data observations from experiments. Modify hypothesis - repeat the cycle

Observations Hypothesis Experiment Cycle repeats many times. The hypothesis gets more and more certain. Becomes a theory A thoroughly tested model that explains why things behave a certain way.

Theory can never be proven. Useful because they predict behavior Help us form mental pictures of processes (models) Observations Hypothesis Experiment

Law Theory (Model) Prediction Experiment Modify Observations Hypothesis Experiment

Matter - anything that occupies space and has mass. mass – measure of the quantity of matter SI unit of mass is the kilogram (kg) 1 kg = 1000 g = 1 x 10 3 g weight – force that gravity exerts on an object weight = c x mass on earth, c = 1.0 on moon, c ~ A 1 kg bar will weigh 1 kg on earth 0.1 kg on moon

1.7

Metric System The metric system is based on a base unit that corresponds to a certain kind of measurement Length = meter Volume = liter Weight (Mass) = gram Prefixes plus base units make up the metric system – Example: Centi + meter = Centimeter Kilo + liter = Kiloliter

Metric System The three prefixes that we will use the most are: – kilo – centi – milli kilo hectodeca Base Units meter gram liter deci centimilli

Metric System So if you needed to measure length you would choose meter as your base unit – Length of a tree branch 1.5 meters – Length of a room 5 meters – Length of a ball of twine stretched out 25 meters

Metric System But what if you need to measure a longer distance, like from your house to school? – Let’s say you live approximately 10 miles from school 10 miles = meters – is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: meters = kilometers (or 16.1 if rounded to 1 decimal place)

Metric System These prefixes are based on powers of 10. What does this mean? – From each prefix every “step” is either: 10 times larger or 10 times smaller – For example Centimeters are 10 times larger than millimeters 1 centimeter = 10 millimeters kilo hectodeca Base Units meter gram liter deci centimilli

Metric System – Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length 1 centimeter = 10 millimeters Example not to scale 1 mm 1 cm

Metric System For each “step” to right, you are multiplying by 10 For example, let’s go from a base unit to centi 1 liter = 10 deciliters = 100 centiliters 2 grams = 20 decigrams = 200 centigrams kilo hectodeca meter liter gram deci centimilli ( 1 x 10 = 10) = (10 x 10 = 100) (2 x 10 = 20) = (20 x 10 = 200)

Metric System An easy way to move within the metric system is by moving the decimal point one place for each “step” desired Example: change meters to centimeters 1 meter = 10 decimeters = 100 centimeters or 1.00 meter = 10.0 decimeters = 100. centimeters kilo hectodeca meter liter gram deci centimilli

Volume – SI derived unit for volume is cubic meter (m 3 ) 1 cm 3 = (1 x m) 3 = 1 x m 3 1 dm 3 = (1 x m) 3 = 1 x m 3 1 L = 1000 mL = 1000 cm 3 = 1 dm 3 1 mL = 1 cm 3 1.7

Density – SI derived unit for density is kg/m 3 1 g/cm 3 = 1 g/mL = 1000 kg/m 3 density = mass volume d = m V 1.7 A piece of platinum metal with a density of 21.5 g/cm 3 has a volume of 4.49 cm 3. What is its mass? d = m V m = d x V = 21.5 g/cm 3 x 4.49 cm 3 = 96.5 g

English and Metric Conversions If you know ONE conversion for each type of measurement, you can convert anything! If you know ONE conversion for each type of measurement, you can convert anything! You must memorize and use these conversions: You must memorize and use these conversions: – Mass: 454 grams = 1 pound – Length: 2.54 cm = 1 inch – Volume: L = 1 quart

Square and Cubic units Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also! Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also! Best way: Square or cube the ENITRE conversion factor Best way: Square or cube the ENITRE conversion factor Example: Convert 4.3 cm 3 to mm 3 Example: Convert 4.3 cm 3 to mm cm 3 10 mm 3 1 cm 1 cm ( ) = 4.3 cm mm cm cm 3 = 4300 mm 3

K = 0 C F = x 0 C K = 0 0 C 373 K = C 32 0 F = 0 0 C F = C (°F - 32) * 5/9 = °C

Convert F to degrees Celsius. 0 F = x 0 C F – 32 = x 0 C 9 5 x ( 0 F – 32) = 0 C C = x ( 0 F – 32) C = x (172.9 – 32) =

1.8 Scientific Notation The number of atoms in 12 g of carbon: 602,200,000,000,000,000,000, x The mass of a single carbon atom in grams: x N x 10 n N is a number between 1 and 10 n is a positive or negative integer

Scientific Notation n > = x 10 2 move decimal left n < = 7.72 x move decimal right Addition or Subtraction 1.Write each quantity with the same exponent n 2.Combine N 1 and N 2 3.The exponent, n, remains the same 4.31 x x 10 3 = 4.31 x x 10 4 = 4.70 x 10 4

Scientific Notation 1.8 Multiplication 1.Multiply N 1 and N 2 2.Add exponents n 1 and n 2 (4.0 x ) x (7.0 x 10 3 ) = (4.0 x 7.0) x ( ) = 28 x = 2.8 x Division 1.Divide N 1 and N 2 2.Subtract exponents n 1 and n x 10 4 ÷ 5.0 x 10 9 = (8.5 ÷ 5.0) x = 1.7 x 10 -5

Significant Figures 1.8 Any digit that is not zero is significant kg 4 significant figures Zeros between nonzero digits are significant 606 m 3 significant figures Zeros to the left of the first nonzero digit are not significant 0.08 L 1 significant figure If a number is greater than 1, then all zeros to the right of the decimal point are significant 2.0 mg 2 significant figures If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant g 3 significant figures AP Chemistry Exam Hint: You must be within 1 sig fig – it does not need to be perfect, but sig figs DO count!

How many significant figures are in each of the following measurements? 24 mL2 significant figures 3001 g 4 significant figures m 3 3 significant figures 6.4 x 10 4 molecules 2 significant figures 560 kg2 significant figures 1.8

Rounding If you round off to a “5”, if the next digit is ODD, round up. If it is EVEN, round down (leave it)! rounded to hundredths is 3.02 (because the next digit (6) is 6 or more) rounded to hundredths is 3.01 (because the next digit (3) is 4 or less) rounded to hundredths is 3.02 (because the next digit is 5, and the hundredths digit (1) is odd) rounded to hundredths is 3.04 (because the next digit is 5, and the hundredths digit (4) is even) rounded to hundredths is 3.05 (because the next digit is 5, but it is followed by non-zero digits)

Significant Figures 1.8 Addition or Subtraction The answer cannot have more digits to the right of the decimal point than any of the original numbers round off to 90.4 one significant figure after decimal point two significant figures after decimal point round off to 0.79 If you round off to a “5”, if the next digit is ODD, round up. If it is EVEN, round down (leave it)!

Significant Figures 1.8 Multiplication or Division The number of significant figures in the result is set by the original number that has the smallest number of significant figures 4.51 x = = sig figsround to 3 sig figs 6.8 ÷ = sig figsround to 2 sig figs = 0.061

Significant Figures 1.8 Exact Numbers Numbers from definitions or numbers of objects are considered to have an infinite number of significant figures The average of three measured lengths; 6.64, 6.68 and 6.70? = = 6.67 Because 3 is an exact number = 7

Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other accurate & precise but not accurate & not precise 1.8

1.9 Dimensional Analysis Method of Solving Problems 1.Determine which unit conversion factor(s) are needed 2.Carry units through calculation 3.If all units cancel except for the desired unit(s), then the problem was solved correctly. 1 L = 1000 mL How many mL are in 1.63 L? 1L 1000 mL 1.63 L x = 1630 mL 1L 1000 mL 1.63 L x = L2L2 mL

The speed of sound in air is about 343 m/s. What is this speed in miles per hour? 1 mi = 1609 m1 min = 60 s1 hour = 60 min 343 m s x 1 mi 1609 m 60 s 1 min x 60 min 1 hour x = 767 mi hour meters to miles seconds to hours 1.9