Presentation on theme: "PWISTA Math of Chemistry"— Presentation transcript:
1 PWISTA Math of Chemistry Scientific measurementAccuracy and PrecisionSig FigsMetric System
2 Types of measurement Quantitative- use numbers to describe Qualitative- use description without numbers4 feetextra largeHot100ºF
3 Scientists prefer Quantitative- easy check Easy to agree upon, no personal biasThe measuring instrument limits how good the measurement is
4 How good are the measurements? Scientists use two word to describe how good the measurements areAccuracy- how close the measurement is to the actual valuePrecision- how well can the measurement be repeated
5 DifferencesAccuracy can be true of an individual measurement or the average of severalPrecision requires several measurements before anything can be said about itexamples
11 In terms of measurement Three students measure the room to be m, 10.3 m and 10.4 m across.Were they precise?Were they accurate?
12 Significant figures (sig figs) How many numbers mean anythingWhen we measure something, we can (and do) always estimate between the smallest marks.21345
13 Sig FigsSignificant digits, which are also called significant figures, are very important in Chemistry.Each recorded measurement has a certain number of significant digits.Calculations done on these measurements must follow the rules for significant digits.
14 Sig FigsThe significance of a digit has to do with whether it represents a true measurement or not.Any digit that is actually measured or estimated will be considered significant.Placeholders, or digits that have not been measured or estimated, are not considered significant.The rules for determining the significance of a digit will follow.
15 Significant figures (sig figs) The better marks the better we can estimate.Scientist always understand that the last number measured is actually an estimate12345
16 Sig FigsWhat is the smallest mark on the ruler that measures cm?142 cm?140 cm?Here there’s a problem does the zero count or not?They needed a set of rules to decide: which zeroes count?All other numbers do count
17 The Standard Rules 1) Digits from 1-9 are always significant. 2) Zeros between two other significant digits are always significant. (sandwich rule)3) One or more additional zeros to the right of both the decimal place and another significant digit are significant.4) Zeros used solely for spacing the decimal point (placeholders) are not significant.
20 EXAMPLES# OF SIG. DIG.COMMENT453 kg3All non-zero digits are always significant.5057 L4Zeros between 2 sig. dig. are significant.5.00Additional zeros to the right of decimal and a sig. dig. are significant.0.0071Placeholders are not sig.
21 Alternate Rule for Significant Digits Rules Courtesy of Fordham Prep website.When you look at the number in question, you must determine if it has a decimal point or not. If it has a decimal, you should think of "P" for "Present". If the number does not have a decimal place, you should think of "A" for "Absent".
22 Alternate Rule for Significant Digits Example, for the number , think "P", because the decimal is present.For the number 6500, you would think "A", because the decimal is absent.
23 Alternate Rule for Significant Digits Now, the letters "A" and "P" also correspond to the "Atlantic" and "Pacific" Oceans, respectively. Assume the top of the page is North, and imagine an arrow being drawn toward the number from the appropriate coast. Once the arrow hits a nonzero digit, it and all of the digits after it are significant.
24 How many significant digits are shown in the number 20 400 ? Example 1 How many significant digits are shown in the number ? (remember that we use spaces, rather than commas, when writing numbers in Science.Well, there is no decimal, so we think of "A" for "Absent". This means that we imagine an arrow coming in from the Atlantic ocean, as shown below;
25 Example 1The first non-zero digit the arrow hits would be the 4, making it, and all digits to the left of it significant. There are 3 significant digits
26 Example 2 How many significant digits are shown in the number ?
27 Example 2Well, there is a decimal, so we think of "P" for "Present". This means that we imagine an arrow coming in from the Pacific ocean, as shown below;0.090
28 ExampleThe first nonzero digit that the arrow will pass in the 9, making it, and any digit to the right of it significant.
29 Answer Example 2 There are 2 significant digits in the number 0.090 Here are the significant digits, shown in boldface. 0.090
30 Which zeros count?Those at the end of a number before the decimal point don’t count12400If the number is smaller than one, zeroes before the first number don’t count0.045
31 Which zeros count? Zeros between other sig figs do. 1002 zeroes at the end of a number after the decimal point do countIf they are holding places, they don’t.If they are measured (or estimated) they do
32 Sig Figs Only measurements have sig figs. Counted numbers are exact A dozen is exactly 12A a piece of paper is measured 11 inches tall.Being able to locate, and count significant figures is an important skill.
33 Sig figs. How many sig figs in the following measurements? 458 g
34 Sig Figs.405.0 g4050 g0.450 gggNext we learn the rules for calculations
35 Problems Same # - Different # sig figs … 50 is only 1 significant figureif it really has two, how can I write it?A zero at the end only counts after the decimal placeScientific notation5.0 x 101now the zero counts.
36 Adding and subtracting with sig figs The last sig fig in a measurement is an estimate.Your answer when you add or subtract can not be better than your worst estimate.have to round it to the least place of the measurement in the problem
37 For example27.936.4+First line up the decimal places27.936.4+27.936.4Then do the addingFind the estimated numbers in the problem34.33This answer must be rounded to the tenths place
38 Rounding rules look at the number behind the one you’re rounding. If it is 0 to 4 don’t change itIf it is 5 to 9 make it one biggerround to four sig figsto three sig figsto two sig figsto one sig fig
39 Adding and Subtracting RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.
40 add 3.76 g g g = gWe look to the original problem to see the number of decimal places shown in each of the original measurements.2.1 shows the least number of decimal places.We must round our answer, 20.69, to one decimal place (the tenth place).Our final answer is 20.7 g
42 Multiplication and Division Rule is simplerSame number of sig figs in the answer as the least in the question3.6 x 653Calculated answer =3.6 has 2 sig figs, 653 has 3 sig figsanswer can only have 2 sig figs2400
43 Multiplying and Dividing RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.
44 EX: cm x 3.10 cm x cm = cm3We look to the original problem and check the number of significant digits in each of the original measurements:22.37 shows 4 significant digits.3.10 shows 3 significant digits.85.75 shows 4 significant digits.
45 EX: cm x 3.10 cm x cm = cm3Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem.shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits.Our final answer becomes 5950 cm3.
46 Multiplication and Division Same rules for divisionpractice4.5 / 6.2454.5 x 6.245x .0433.876 / 198316547 / 714
49 Measuring The numbers are only half of a measurement It is 10 long what?Numbers without units are meaningless.I’ll pay you 100 to mow the lawn … then give the person 100 cents. Won’t make friends that way.
50 The Metric System Easier to use because it is a decimal system Every conversion is by some power of 10.A metric unit has two partsA prefix and a base unit.prefix tells you how many times to divide or multiply by 10.
51 Base Units Length - meter more than a yard - m Mass - grams - a bout a raisin - gTime - second - sTemperature - Kelvin or ºCelsius K or CEnergy - Joules- JVolume - Liter - half f a two liter bottle- LAmount of substance - mole - mol
63 Density how heavy something is for its size the ratio of mass to volume for a substanceD = M / VIndependent of how much of it you havegold - high densityair low density.
64 Calculating The formula tells you how (d=mass / volume) BETTER YET … the UNITS tell you how!units will be g/mL or g/cm3
65 We know the units for density are g/ml A piece of wood has a mass of 11.2 g and a volume of 23 mL what is the density?We know the units for density are g/mlThe unit tells us that grams goes on top and ml goes on the bottom; so let’s do that.11.2g / 23ml = 0.49 g/ml
66 The Unit you want to find ALWAYS goes on top. A piece of wood has a density of 0.93 g/mL and a volume of 23 mL what is the mass?The Unit you want to find ALWAYS goes on top.We have 0.93 g/ml. We want to get rid of the ml on the bottom. So multiply by ml on top. (ml on top and bottom cancel out)0.93g/ml x 23 ml / 1 = g
67 CalculatingA piece of wood has a density of 0.93 g/mL and a mass of 23 g what is the volume?The units must always work out.Algebra 1Get the thing you want by itself, on the top.What ever you do to onside, do to the other
68 Floating Lower density floats on higher density. Ice is less dense than water.Most wood is less dense than waterHelium is less dense than air.A ship is less dense than water
69 Density of water 1 g of water is 1 mL of water. density of water is 1 g/mLat 4ºCotherwise it is less
70 Measuring Temperature 0ºCCelsius scale.water freezes at 0ºCwater boils at 100ºCbody temperature 37ºCroom temperature ºC
71 Measuring Temperature 273 KKelvin starts at absolute zero (-273 º C)degrees are the same sizeC = K -273K = C + 273Kelvin is always bigger.Kelvin can never be negative.
73 Temperature is different than heat.Temperature is which way heat will flow (from hot to cold)Heat is energy, ability to do work.A drop of boiling water hurts,kilogram of boiling water kills
74 Units of heat are calories or Joules 1 calorie is the amount of heat needed to raise the temperature of 1 gram of water by 1ºCa food Calorie is really a kilocalorieHow much energy is absorbed to heat 15 grams of water by 25ºC1 calorie = 4.18 J
75 Some things heat up easily some take a great deal of energy to change their temperature.The Specific Heat Capacity amount of heat to change the temperature of 1 g of a substance by 1ºCspecific heat SHS.H. = heat (cal) mass(g) x change in temp(ºC)
76 Specific Heat Water has a high specific heat 1 cal/gºC units will always be cal/gºCor J/gºCthe amount of heat it takes to heat something is the same as the amount of heat it gives off when it cools because...
77 ProblemsIt takes 24.3 calories to heat 15.4 g of a metal from 22 ºC to 33ºC. What is the specific heat of the metal?Iron has a specific heat of 0.11 cal/gºC. How much heat will it take to change the temperature of 48.3 g of iron by 32.4ºC?