Presentation on theme: "Mathematical Relationships in Chemistry"— Presentation transcript:
1 Mathematical Relationships in Chemistry CP Chemistry
2 What You’ll Learn in this Unit MeasurementDimensional AnalysisScientific NotationSignificant FiguresErrorDensity
3 Measurement Every measurement has two parts Number with the correct sig - figsScale (unit)SI system (le Systeme International) based on the metric systemPrefix + base unitPrefix tells you the power of 10 to multiply by - decimal system -easy conversions
4 MeasurementCOMMON 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/sWe use the SI (not the Sports Illustrated) It is called the Systeme Internationale.
5 Metric SI Units Mass - kilogram (kg) Length- meter (m) Time - second (s)Temperature - Kelvin (K)Electric current - ampere (amp, A)Amount of substance - mole (mol)
7 Using Units to solve problems Dimensional AnalysisUsing Units to solve problems
8 Dimensional 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.
9 Example Problem There are 2.2 lb in 1 kg If you weigh 158 lbs, how many kg do you weigh?
10 Example Problems 11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mile1 mile = 1.6 kmThe Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers?
15 Answers2.387 x 1037.031 X 10-52.9 x 1098.900 X 10-39.01 X 1072.10 X 10-6
16 Uncertainty Basis for significant figures All measurements are uncertain to some degreePrecision- how repeatableAccuracy- how correct - closeness to true value.Random error - equal chance of being high or low- addressed by averaging measurements - expected
17 Uncertainty Systematic error- same direction each time Want to avoid thisBetter precision implies better accuracyYou can have precision without accuracy, and vice versa
18 Precision vs. AccuracyPrecision- the degree of agreement among several measurements of the same quantity.Accuracy- the agreement of a particular value with the true value
20 Significant Figures Meaningful digits in a MEASUREMENT The number of significant figures in your measurement will tell the reader how exact the instrumentation isIf it is measured or estimated, it has sig figs.If not, it is exact.
21 Significant Figures All numbers except zero are significant. Some zeros are, some aren’t
22 Which Zeros Count? In between other sig figs does Before the first number doesn’tAfter the last number counts if it is after the decimal pointthe decimal point is written insig figssig figs
23 Doing 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.
24 Volume The space occupied by any sample of matter Calculated for a solid by multiplying the length x width x heightSI derived unit = cubic meter (m3)Everyday unit = Liter (L), which is non-SI
25 Units 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
26 Working with MassThe SI unit of mass is the kilogram (kg), even though a more convenient unit is the gramMeasuring instrument is the balance scale
27 Density Which 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
28 Density The formula for density is: mass volume Common units are g/mL, or possibly g/cm3, (or g/L for gas)Density =
29 Density Useful for identifying a compound Useful for predicting weight An intrinsic property- does not depend on what the material isIntensive PropertyDensity is a physical property, and does not depend upon sample size
30 Things related to density Corn oil density – 0.921g/mLWater density – 1.000g/mLWhat happens when corn oil and water are mixed?Why?Will lead float in water?
31 Example ProblemAn empty container weighs g. Filled with carbon tetrachloride (density=1.53 g/cm3), the full container weighs g. What is the volume of the container?
32 Density 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
33 Density and water Water is an important exception Over certain temperatures, the volume of water increases as the temperature decreasesDoes ice float in liquid water?Why?
34 Specific 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
35 Specific Gravity Formula D of substance (g/cm3)D of water (g/cm3)Note there are no units left, since they cancel each otherMeasured with a hydrometerUses? Tests urine, antifreeze, batterySG =
36 Temperature 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
37 Temperature Heat moves from warmer object to the cooler object Glass of iced tea gets colder?Remember that most substances expand with a temp. increase?Basis for thermometers
38 Temperature scales Celsius scale- named after a Swedish astronomer Uses the freezing point(0 oC) and boiling point (100 oC) of water as referencesDivided into 100 equal intervals, or degrees Celsius
39 Temperature scales Kelvin 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
40 Temperature scales Water freezes at 273 K Water boils at 373 K 0 K is called absolute zero, and equals –273 oC