chapter 2 quantitative measurements give results in a definite form, usually a number example...
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Chapter 2Chapter 2
Quantitative measurementsQuantitative measurements
give results in a definite form, give results in a definite form, usually a numberusually a number
Example
ThermometerThermometer
Color of a reactionColor of a reaction
Qualitative measurementsQualitative measurements
gives results in a descriptive formgives results in a descriptive form
Example
non-numeric valuenon-numeric value
Reproducibility of the measurementReproducibility of the measurement
How close a measurement comes to How close a measurement comes to the true valuethe true value
AccuracyAccuracy
PrecisionPrecision
include all digits that can be known include all digits that can be known accurately plus a last digit that is accurately plus a last digit that is
estimatedestimated
Significant FiguresSignificant Figures
Rules for Significant FiguresRules for Significant Figures
(All have 3 Sig. Figs.)(All have 3 Sig. Figs.)
1.1. Every nonzero digit in a recorded Every nonzero digit in a recorded measurement is significantmeasurement is significant
Examples
65.65.22
0.0.262688
126126
2. Zeros between nonzero digits are 2. Zeros between nonzero digits are significantsignificant
Example
22000044
6600.39.39 8.68.60022
(All have 4 Sig. Figs.)(All have 4 Sig. Figs.)
3. Zeros in front of all nonzero digits 3. Zeros in front of all nonzero digits are are NOTNOT significant. They act as significant. They act as place-holders.place-holders.
Examples
00..00006622
00.58.58 00..0000002277
(2 Sig. Figs.) (2 Sig. Figs.)
4. Zeros at the end of a number and 4. Zeros at the end of a number and to the right of a decimal point are to the right of a decimal point are significantsignificant
Examples
61.61.0000 1.031.0300 8.8.000000
(4 Sig. Figs.)(4 Sig. Figs.)
Zeros at the end of a measurement Zeros at the end of a measurement and to the left of the decimal can and to the left of the decimal can be confusing. be confusing.
If they are place-holders to show If they are place-holders to show the magnitude of a number, they the magnitude of a number, they are not significantare not significant
Examples
300 700 300 700 2721027210
ambiguousambiguous
If the zeros were measured- If the zeros were measured- significantsignificant
700.
To avoid confusion use scientific To avoid confusion use scientific notationnotation
3.00 x 10 3.00 x 10 22
How Many Sig. Figs.?How Many Sig. Figs.?
123 123
0.123 0.123
40,506 40,506
9.8000 x 10 9.8000 x 10 44
98,000 98,000
0.07080 0.07080
0.078 0.078
33
55
33
55
22
22
44
Sig. Figs in calculationsSig. Figs in calculations
If digit following last sig fig is <5, all If digit following last sig fig is <5, all digits are droppeddigits are dropped
If digit following last sig fig is >5, digit in If digit following last sig fig is >5, digit in last sig fig place is increased by onelast sig fig place is increased by one
Round These…….
314.72314.72110.001770.0017755
64.32 x 10 64.32 x 10 -1-1
4 sig figs4 sig figs 314.7314.7
2 sig 2 sig figsfigs
0.00180.0018
1 1 sig sig figfig
60 x 10 60 x 10 --
1 1 or 6 or 6
Addition and SubtractionAddition and Subtraction
The answer cannot contain any The answer cannot contain any more digits to the right of the more digits to the right of the decimal point than are contained in decimal point than are contained in the measurement with the least the measurement with the least number of digits to the right of the number of digits to the right of the decimal pointdecimal point
12.52+
349.0
8.24
369.8 or 3.698 x 10 2
Sample Problem
+
Multiplication and DivisionMultiplication and Division
Answer must contain no more sig figs than Answer must contain no more sig figs than the measurement with the least number the measurement with the least number
of sig figs. of sig figs.
*Decimal point has nothing to do with *Decimal point has nothing to do with determining this!determining this!
Example Problems
755755 x .0 x .03434 = =2626
3 sig. figs. 2 sig. figs 2 sig. figs
2.4526 2.4526 8.4 8.4 ==
0.290.29
►Metric SystemMetric System
►SI system (International SI system (International System of Units)- System of Units)- Developed in 1790 in Developed in 1790 in FranceFrance
QuantityQuantity SI Unit Non-SI
Length m
Volume m3 Liters
Mass kg grams
Density g/cm³, g/ml
Temperature K oC
Time s
Pressure pa (pascal) atmospheres, mm Hg
Energy J (joules) calories
PrefixPrefix Symbol Symbol Magnitude Magnitude
kilokilo KK 1000x1000x
hecto hecto hh 100x100x
decadeca dada 10x10x
unitunit m, L, gm, L, g x x
decideci dd .1x.1x
centicenti cc .01x.01x
millimilli mm .001x.001x
micromicro uu 1 x 10 1 x 10 -6 -6 x x
nanonano nn 1 x 10 1 x 10 -9 -9 x x
picopico pp 1 x 101 x 10-12 -12 x x
Units of Measurement – Meter (m)Units of Measurement – Meter (m)
Units of Volume – Liter (L)Units of Volume – Liter (L)
Volume of a cube-10 cm x 10 cm Volume of a cube-10 cm x 10 cm x 10 cm= 1000 cm x 10 cm= 1000 cm 33
►1 L = 1 dm 1 L = 1 dm 33 = 1000 cm = 1000 cm 33
1 cm 1 cm 33 = 1 mL = 1 mL
►MassMass- quantity of matter- quantity of matter►WeightWeight- a force- a force►Unit of mass – gram (g) = Unit of mass – gram (g) =
mass of 1 cm mass of 1 cm 33 of H of H22O at 4 ºCO at 4 ºC
Units of Mass – (g)Units of Mass – (g)
►DensityDensity- ratio of mass of an - ratio of mass of an object to volumeobject to volume
D= M = g/mL or g/cm D= M = g/mL or g/cm 33
VV
►Specific GravitySpecific Gravity- - comparison of the density comparison of the density of a substance to the of a substance to the density of a reference density of a reference substancesubstance
Specific Gravity Specific Gravity
Specific Gravity Cont’dSpecific Gravity Cont’d
Sp. Gravity = density of substance g/cm Sp. Gravity = density of substance g/cm 33
density of Hdensity of H22O g/cm O g/cm 33
Sp. Gravity of a liquid is measured with Sp. Gravity of a liquid is measured with a hydrometera hydrometer
►TemperatureTemperature- Degree of hotness - Degree of hotness or coldness of an objector coldness of an object Determined direction of heat Determined direction of heat
transfertransfer►Heat transferHeat transfer- occurs when two - occurs when two
objects at different objects at different temperatures contact each other temperatures contact each other Heat goes from high Heat goes from high
temperature to low temptemperature to low temp
FahrenheitFahrenheit
32ºF - FP of H32ºF - FP of H22OO
212ºF - BP of H212ºF - BP of H22OO
Celsius (centigrade)Celsius (centigrade)
0ºC - 0ºC - FPFP of H of H22OO
100ºC - BP of H100ºC - BP of H22OO
KelvinKelvin
273 K - 273 K - FPFP of H of H22OO K = K = ooCC + 273 + 273
373 K - BP of H373 K - BP of H22OO
Temperature ScalesTemperature Scales
HeatHeat
►HeatHeat- measured in joule (J) or - measured in joule (J) or calories (cal)calories (cal) One calorie is the quantity of One calorie is the quantity of
heat that raises the heat that raises the temperature of 1 g of Htemperature of 1 g of H22O 1ºCO 1ºC►1 cal = 4.18 J1 cal = 4.18 J
Calorie in nutritional terms Calorie in nutritional terms means kilocaloriemeans kilocalorie
Heat Cont’dHeat Cont’d
►Heat CapacityHeat Capacity- quantity of heat - quantity of heat required to change an objects required to change an objects temperature by exactly 1ºCtemperature by exactly 1ºC Depends on mass and type of Depends on mass and type of
substancesubstance
Specific HeatSpecific Heat
►The quantity of heat required to The quantity of heat required to raise 1g of a substance 1raise 1g of a substance 1ºCºC Sp. Heat = heat = qSp. Heat = heat = q
mass x mass x T (m) (T) T (m) (T)
Units of Specific Heat:Units of Specific Heat:
J/gJ/g°C or cal/g°C°C or cal/g°C
Chapter Chapter 2B2B
Problem Solving in Problem Solving in ChemistryChemistry
► Three easy steps to problem Three easy steps to problem solving. . . solving. . .
Step 1 : AnalyzeStep 1 : Analyze
► Identify a knownIdentify a known Determine where you are starting Determine where you are starting
from.from. What information do you already What information do you already
have to work with?have to work with?
Step 1 cont’d…Step 1 cont’d…
►Identify an unknown Identify an unknown Where are you going?Where are you going? What are you looking for?What are you looking for?
►Plan a solutionPlan a solution How are you going to get there?How are you going to get there?
Step 2: CalculateStep 2: Calculate
► May involve substituting known May involve substituting known quantities and doing the arithmetic quantities and doing the arithmetic needed to solve for unknown.needed to solve for unknown.
► You may also need to convert.You may also need to convert.
Step 3: EvaluateStep 3: Evaluate
► Go over your answersGo over your answers Does the answer make sense?Does the answer make sense? Did you use correct units?Did you use correct units?
►Check your workCheck your work Make sure you copied down the given Make sure you copied down the given
information correctly.information correctly.
Sample ProblemSample Problem
►What is the mass, in What is the mass, in grams, of a piece of lead grams, of a piece of lead that has a volume of that has a volume of 19.84 cm19.84 cm³?³?
Step 1 : AnalyzeStep 1 : Analyze
►List Knowns and UnknownsList Knowns and Unknowns KnownsKnowns : :
►Volume of lead: 19.84 cmVolume of lead: 19.84 cm³³►Density of lead = 11.4 g/cm³ Density of lead = 11.4 g/cm³
(according to table 3.7)(according to table 3.7)►Density = massDensity = mass
volumevolume UnknownsUnknowns: mass = ?g: mass = ?g
► Density = mass -or- Mass = volume x Density = mass -or- Mass = volume x densitydensity
volumevolume
► Mass = 19.84 cm Mass = 19.84 cm ³ x 11.4 g/cm ³³ x 11.4 g/cm ³
= 226.176 g= 226.176 g
Mass = 226 gMass = 226 g
Step 2: CalculateStep 2: Calculate
Step 3: EvaluateStep 3: Evaluate
►Has the unknown been found? Has the unknown been found? Yes, problem asks for massYes, problem asks for mass
►Do you have the correct units? Do you have the correct units? Yes, units canceled correctly to yield grams Yes, units canceled correctly to yield grams
(g)(g)► Is the number of sig figs correct?Is the number of sig figs correct?
Yes, answer has 3 sig figsYes, answer has 3 sig figs
Mass = 226 gMass = 226 g
What is the volume, in What is the volume, in cubic centimeters of a cubic centimeters of a sample of cough syrup sample of cough syrup that has a mass of 50.0g? that has a mass of 50.0g? The density of cough The density of cough syrup is 0.950g/cmsyrup is 0.950g/cm³.³.
Volume = mass
density
Volume = 50.0g = 52.6316 cm³
0.950g/cm³
Volume = 52.6 cm³
Your school club has sold 600 Your school club has sold 600 tickets to a chili-supper tickets to a chili-supper
fundraising event, and you have fundraising event, and you have volunteered to make chili. You volunteered to make chili. You have a chili recipe that serves have a chili recipe that serves 10. The recipe calls for two 10. The recipe calls for two
teaspoons of chili powder. How teaspoons of chili powder. How much chili powder do you need much chili powder do you need
for 600 servings?for 600 servings?
Servings Needed = 600Servings Needed = 600
10 servings = 2 tsp chili powder10 servings = 2 tsp chili powder
Amount of chili powder = ? tspAmount of chili powder = ? tsp
600 servings x 2 tsp chili powder = 600 servings x 2 tsp chili powder =
10 servings10 servings
1200 tsp chili powder = 120 tsp chili 1200 tsp chili powder = 120 tsp chili powderpowder
1010
►How many cups are in 120 How many cups are in 120 teaspoons of chili powder?teaspoons of chili powder?
120 tsp x 1 tbs x 1 cup = 120 tsp x 1 tbs x 1 cup =
3 tsp 16 tbs3 tsp 16 tbs
120 cups = 120 cups = 2.5 cups2.5 cups
4848
►Express 750 dg in gramsExpress 750 dg in grams
Mass = 750 dgMass = 750 dg
1 g = 10 dg1 g = 10 dg
Mass = ?gMass = ?g
750 dg x 1g = 750 dg x 1g = 75 g75 g
10 dg 10 dg
►What is 0.073 km in cm?What is 0.073 km in cm?
0.073 km x 1000 m x 100 cm = 0.073 km x 1000 m x 100 cm =
1 km 1 m 1 km 1 m
7300 cm = 7300 cm = 7300 cm7300 cm
1 1
► How many seconds are in How many seconds are in one day?one day?
1 day x 24 h x 60 min x 60 s 1 day x 24 h x 60 min x 60 s = =
1 day 1 h 1 min1 day 1 h 1 min
86400 s = 8.64 x 1086400 s = 8.64 x 104 4 ss
11