2What You’ll Learn in this Unit Significant FiguresScientific NotationMeasurementDimensional AnalysisErrorDensityGraphical analysis
3Review of Measurement Terms Qualitative measurements - wordsQuantitative measurements – involves numbers (quantities)Depends on reliability of instrumentDepends on care with which it is read
4Precision vs. AccuracyPrecision- the degree of agreement among several measurements of the same quantity.Accuracy- the agreement of a particular value with the true value
5Uncertainty Basis for significant figures All measurements are uncertain to some degreeRandom error - equal chance of being high or low- addressed by averaging measurements - expected
6Significant Figures Meaningful digits in a measurement The number of significant figures in your measurement will tell the reader how exact the instrumentation usedIf it is measured or estimated, it has sig figs.If not it is exact (e.g. 5 apples).
7Significant Figures All numbers 1-9 are significant. The problem are the ZEROS.Which ones count and which don’t?In between numbers 1-9 doesExample: ……… has 4 sig figsNow let me tell you a story…
8Left handed ArcherThere once was a left handed archer who loved to shoot decimals. Zeros could not stop his arrow but numbers could.If there is a decimal in the number begin on the left. Go through any zeros, come to the first number then all other numbers that follow are SIGNIFICANT!→0.0040→50.401
9No decimalsIf a number has no decimals you begin on the right hand side.Go through any zeros , come to the first number.Then all numbers after that count5000←405,000 ←
10Doing the MathMultiplication and division, same number of sig figs in answer as the least in the problemAddition and subtraction, same number of decimal places in answer as least in problem.
11Scientific Notation 100 = 1.0 x 102 0.001 = 1.0 x 10-3 -- This provides a way to show significant figures.
12TOO QUICK FOR YOU! So here are the rules.. slowly! Place decimal point after 1st real non-zero integer. (ex) 1.0 NOT 10.0Raise 10 to the exponential which equals the number of places you moved.
13Scientific NotationThe product of 2.3 x 10 x 10 x 10 equals 2300 (2.3 x 103)Note:Moving the decimal to the left will increase the power of 10Moving the decimal to the right will decrease the power of 10
15Answers2.387 x 1037.031 X 10-52.9 x 1098.900 X 10-39.01 X 1072.10 X 10-6
16Scientific Notation Multiplication and Division Use of a calculator is permitteduse it correctlyNo calculator? Multiply the coefficients, and add the exponents(3 x 104) x (2 x 102) =(2.1 x 103) x (4.0 x 10-7) =6 x 1068.4 x 10-4
17Scientific Notation Multiplication and Division In division, divide the coefficients, and subtract the exponent in the denominator from the numerator3.0 x 1056.0 x 1025 x 102=
18Scientific Notation 7 x 10-8 3.17 x 10-5 (6.6 x 10-8) + (4.0 x 10-9) = Addition and SubtractionBefore numbers can be added or subtracted, the exponents must be the sameCalculators will take care of thisDoing it manually, you will have to make the exponents the same- it does not matter which one you change.(6.6 x 10-8) + (4.0 x 10-9) =(3.42 x 10-5) – (2.5 x 10-6) =7 x 10-83.17 x 10-5
19Measurement Every measurement has two parts COMMON SI UNITSSymbol Unit Name Quantity Definition mmeterlengthbase unit kgkilogrammass ssecondtime Kkelvintemperature °Cdegree Celsius** temperature m3cubic metervolumem3 Lliter**dm3 = m3 Nnewtonforcekg·m/s2 JjouleenergyN·m WwattpowerJ/s PapascalpressureN/m2 Hzhertzfrequency1/sEvery measurement has two partsNumber with the correct sig - figsScale (unit)We use the Systeme Internationale (SI).
20Metric Base Units Mass - kilogram (kg) Length- meter (m) Volume- (L) Time - second (s)Temperature- Kelvin (K)Electric current- ampere (amp, A)Amount of substance- mole (mol)Energy – joule (j)
21Prefixes giga- G 1,000,000,000 109 mega - M 1,000,000 106 kilo - k 1,deci- dcenti- cmilli- mmicro- mnano- n
22Using Units to solve problems Dimensional AnalysisUsing Units to solve problems
23Dimensional Analysis Use conversion factors to change the units 1 foot = 12 inches (equivalence statement)12 in = = 1 ft ft in2 conversion factorsmultiply by the one that will give you the correct units in your answer.
24Example ProblemThe speed of light is 3.00 x 108 m/s. How far will a beam of light travel in 1.00 ns?Well, we know that 1.00 ns = 10-9 seconds(3.00 x 108 m) X (10-9 s) = x m/nss (1.00 ns)
25Example Problems 11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mileThe Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers?A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?
26Volume The space occupied by any sample of matter Calculated for a solid by multiplying the length x width x heightSI unit = cubic meter (m3)Everyday unit = Liter (L), which is non-SI
27Units of Mass Mass is a measure of the quantity of matter Weight is a force that measures the pull by gravity- it changes with locationMass is constant, regardless of location.The SI unit of mass is the kilogram (kg), even though a more convenient unit is the gramMeasuring instrument is the balance scale
28DensityWhich is heavier- lead or feathers?It depends upon the amount of the materialA truckload of feathers is heavier than a small pellet of leadThe relationship here is between mass and volume- called Density
29Density Common units are g/mL, or possibly g/cm3, (or g/L for gas) Ratio of mass to volumeD = m/VCommon units are g/mL, or possibly g/cm3, (or g/L for gas)Useful for identifying a compoundUseful for predicting weightAn intensive property- does not depend on what the material is
30Things related to density density of corn oil is 0.89 g/mL and water is 1.00 g/mLWhat happens when corn oil and water are mixed?Why?Will lead float?
31Example ProblemAn empty container weighs g. Filled with carbon tetrachloride (density 1.53 g/cm3 ) the container weighs g. What is the volume of the container?
32Density and Temperature What happens to density as the temperature increases?Mass remains the sameMost substances increase in volume as temperature increasesThus, density generally decreases as the temperature increases
33Density and waterWater is an important exceptionOver certain temperatures, the volume of water increases as the temperature decreasesDoes ice float in liquidwater?Why?
34Specific GravityA comparison of the density of an object to a reference standard (which is usually water) at the same temperatureWater density at 4 oC = 1 g/cm3
35Formula Note there are no units left, since they cancel each other D of substance (g/cm3)D of water (g/cm3)Note there are no units left, since they cancel each otherMeasured with a hydrometerUses?Gem puritydifferentiating between different types of crude oils/gasolineurine tests for concentration of all chemicals in your urineSpecific gravity =
36TemperatureHeat moves from warmer object to the cooler objectGlass of iced tea gets colder?Remember that most substances expand with a temperature increase?Basis for thermometers
37Temperature scalesCelsius scale- named after a Swedish astronomerUses the freezing point (0 oC) and boiling point (100 oC) of water as referencesDivided into 100 equal intervals, or degrees Celsius
38Temperature scalesKelvin scale (or absolute scale)Named after Lord KelvinK = oC + 273A change of one degree Kelvin is the same as a change of one degree CelsiusNo degree sign is used
39Temperature scalesWater freezes at 273 KWater boils at 373 K0 K is called absolute zero, and equals –273 oC
40Temperature A measure of the average kinetic energy Different temperature scales, all are talking about the same height of mercury.In lab take the reading in ºC then convert to our SI unit KelvinºC = K
42Example problemA 55.0 gal drum weighs 75.0 lbs. when empty. What will the total mass be when filled with ethanol? density g/cm gal = L1 lb = 454 g
43Error Calculations X 100 accepted value Error = Experimental value- accepted value% error = [error]accepted valueX 100
44GraphingThe relationship between two variables is often determined by graphingA graph is a “picture” of the data
45Graphing Rules – 10 itemsPlot the independent variable on the x-axis (abscissa) – the horizontal axis. Generally controlled by the experimenterPlot the dependent variable on the y-axis (ordinate) – the vertical axis.3. Label the axis.Quantities (temperature, length, etc.) and also the proper units (cm, oC, etc.)4. Choose a range that includes all the results of the data
46Graphing Rules5. Calibrate the axis (all marks equal) 6. Enclose the dot in a circle (point protector) 7.Give the graph a title (telling what it is about) 8. Make the graph large – use the full piece of paper 9. Indent your graph from the left and bottom edges of the page 10. Use a best fit line, do not connect points