Booth's Website



Unit 2: Chemistry Math Tools & Nomenclature (Hebden Units II & IV)When studying the physical sciences we often perform calculations with VERY small or VERY large numbers. For example: the speed of light is 300 000 000 m/sec and 0.00000000000000000000000167 g is the mass of a Hydrogen atom! This poses several problems: As things get very large or very small, how accurately can we measure them? How many place values can we be “certain” are represented precisely by our measurements? How do we enter these very small or large numbers into our calculators for calculations if they only compute a certain number of digits at a time?2.1 - Scientific NotationScientific notation is used to express very large or very small numbers as a value, between 1 and 10, that is multiplied by a power of base 10.Regular NotationScientific NotationE.g. 1602 L1.602 × 103 LE.g. 0.00 000 000 123 mol 1.23 × 10-9 mol* General Rule: Any number greater than 1000 (one thousand) or less then 0.001 (one thousandth) should be converted to scientific notation when working with calculations.* Rule of a Thousand: In chemistry, your final answer in any question involving calculations should be expressed as a value between 0.001 and 1000.Rules for Writing Numbers in Scientific Notation:Step 1:Move the decimal place so the resulting number has a value between 1 and 10 (1.01 and 9.99).Step 2: Drop the zeros (trailing ones).Step 3: Multiply the decimal by a power with a base of 10.Step 4: The number of place values you have moved the decimal, is the exponent on the power 10.* If you move the decimal LEFT to its new position, the exponent will be POSITIVE.* If you move the decimal RIGHT to its new position, the exponent will be NEGATIVE.Practice:Convert the following Numbers into Scientific Notation: 675 400 000 0000.000 000 765 4550023 4500.000 1540.002980 000 0000.000 005 6Convert the following Numbers into Standard Decimal Form (working backwards):3.45 x 10-53.45 x 1056.789 x 10-61.2 x 10-49.1 x 10-34.567 x 1079Entering scientific notation into your calculator:e.g. 6.02 x 1023 Multiplying and dividing numbers in scientific notation(6.2 x 105)(3.5 x 108) = 2.17 E14 which is 2.17 x 1014(7.2 x 107)(8.0 x 10-16) = (5.0 x 1015)/(2.5 X 10-5) =2.2 - Significant Figures a.k.a. “sig-figs” (Hebden p. 27-34)A significant figure is a measured or meaningful digit.Used to give an idea of the degree of uncertainty in measurement – the more digits in a measurement, the more “certain” you are about the measurement.Sig. Figs. are digits that are known accurately (certain) plus one digit (estimate).Inexact numbersNumbers from experimental measurements are inexact.The uncertainty in the measurement depends on the sensitivity of the instrument being used e.g. the mass of a coin could be 2.6 g (2 sig figs) on a standard laboratory scale or 2.6217 g (5 sig figs) on an analytical balance.Exact NumbersNumbers that represents a count of objects is an exact number e.g. 5 apples, 4 experiments, 20 moleculesSig Fig Rules1) Significant digits include ALL digits correctly reported from a measurement EXCEPT LEADING ZEROS.Leading zeros are the zeros at the beginning of a decimal and are written only to locate the decimal point.e.g. 6.20 mL (3 significant digits) has the same number of significant digits as 0.00620 L2) TRAILING ZEROS are NOT significant, UNLESS THERE IS a decimal.e.g. 500 000 mL 1 sig fige.g. 810 000.0 g 7 sig figs 3) When a number is expressed in scientific notation, all digits are significant.e.g. 2.63 × 105 cm3 sig figse.g. 8.0 × 107 mm2 sig figse.g. 4.78001 × 10-6 g 6 sig figs4) Conversion factors have no uncertainty - they have an infinite number of sig figs.e.g. 100 cm1m e.g. 1 km1000 mPractice:Determine how many sig figs are in each of the following:834 000 000 km0.000 012 m6.090 x 10-8 g700 L25 people1000 g/ 1kgThe “Certainty Rules” for Calculations (aka “How do I know how many sig figs I’m allowed?”)1) multiplying and dividing - the calculated answer should have the same number of sig figs as the value with the LOWEST NUMBER of significant digits used in the calculation. * If necessary, you MUST round-off your calculated answer to the least number of sig figs that was present in the number used in your calculations.* Rounding-off Rule - If the left most digit to be dropped is 5 or higher, then increase the last remaining digit by one…round up! If the number is less than 5 keep it the same.e.g. 1.15 g/mL is rounded to 1.2 g/mL if the answer should have 2 sig figs e.g. 5.92 cm × 3.0 cm = 17.76 cm2 final answer needs to have 2 sig figs 18 cm2e.g. 17.001 m × 1.8 m= 30.6018 m2 final answer needs to have 2 sig figs 31 m22) Adding and Subtracting - the calculated answer should have NO MORE DECIMAL PLACES than the least precise one in the problem (the one with the least decimal places). e.g. 26.2 mL – 0.3 mL = 25.9 mL final answer should have 1 decimal place 25.9 mLe.g. 16.04 g + 0.002 g =16.042 g final answer should have 2 decimal places 16.04 ge.g. 4.55 × 10 -5 m+3.1 × 10-5 m=7.61 × 10-5 m final answer should have 1 decimal place 7.6 × 10-5 me.g. 6.71 × 107L - 5.6 × 106 L=6.15 × 107L final answer should have 1 decimal place 6.2 × 107 LRoundingIf the left most digit to be dropped is 5 or higher, then increase the last remaining digit by one……rounding up, if it is less than 5 then leave it the same.e.g. 1.15 g/mL is rounded to 1.2 g/mL if there are only 2 sig figs.Practice:Perform the indicated operations and give the answer to the correct number of sig figs.6.789 x 0.56 =(9.81 x 10-4)/(6.7 x 106) =0.00345 x 0.10 =15.1 + 75.32 =178.904 – 125.8 =1.2527 x 103 + 8.769 x 102 = Practice : 1) Review of Significant Figures & Scientific Notation Worksheet2) Hebden p. 28 # 42 / p. 55 # 55 / p. 39 # 56 / p. 40 # 57-59Do as many as you need until you feel comfortable getting the correct answersMeasurementHow certain you are about a measurement depends on 2 factors:i) the precision of the instrumentii) the value of the measured quantityMore precise instruments give more certain values.When taking measurements, select an instrument that is convenient and that provides the precision that suits the purpose.e.g. You wouldn’t use a metre stick to measure the thickness of Al foilPrecision vs Accuracy - * See Hebden p 28The ACCURACY of a value is an expression of how close the experimental value is to the accepted or predicted value. The PRECISION of a measured or calculated value is the place value of the last measurable digit (ie. More sig figs means more precision).Precision is determined by the instrument used to obtain the measure.Precision is a measure of the reproducibility or consistency of a result.Precision errors are generally attributed to a random error of measurement.585470115570How to Read a Scale:On a scale, numbered and unnumbered divisions are calibrated (i.e. marked off at regular intervals)Stepsi) Determine the difference between each numbered division e.g. 1,2,3 or 10, 20, 30 etc. ii) Find the value of each unnumbered divisioniii) Make the measurement and estimate how far along the unnumbered subdivision the measurement is. * Note: your uncertain digit is one digit, beyond the unnumbered digits.e.g. The measurement of b = 3.30 cme = _________c = _________d= _________-551815208915What do you do if the measurement is on a numbered or unnumbered division?Determine how many digits can be read on the measuring device and add sufficient zeros.Determine the volumes in each of the following Graduated Cylinder.Practice from Hebden:p. 29 # 44,45 / p. 32 # 48 / p. 33 # 49 / p. 34 # 50 SI Units and Unit Conversion Method (Hebden p. 9-22)The International System (SI) is the system of measurement used in the scientific community all over the world. SI prefixes make it very convenient to convert from one value to another.These conversions are necessary to follow certainty and precision rules and the rule of a thousand.Metric Prefixes - * You need to memorize this chart!!PrefixSymbolValueGigaG109MegaM106Kilok103Centic10-2Millim10-3Micro?10-6Base units of the SI system, is the basic unit of measurement, all other units are multiples of the base units.i) m = metre (distance)ii) L = litre (volume)iii) g = gram (mass)If you add a prefix to the base unit it allows you to demonstrate a very large or very small measurement.e.g. mm = millimetre 1 mm = 10-3 m (1/1000 of a metre) e.g. mL = millilitre 1 mL = 10-3 L(1/1000 of a litre)Unit Conversion Method * See Hebden p 19 to 22 for practice and examplesThis method can be used to convert between prefixes within the SI system and will also come in handy when doing conversions in the mole unit.Ask yourself a few questions:i) What are you being asked to solve for?ii) What is the given info?iii) What is the conversion factor?Practice:How many grams are in 56.7 kg?How many GL are in 1.2 x 106 L?How many mg are in 8.9 kg?How many ?g are in 1.78 x 10-7 kgPractice:Hebden p. 21 # 17 (a-k)Density(Hebden p. 24-26)Density = the mass contained in a given volume of a substance (mass divided by volume)Mass (m) units: g, kgVolume (V) units: mL, L, cm3, m3Density (d) units: g/mL, kg/L, kg/m3This is a derived quantity, made up of two units mass and volumeLess dense liquids and objects will float on liquids having a greater densityWater has a density of 1.0000 g/mLExamples:1. An iron nail has a mass of 3.93 g and has a volume of 0.50 mL. What is the density of the nail? (don’t forget sig figs and units!)2. Copper has a density of 8.96 g/cm3. If a Cu sample has a mass of 90.0 g. What volume does the sample occupy? (don’t forget sig figs and units!)3. If the density of Au is 19.3 g/mL, Ag is 10.5 g/mL. If a ring has a mass of 29.0 g and a volume of 1.50 mL. What is the ring made of? (don’t forget sig figs and units!) A block of copper has dimensions: 2.0 cm x 2.0 cm x 3.5 cm and a mass of 125.0 g. What is the density of copper? (don’t forget sig figs and units!)Practice:Hebden p. 26 # 31-35GraphingIn science we often produce graphs after doing an experiment. This involves plotting one set of data with another set of data. The graph is an illustration of how one variable behaved with respect to another one. One type of graph we will use in Chemistry 11 is a linear graph.2435225231140A linear graph is a graph that would allow you to draw a straight line through most or all of the data points.Slope of a linear graph = rise/run Slope = Y2 – Y1 X2 – X1Characteristics of a good graph:Size – should take up most of the graph paper, with only one graph per page.Title – this should be meaningful and be representative of the experimentBoth axes labelled and with units – dependant variable is on the y-axis, independent variable is on the x-axisBoth axes have appropriate scales – ie. Increments with factors of 1,2,5 or 10 etc.Best straight line drawn through data points – this line does not have to include any data point, but should have as many points above the line as below the line, if possible.Slope point shown – these points usually will not be data points, but intersections of the line and grid-8435243461Slope calculations shown with units 2.3 – Names & Formulas of Chemical Compounds (Hebden Unit IV)There are two sets of rules for naming compounds. The first step is to decide whether or not the compound you are naming is an:i) Ionic Compound (comprised of metal and non-metal)ii) Covalent Compound (comprised of 2 or more non-metal atoms)Ionic NomenclatureIonic bonds occur between a metal and a non-metal atom.Involves a transfer of electrons.The ionic bond forms from the electrostatic attraction of ions that results from the transfer of electrons.Writing Chemical Formulas of Ionic Compounds1) Write the symbols with the combining capacitye.g. aluminum oxidecharge for both the metal and non-metal ions.2) Criss-cross the combining capacity numbers.* Understand that criss-crossing is a short-cut to balancing charges – should have a NET ZERO overallcharge on the ionic compound when finished.3) Tidy up the formula e.g. if both subscripts can bereduced, do so (if you reduce one subscript youmust make the same reduction to the others). * If a polyatomic ion ( 2 or more atoms e.g. magnesium hydroxidewith an overall ionic charge) is involved, use brackets to group the polyatomic ion if there’s more than onee.g. OH- or SO42-* See Hebden p 341 for a full list of common Polyatomic ionsNaming Ionic Compounds When Given a Chemical Formula1) The metal ion’s name DOES NOT change regardless of combining capacity (charge).2) The non-metal ion’s name ends in “– ide”.*Note: Most transition metals have more than one combining capacity, when naming compounds with a transition metal you must indicate the combining capacity charge with roman numerals. This identifies which ion is in the compound.Recall that the transition metals include elements with atomic numbers of 21 to 30, 39 to 48 and 57 to 80.1) Determine the name of the metal and determine e.g. CuNO3if it has more than one possible charge. If it does,you will need roman numerals:I – oneIV - fourII – twoV - fiveIII – threeVI - sixThe roman numeral used in the formula is determined by the combining capacity (charge) of the ion present in the compound.2) Determine the name and charge of the non-metal e.g. MnOpart of the compound.* Check the list of common polyatomic ions.3) Change the ending of the non-metal elemention’s name so it ends with “-ide”.(For a polyatomic ion do not change the ending)Practice:Determine the chemical formula for the following compounds.Tin (IV) fluorideAluminum hydroxidePotassium chlorideManganese (IV) acetateZinc chlorateLead (II) oxideLead (IV) oxideAmmonium carbonatePractice:Determine the name for the following ionic compounds.CaCl2Al2(SO4)3NH4NO3NaCH3COOFe(OH)3PbO2CrOZnSO4Practice:1) Hebdenp. 68 # 1 (Read definitions at top of page) / p. 71 # 4 / p. 72 # 52) There may also be extra practice worksheets available in class.Hydrates (Hebden p. 72)When a crystal of an ionic compound is grown by evaporation from aqueous solution, frequently it is found that the crystal structure will include water molecules hydrate.The prefixes below are used to identify how many water molecules are present hydrated compounds.mono – 1di – 2tri – 3tetra – 4penta – 5hexa – 6hepta – 7octa – 8nona – 9deca - 10e.g. CuSO4 ● 5H2O copper (II) sulphate pentahydrateSome Common Acids – (* memorize)A compound is typically an “acid” if it has a chemical formula starting with “H” * H2O is AN EXCEPTION HCl hydrochloric acidHCH3COOacetic acid H3PO4phosphoric acidH2SO4 sulphuric acidPractice:Determine the name or formula for the following hydrates.a) copper (II) chloride dihydrateb) Ca(NO3)2●4H2Oc) zinc acetate dihydratePractice:Hebden p. 73 # 6, 7Naming Covalent Compounds(Hebden p. 73-74)Covalent bonds occur between a non-metal and a non-metal and involves a sharing of electrons.Many covalent compounds have common names such as “methane”, “ammonia” and “water”.Simple covalent compounds are generally named by using prefixes to indicate how many atoms of each element are in the formula.1 mono-4 tetra-7 hepta-10 deca-2 di-5 penta-8 octa-3 tri-6 hexa-9 nona-* Note - The mono- prefix is usually not used for the first element in the formula. * The "o" and "a" endings of these prefixes are dropped when they are attached to "oxide."In formulas for covalent compounds, generally elements are listed in the same left-to-right order as they are on the periodic table.* One exception – hydrogen should be “squeezed” in between nitrogen and oxygenSimilarly to naming ionic compounds, the most negative element’s (last element in the formula) name ending is changed to “- ide”.CO2Si2I6CON2O4Writing Formulas for Covalent CompoundsThe prefix is the number of each atom in the compound (DO NOT criss-cross!!)1) Look at the first word of the compound’s name and identify the element. Write down its symbol.2) If the first name of the compound has a prefix, write the number the prefix refers to as the symbol’s subscript.3) Look at the second word in the compound’s name and identify the element - write its symbol.* Only the root of the element’s name is used so the ending will be different.4) Determine the number that the prefix of the second name refers to and write this number after the second symbol as a subscript. tricarbon disulphidedihydrogen monoxidephosphorous pentachloridePractice:Hebden p. 74 # 8-9* There may also be extra practice worksheets available in class.For practice with all types of compounds:Hebden p. 75-76 # 14-163(You must be able to name/write formulas without being told what type of compound it is) ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download