1Measurement and ChemicalCalculations.Chapter 3Measurement and ChemicalCalculations• Very large and very small numbers: exponentialnotation• Metric system and SI base units– Mass, length, temperature, amount of material– Derived units (for other physical properties)• Converting between units• Calculations using dimensional analysis• Quantifying and communicating uncertainty inmeasurements• Significant figures and rounding2Very large and very small• Numbers in chemistry tend to be much larger, and muchsmaller, than numbers in “every day life”– Number of atoms in 12.00g of carbon602214179000000000000000– Length of the bond between two carbon atoms inbenzene0.000000000139 m• We will express numbers using exponential notation– 6.02214179 × 1023 (Avogadro's Constant)– 1.39 x 10-10 mExponential notationBpB = basep = power!= " " " == = " " " = =44410 10 10 10 10 100001 1 1 1 1 110 0.0 00110 10 10 10 10 10000We generally use base 10, B=10Large and small numbers are written as a.bcd x 10eone digit before the decimal point3Converting numbers into exponentialnotation: moving the decimal point• Convert 724000 into standard exponential notation We want 7.24 x 10?• How far do we need to move the decimal point?724000.0 7.240000 moved 5 places left Answer: 7.24 x 105Reality check - 105 is 100000 - a large numberone digit before the decimal pointConverting numbers into exponentialnotation: moving the decimal point• Convert 0.000427 into standard exponential notation We want 4.27 x 10?• How far do we need to move the decimal point?0.000427 00004.27 moved 4 places right(different direction) Answer: 4.27 x 10-4Reality check - 10-4 is 0.0001 - a small numberone digit before the decimal point4Exponential notation into “ordinary”decimal form• Convert 4.71 x 10-4 into “ordinary” decimal form• Note: it is a negative exponent so this is going to be avery small number (zeros after the decimal point)• Move the decimal point 4 places to the left00004.71 0.000471 moved 4 placesExponential notation into “ordinary”decimal form• Convert -7.2 x 105 into “ordinary” decimal form• Note: it is a positive exponent so this is going to be avery large number (zeros before the decimal point)• Move the decimal point 5 places to the right-7.200000 -720000 moved 5 places• Notice that the minus sign for -7.2 stays the same.-720,000 is a large negative number5The metric system• Measurements everywhere in the world, with theexception of the US, Burma and Liberia are made inthe metric system– the tiny island of St. Lucia converted to metric on April 1st 2008• In the metric system units that are larger, or smaller,than the base unit are multiples of 10g (grams), kg (kilograms = g x 1000) for weightsm (meters), km (kilometers = m x 1000) for distanceYou can convert units by simply “moving the decimalpoint” and using exponential notation.SI Units• SI units are a subset of all metric units• SI is an abbreviation for the French name for theInternational System of Units• The SI system is defined by seven base unitsMass kilogramLength meterTemperature kelvinTime secondAmount of substance moleElectrical current ampereLuminous intensity candelaAntoine Lavoisier6It is worth learning these (basic scientific literacy)These are quantities that are very common in chemistry and biochemistryMass• The SI unit of mass is thekilogram, kg• It is defined as the mass of aplatinum-iridium cylinderstored in a vault in France (!)• It is the only SI unit that is stilldefined in relation to anartifact rather than to afundamental physical propertythat can be reproduced indifferent laboratories• A new 1kg sphere made ofsilicon is in the works. It willcontain 2.15 x 1025 atoms7Length• The SI unit of lengthis the meter, m• It is defined as thedistance light travelsin a vacuum in1/299,792,468second.Volume• The SI unit of volume is the cubic meter, m3• A more practical unit for laboratory work is the cubiccentimeter, cm3.8Volume• One liter (L) is defined asexactly 1000 cubiccentimeters• Volume of a 10cm x 10cmx 10cm box• One liter of water weighs1000g = 1 kilogram• 1 mL = 0.001 L = 1 cm3Temperature• FahrenheitTemperature Scale:– Water freezes at 32°Fand boils at 212°F• Celsius TemperatureScale:– Water freezes at 0°Cand boils at 100°C• T°F – 32 = 1.8 x T°C9• The other temperature scales have arbitary zeropoints• Zero on the kelvin scale (0 K) is absolute zero - thelowest temperature possible• Relationship between kinetic energy, the movementof particles, and temperature (in K)• When the temperature is 0 K, all the particles/atomsin the material are stationary (v = 0)• TK = T°C + 273Absolute temperature (kelvin)= =21 32 2EKmv kBTAmount of substance• One mole is the amount of substance of a systemwhich contains as many "elemental entities" (eg,atoms, molecules, ions, electrons) as there are atomsin 12 g of carbon-12: 6.022 x 1023• You could use the mole as a unit of measurement foramounts of other things– eggs in SI units?– Not very practical!1.9926 x 10-23 moles eggsThe ‘dozen’ is a better unit!1 mole carbon atoms10“Derived” units• The SI units for all other physical propertymeasurement are derived from their relationship tothe 7 base units• Examples– Common unit for force or weight is the Newton (N)– SI unit is or – Common unit for pressure is the pascal (Pa), N/m2– SI unit is or– Common unit for energy, heat or work is the joule, (J), Nm– SI unit is or!2m kgs!2. .m kg s!2kgm s! !1 2. .m kg s!22m kgs!2 2. .m kg sExample: units for density• The mass and volume of a substance are directlyproportional (more mass means more volume!),m ∝ V• The proportionality is changed into an equation byinserting a proportionality constant, densitymass = D x volume or D =• The mass per unit volume• The SI units of density are kg/m3, but we most oftenuse g/cm3 or g/mL– water has a density very close to 1 g/cm3– osmium has a density of 22.6 g/cm3massvolume11Example: units for density• Notice that 1 kg/m3 ≠ 1 g/cm3• 1 kg = 103 g• 1 m3 = 100 x 100 x 100 = 106 cm3• So1 kg/m3 = = 10-3 g/cm3 1g/cm3 = 1000 kg/m3103 g106 cm3Density example calculations• A piece of wood has a mass of 35 g. If its volume is7 cm3, What is its density? Density =