Significant Digits and Scientific Notation Activities of Science Describing Matter Unit 1: Fundamentals of Chemistry Significant Digits and Scientific Notation Qualitative and quantitative measurements Use of the International System of Measurements (SI) Qualitative measurements Measurements that give descriptive, nonnumeric results Eamples: color, touch, etc. Vary in measurement from person to person Quantitative measurements Measurements that give definite, usually numeric results Eamples: temperature, speed, acceleration, distance, time Can be no more reliable than the instrument used to make the measurement and the care with which it is used and read Scientific notation Epression of numbers in the form a 10 b where a is equal to or greater than 1 and less than 10 and b is an integer Used to abbreviate very big or very small numbers Eamples If the eponent of 10 is positive n, move the decimal point n spaces to the right and fill in etra spaces with zeros. If the eponent of 10 is negative n, move the decimal point n spaces to the left and fill in etra spaces with zeros. Eponents on 10 must be the same to add and subtract.
3.4 10 4 = 3.4 10 10 10 10 = 34000 3.0 10 4 = 3.0 2.0 10-3 2.0 10 4-(-3) = 1.5 10 7 7.9 10-3 = 7.9 10 3 = 7.9 10 10 10 = 0.0079 + 5.4 10 4 5.40 10 4 6.0 10 3 0.60 10 4 6.00 10 4 Significant figures All the digits that can be known precisely in a measurement, plus a last estimated digit Eample: a graduated cylinder that can be read to the centiliter must be estimated to the milliliter (read: 0.74 ml significant: 0.742) Must know the equipment to know where it is eact and where you need to guess Rules for significant figures Every nonzero digit in a reported measurement is assumed to be significant. (2.853 has 4 significant digits) Zeros appearing between digits are significant. (10.002 has 5 significant digits) Leftmost zeros appearing in front of nonzero digits are not significant. (0.000032 has 2 significant digits) Zeros at the end of a number and to the right of the decimal point are always significant. (34.000 has 5 significant digits) Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant. (340000 has 2 significant digits) Two cases of unlimited number of significant digits Direct counting Eactly defined quantities for converting units
1.2543 10.543 9870.0 9870. 0.000025 0.00000250 78000006 20 students 1000 ml = 1 L Problem Set
Rules for where to round The answer to an addition or subtraction calculation should be rounded to the same number of decimal places as the measurement with the least number of decimal places. Eample: 39.892 + 9.45 + 6.9075 = 56.2495 Since the least accurate measurement is 9.45 and it has only two decimal places, the answer must be rounded to two decimal places. Answer: 56.25 The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least significant digits. Eample: 7.546 2.58 18.325 = 356.763561 Since the measurement with the least significant digits is 2.58 and it has only three significant digits, the answer must be rounded to three significant digits. Answer: 357 When rounding fives, if the last significant digit is odd, increases its value by one; if the last significant digit is even, do not change it. Eample: 25.5 rounded to two significant figures 26 26.5 rounded to two significant figures 26 Unit 1: Fundamentals of Chemistry Activities of Science
Scientific method A method of inquiry involving observations, eperiments, hypotheses, and broad eplanations called theories Used in biology, chemistry, physics, finance, etc. Steps of the scientific method Observation Information obtained through the senses Often involves a measurement Hypothesis A proposed eplanation for observations NOT the same as a scientific theory or law Often referred to as an educated guess Eperiment A carefully-controlled, repeatable procedure for gathering data in order to test a hypothesis Can either support or discard a hypothesis Eperimental flaws/errors Data Analysis Analyzing data that has been recorded during the eperiment Looking for trends in data to support or discard the hypothesis Conclusions Results from analyzing data and checking for errors in the eperiment Serves as a summary to support or discard the hypothesis Scientific theory Broad and etensively-tested eplanation of why eperiments yield certain results Can never be proven but can be disproven Eplains why things happen Scientific law Concise statement that summarizes the results of many observations and eperiments Widely-accepted Eplain what things happen Units of Measurement (* refers to SI base unit) Quantity SI base unit or SI derived unit Symbol Non-SI unit Symbol Length meter * m Volume cubic meter m 3 liter L Mass kilogram * kg Density grams per cubic centimeter or g/cm 3 g/ml grams per milliliter Temperature kelvin * K degree Celsius C Time second * s Pressure Pascal Pa atmosphere millimeter of mercury calorie Energy Joule J Amount of mole * mol substance Luminous candela * cd intensity Electric current ampere * A Atm mm Hg cal Commonly Used Prefies in the Metric System Prefi Symbol Meaning Factor mega kilo deci centi milli micro nano pico M k d c m n p 1 million times larger than the unit it precedes 1000 times larger than the unit it precedes 10 times smaller than the unit it precedes 100 times smaller than the unit it precedes 1000 times smaller than the unit it precedes 1 million times smaller than the unit it precedes 1000 million times smaller than the unit it precedes 1 trillion times smaller than the unit it precedes Scientific notation 1 000 000 10 6 1000 10 3 1/10 10-1 1/100 10-2 1/1 000 10-3 1/1 000 000 10-6 1/1 000 000 000 10-9 1/1 000 000 000 000 10-12
International System of Units (SI System) Universal system of units Seven SI units to know Length: meter (m) Mass: kilogram (kg) Temperature: kelvin (K) Time: second (s) Pressure: pascal (Pa) Energy: joule (J) Amount of substance: mole (mol) Prefies to use that represent relationships (three to know) Centi- (c) 100 cm = 1 m 100 cg = 1 g 100 cgeist = 1 Geist Milli- (m) 1000 mm = 1 m 1000 ml = 1 L 1000 mhawk = 1 Hawk Kilo- (k) 1 km = 1000 m 1 kg = 1000 g 1 kblake = 1000 Blake Micro- (μ) 10 6 μm = 1 m 10 6 μl = 1 L 10 6 μhawk = 1 Hawk Converting units and measurements 5 1 = 5 Conversion factor Ratio of equivalent measurements The same as multiplying times one (1) Eample 100 cm = 1 m 100 cm 100 cm = 1 1m 100 cm When converting to other units, start with what you are given, and use conversion factors to change to cancel out units to get what you want. Dimensional analysis (basic conversions) How many centimeters are in 5.2 kilometers? 1 km = 1000 m 1 m = 100 cm 2 s.f. s.f. s.f. (2 significant figures) = 520000 cm (or 5.2 10 5 cm)
Dimensional analysis (basic conversions) Convert 40.0 km/hr to m/s. 1 km = 1000 m 60 s = 1 min 60 min = 1 hr 3 s.f. s.f. s.f. s.f. (3 significant figures) = 11.1 m/s = 11.1 m/s Dimensional analysis (advanced conversions) The speed limit in residential zones is 25 miles per hour. If you were living in the UK, what would this speed limit be in meters per second? 5280 ft = 1 mi 12 in = 1 ft 2.54 cm = 1 in (back of periodic table) 1 m = 100 cm 60 min = 1 hr 60 s = 1 min 2 s.f. s.f. s.f. s.f. s.f. s.f. s.f. 5.2km 1000m 1hr 1km 100cm 1cm (2 significant figures) = 11 m/s 2.54cm 1in 1m 100cm 1hr 1min 60min 60s Dimensional analysis (advanced conversions) Tire pressure in your car tires should be 35.0 psi (pounds per square inch or lb/in 2 ). What pressure is this in kilograms per square centimeter (kg/cm 2 )? 1 lb = 0.4536 kg (back of periodic table) 1 in = 2.54 cm (back of periodic table) 35.0 lb 0.4536 kg 1 in 1 in 1 in 2 1 lb 2.54 cm 2.54 cm 35.0 lb 0.4536 kg 1 in 2 1 lb 1in 2.54 cm 2
3 s.f. s.f. s.f. 35.0 lb 0.4536 kg 12 in 2 1 in 2 1 lb 2.54 2 cm 2 (3 significant figures) = 2.46 kg/cm 2 Matter Anything that takes up space and has mass Substance Has uniform and definite composition Contains only one kind of matter Properties Physical properties Qualities of substances that can be observed or measured without changing the substance s chemical composition Eamples Color Solubility Odor Hardness Density Melting point Boiling point Chemical properties Abilities of substances to undergo chemical reactions and to form new substances Eamples Flammability Reactivity to oygen Reacts with acids Physical changes Changes that occur without altering the identity of the substance Eamples Cutting Bending Freezing Melting Sublimating Evaporating Condensing Vaporizing Physical states of matter Determine many distinguishing characteristics of matter Deal with the same substance but in different physical means of eistence Changes of states of matter in a substance are physical changes, NOT chemical changes Chemical changes Changes that occur that alter the identity of the substance Eamples Burning Reacting Combusting
Physical States of Matter States of Matter Property Solid Liquid Gas Shape Definite shape Shape depends on container Shape depends on container Volume Definite volume Definite volume Indefinite volume Epansion/ Compressibility Eample with Water Specific notes Some epansion but minimal Some epansion when heated Easily compressed and epanded Ice Water Steam Gas: gaseous state of a substance not generally a liquid or solid at room temperature Vapor: gaseous state of a substance that is generally a liquid or solid at room temperature Plasma Gas-like phase consisting of charged particles (ions) Eists at etremely high temperatures Eamples The sun (ionized particles) Lightning Most of the universe is plasma. Stars Other hot stellar bodies Unit 1: Fundamentals of Chemistry Describing Matter Miture Physical blend of two or more substances Compositions may vary. Classifications Heterogeneous miture A miture that is not uniform in composition Eample: salad Portions differ from other portions Homogeneous miture A miture that is uniform in composition Eample: saltwater Portions the same as other portions Solution Special name of a homogeneous miture Can be same or different phases of matter together Do not scatter light and are uniform throughout
Kinds of solutions» Gas-gas: carbon dioide and oygen (air)» Liquid-gas: water vapor in air (moist air)» Gas-liquid: oygen in water (ocean water)» Liquid-liquid: hydrochloric acid in water» Solid-liquid: saltwater (salt in water)» Solid-solid: copper in silver (sterling silver) Separating mitures Distillation Purification of water by evaporation and condensing Caused by difference in melting and boiling points Filters Other methods Element Simplest form of matter that can eist under normal laboratory conditions Can be found on the Periodic Table of Elements Building blocks for all other substances Atoms are each classified by names of elements Eamples Carbon (C) Oygen (O) Nitrogen (N) Sodium (Na) Lead (Pb) Copper (Cu) Cobalt (Co) Symbol One- or two-letter representation for an element Letters for symbol are generally English, Latin, or Greek in origin Eamples Na (Latin from natrium for sodium ) Au (Latin from aurum for gold ) He (English for helium ) W (German from wolfram for tungsten ) Pb (Greek from plumbum for lead ) Compound Substance that can be separated into simpler substances only by chemical means Two or more elements that chemically combine with one another Eamples Carbon monoide (CO) Carbon dioide (CO 2 ) Sodium chloride (NaCl) Glucose (C 6 H 12 O 6 ) RDX (C 3 H 6 N 6 O 6 ) Acetone (CH 3 COCH 3 )
Decomposition of compounds Electrolysis Passing an electric current through a substance, causing it to decompose into new kinds of matter Separation into constituent elements/compounds Can be done with water DIFFERENT THAN DISTILLATION Law of definite proportions In samples of any chemical compound, the masses of the elements are always in the same proportion. Ratios of compounds are always the same or they are different compounds. Law of Multiple Proportions Whenever two elements form more than one compound, the different masses of one element that combine with the same mass of the other element are in the ratio of small whole numbers. Compounds can be made up of formula units or molecules. Density Ratio between the mass and the volume of a substance Calculated by taking the mass and dividing by the volume Density (d) = Density is a rate, meaning it can be calculated from a slope. Slope (m) = Mass m = Volume V y 2 y 1 2 1 Density (d) = m 2 m 1 V 2 V 1 Independent data on the horizontal ais (-ais) -- volume Dependent data on the vertical ais (y-ais) -- mass
Volume (in ml) Mass (in g) 6.0 53.52 7.0 62.44 8.0 71.36 d = m2 - m1 V2 - V1 = 71.36-53.52 = 17.84 8.0 6.0 2.0 = 8.9 g/ml