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8/14/2019 Continuation to Periodic Table, Measurement, Dimensional Analysis, Gases and Kinetic Molecular Theory of Gases
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IsotopesIsotopes
The different possibleThe different possible
versions of the sameversions of the sameelement havingelement having
different numbers of different numbers of neutron.neutron.
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Natural AbundanceNatural Abundance
The relativeThe relative
abundance of anabundance of anisotope in nature asisotope in nature as
compared to thecompared to theother isotope of theother isotope of the
same element.same element.
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Atomic Weight of Atomic Weight of ElementElement
This is defined as theThis is defined as the
average atomicaverage atomicmasses of differentmasses of different
isotopes of theisotopes of theelement.element.
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Atomic Weight of Atomic Weight of ElementElement
The light metal lithiumThe light metal lithiumdiscovered by Arfvedson havediscovered by Arfvedson havetwo stable isotopes. Calculatetwo stable isotopes. Calculate
the atomic weight of lithiumthe atomic weight of lithiumgiven the percent abundance of given the percent abundance of Lithium-6 to be 7.5% and anLithium-6 to be 7.5% and an
atomic mass of 6.015122 amu.atomic mass of 6.015122 amu.On the other hand, Lithium-7On the other hand, Lithium-7has an isotopic abundance of has an isotopic abundance of
92.5% and an atomic mass of 92.5% and an atomic mass of
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(7.5%)(6.015122) +(7.5%)(6.015122) +(92.5%)(7.016003)(92.5%)(7.016003)
=(0.45113415) +=(0.45113415) +
(6.489802775)(6.489802775)= 6.940936925= 6.940936925
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Powers of ten
•are used for convenience withsmaller or larger units in the SI
system.
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Unit…Unit…
ia group or troopa group or troopia component ora component or
thingthing
i
a part or piecea part or pieceia divisiona division
ia quantitya quantity
i f
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Units of Units of
Measurement Measurement
There are two types of units:fundamental (or base)units;
derived units.
There are 7 base units in the
Système International(SI) system.
Derived units are obtained
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Units of Measurement Units of Measurement
PHYSICALQUANTITY
Name of UnitAbbreviationMass
Length
Time
Electric current
Temperature
Luminousintensity
Kilogram
Meter
Second
Ampere
Kelvin
Candela
Mole
kg
m
s
a
K
cd
mol
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Unit of velocity =
————————— unit of time
unit of distance
= m/s
meters
seconds=
they are obtained from the baseunits
Derived unitsDerived units
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Units of Measurement Units of Measurement
PHYSICALQUANTITY
Name of Unit
Area
Volume
Velocity
Acceleration
Current density
Luminance
Magnetic field
Square meter, m2
Cubic meter, m3
Meter/second, m/s
Meter/second
squared, m/s
2
Ampere/square meter,A/m2
Candela/square
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Units of Measurement Units of Measurement
TemperatureTemperature
•Celsius ScaleUsed in science.
Water freezes at 0oC and boils at 100oC.To convert: K = oC + 273.15.
•Kelvin ScaleAlso used in science.Same temperature increment as Celsiusscale.Lowest temperature possible is zeroKelvin.
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Units of Measurement Units of Measurement
TemperatureTemperature
•Fahrenheit ScaleNot generally used in science.
Water freezes at 32oF and boils at212oF.To convert:
( )32-F95C ° ( ) 32C
59F +
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Units of Measurement Units of Measurement
Volume
q The units forvolume are givenby (units of
length)3.i.e., SI unit for
volume is 1 m3.
qWe usually use 1mL = 1 cm3.
qOther volume
units:
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Units of Measurement Units of Measurement
DensityUsed to characterize substances.
Defined as mass divided by
volume.
Units: g/cm3.
Originally based on mass (thedensity was defined as the mass of 1.00 g of pure water).
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All scientific measures are subjectAll scientific measures are subjectto error.to error.
These errors are reflected in the These errors are reflected in the
number of figures reported for thenumber of figures reported for themeasurement.measurement.
These errors are also reflected in These errors are also reflected in
the observation that twothe observation that two
successive measures of the samesuccessive measures of the same
quantity are different.quantity are different.
Points to Ponder?
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Precision and AccuracyMeasurements that are close to the
“correct” value are accurate.
Measurements which are close toeach other are precise.
Measurements can be:
accurate and precise;precise but inaccurate;
neither accurate nor precise.
Uncertainty in Measurement Uncertainty in Measurement
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Comparison of Precision andAccuracy
Uncertainty in Measurement Uncertainty in Measurement
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Uncertainty in Measurement Uncertainty in Measurement
The number of digits reported in ameasurement reflect the accuracy of themeasurement and the precision of themeasuring device.
All the figures known with certainty plusone extra figure are called significantfigures.
In any calculation, the results arereported to the fewest significant figures(for multiplication and division) or fewest
decimal places (addition and
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Uncertainty in Measurement Uncertainty in Measurement
Significant Figures
Non-zero numbers are alwayssignificant.
Zeros between non-zero numbers are
always significant.
Zeros before the first non-zero digit arenot significant. (Example: 0.0003 has
one significant figure.)Zeros at the end of the number after a
decimal place are significant.
Zeros at the end of a number before a
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Method of calculation utilizing aknowledge of units.
Given units can be multiplied or
divided to give the desired units.Conversion factors are used to
manipulate units:
Desired unit = given unit × (conversion factor)
The conversion factors are simple
Dimensional AnalysisDimensional Analysis
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Conversion factor Conversion factor
unitgiven
unitdesiredfactorConversion =
1000cm3
1L
1000cm3
1LOR
Dimensional AnalysisDimensional Analysis
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Dimensional AnalysisDimensional Analysis
Example to convert length in metersto length in inches:
(length in m)×(conversion factor form→cm)×(conversion factor for cm→
inches).
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Dimensional AnalysisDimensional Analysis
In dimensional analysis alwaysask three questions:
What data are we given?
What quantity do we need?
What conversion factors areavailable to take us from whatwe are given to what we need?
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Question?Question?
We measure length inWe measure length in metersmeters using ausing a
meter stick or a rulermeter stick or a ruler..
We measure time in seconds using aWe measure time in seconds using a
clock or a timerclock or a timer..
We measure temperature inWe measure temperature in °C, °F or K °C, °F or K using ausing a thermometerthermometer..
We measure volume inWe measure volume in litersliters using ausing a
graduated cylinder or containergraduated cylinder or container..
We measure speed inWe measure speed in m/sm/s using ausing a
speedometer (or combination of #1speedometer (or combination of #1& #2& #2)..
We can measure mass, length, time,temperature, volume, etc. Wemeasure mass in grams using a
balance or a weighing scale.How can you measure length?
How can you measure time?
How can you measure temperature?
How can you measure volume?
How can you measure speed?
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We count atoms,
molecules, substances,particles, and pieces inMOLES.
How can you measure, or
count atoms, molecules,substances and/or
particles?
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MolesMoles
Defined as the numberDefined as the numberof carbon atoms inof carbon atoms in
exactly 12 grams of exactly 12 grams of carbon-12.carbon-12.
1 mole is 6.02 x 101 mole is 6.02 x 102323
particles.particles.
6.02 x 106.02 x 102323
is calledis called’
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Representative particlesRepresentative particles
The smallest pieces of a The smallest pieces of asubstance.substance.
For a molecular compoundFor a molecular compoundit is ait is a moleculemolecule..
For an ionic compound it isFor an ionic compound it is
aa formula unitformula unit..
For an element it is anFor an element it is an
atomatom..
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Types of questionsTypes of questions
How many oxygen atoms in theHow many oxygen atoms in thefollowing?following?
CaCOCaCO33
AlAl22(SO(SO44))33
How many ions in the following?How many ions in the following?
CaClCaCl22NaOHNaOH
AlAl22(SO(SO44))33
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Types of questionsTypes of questions
How many molecules of COHow many molecules of CO22 are theare thein 4.56 moles of COin 4.56 moles of CO22 ??
How many moles of water is 5.87 xHow many moles of water is 5.87 x
10102222 water molecules?water molecules?
How many atoms of carbon areHow many atoms of carbon are
there in 1.23 moles of Cthere in 1.23 moles of C66HH1212OO66 ??
How many moles is 7.78 x 10How many moles is 7.78 x 102424
formula units of MgClformula units of MgCl22??
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Measuring MolesMeasuring Moles
remember relative atomic mass?remember relative atomic mass?the amu was one twelfth thethe amu was one twelfth the
mass of a carbon-12 atom.mass of a carbon-12 atom.
since the mole is the number of since the mole is the number of
atoms in 12 grams of carbon-12,atoms in 12 grams of carbon-12,
the decimal number on thethe decimal number on theperiodic table is also the mass of periodic table is also the mass of
1 mole of those atoms in grams.1 mole of those atoms in grams.
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Gram Atomic MassGram Atomic Mass
The mass of 1 mole of an The mass of 1 mole of an
element in grams.element in grams.
12.01 grams of carbon has the12.01 grams of carbon has the
same number of pieces as 1.01same number of pieces as 1.01grams of hydrogen and 55.85grams of hydrogen and 55.85
grams of iron.grams of iron.
We can write this asWe can write this as
12.01 g C = 1 mole12.01 g C = 1 mole
We can count things by weighingWe can count things by weighing
l
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ExamplesExamples
How much would 2.34 moles of How much would 2.34 moles of carbon weigh?carbon weigh?
How many moles of magnesiumHow many moles of magnesium
in 24.31 g of Mg?in 24.31 g of Mg?
How many atoms of lithium inHow many atoms of lithium in
1.00 g of Li?1.00 g of Li?How much would 3.45 x 10How much would 3.45 x 102222
atoms of U weigh?atoms of U weigh?
f d ?
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Mass of compounds?Mass of compounds?
in 1 mole of Hin 1 mole of H22O molecules thereO molecules thereare two moles of H atoms and 1are two moles of H atoms and 1
mole of O atomsmole of O atoms
To find the mass of one mole of a To find the mass of one mole of acompoundcompound
determine the moles of thedetermine the moles of the
elements they haveelements they have
find out how much they wouldfind out how much they would
weighweigh
add them u
G M l l M
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Gram Molecular MassGram Molecular Mass
What is the mass of one mole of What is the mass of one mole of
CHCH44??
1 mole of C = 12.01 g1 mole of C = 12.01 g
4 mole of H x 1.01 g = 4.04g4 mole of H x 1.01 g = 4.04g1 mole CH1 mole CH44 = 12.01 + 4.04 = 16.05g= 12.01 + 4.04 = 16.05g
The The Gram Molecular massGram Molecular mass of CHof CH44 isis16.0516.05
The mass of one mole of a molecular The mass of one mole of a molecular
compound.compound.
lG F l M
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Gram Formula MassGram Formula Mass
The mass of one mole of an ionic The mass of one mole of an ionic
compound.compound.
Calculated the same way.Calculated the same way.
Example, what is the GFM of Example, what is the GFM of FeFe22OO33??
2 moles of Fe x 55.85 g = 111.702 moles of Fe x 55.85 g = 111.70gg
3 moles of O x 16.00 g = 48.003 moles of O x 16.00 g = 48.00
lM l M
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Molar MassMolar Mass
The generic term for the mass of one The generic term for the mass of one
mole.mole.
The same as gram molecular mass, The same as gram molecular mass,
gram formula mass, and gramgram formula mass, and gram
atomic mass.atomic mass.
The number of grams of 1 mole of The number of grams of 1 mole of
atoms, ions, or molecules.atoms, ions, or molecules.Using molar mass, we can makeUsing molar mass, we can make
conversion factors and;conversion factors and;
We can chan e rams of aWe can chan e rams of a
F lF l
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For exampleFor example
How many moles is 5.69 g of How many moles is 5.69 g of
NaOH?NaOH?
F lF l
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For exampleFor example
How many moles is 5.69 g of How many moles is 5.69 g of
NaOH?NaOH?
F lF l
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For exampleFor example
How many moles is 5.69 g of How many moles is 5.69 g of
NaOH?NaOH?
NaOHmol? NaOHg ?
NaOHmol ?
NaOHg69.5 =
q need to change grams to moles
F lF l
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For exampleFor example
How many moles is 5.69 g of How many moles is 5.69 g of
NaOH?NaOH?q
need to change grams to molesq for NaOH:
q1mole Na = 22.99g
q1 mol O = 16.00 g
q1 mole of H = 1.01 g
F lF l
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For exampleFor example
How many moles is 5.69 g of How many moles is 5.69 g of
NaOH?NaOH?
40.00g
mol1
qneed to change grams to moles
qfor NaOH:q1 mole NaOH = 40.00 g
F lF l
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For exampleFor example
How many moles is 5.69 g of How many moles is 5.69 g of
NaOH?NaOH?
?40.00
mol1g69.5 =
g
q
need to change grams to molesqfor NaOH:
q1 mole NaOH = 40.00 g
F lF l
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For exampleFor example
How many moles is 5.69 g of How many moles is 5.69 g of
NaOH?NaOH?
NaOHmol0.142 =40.00mol1g69.5
g
E lE l
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ExamplesExamples
How many moles is 4.56 g of How many moles is 4.56 g of COCO22??
How many grams is 9.87 molesHow many grams is 9.87 moles
of Hof H22O?O?
How many molecules in 6.8 g of How many molecules in 6.8 g of
CHCH44??
49 molecules of C49 molecules of C66HH1212OO66 weighsweighs
how much?how much?
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Gases and the MoleGases and the Mole
St d d T t dSt d d T t d
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Standard Temperature andStandard Temperature andPressurePressure
0ºC and 1 atm0ºC and 1 atmabbreviated STPabbreviated STP
At STP 1 mole of gas occupiesAt STP 1 mole of gas occupies22.42L22.42L (called the molar(called the molar
volume)volume)
Note: Avogadro’s Hypothesis - at theNote: Avogadro’s Hypothesis - at the
same temperature and pressuresame temperature and pressure
equal volumes of gas have the sameequal volumes of gas have the same
E lExamples
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ExamplesExamples
What is the volume of 4.59 moleWhat is the volume of 4.59 moleof COof CO22 gas at STP?gas at STP?
How many moles is 5.67 L of OHow many moles is 5.67 L of O22
at STP?at STP?
What is the volume of 8.8g of What is the volume of 8.8g of
CHCH44 gas at STP?gas at STP?
Densit of a gasDensity of a gas
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Density of a gasDensity of a gas
D = m /VD = m /V
for a gas the units will be g / Lfor a gas the units will be g / L
We can determine the density of We can determine the density of
any gas at STP if we know itsany gas at STP if we know itsformula.formula.
To find the density we need the To find the density we need the
mass and the volume.mass and the volume. If you assume you have 1 moleIf you assume you have 1 mole
then the mass is the molar mass.then the mass is the molar mass.
ExamplesExamples
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ExamplesExamples
Find the density of COFind the density of CO22 at STP.at STP.Find the density of CHFind the density of CH
44 atat
STP.STP.
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What I expected you to haveWhat I expected you to have
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What I expected you to haveWhat I expected you to havelearned:learned:
change moles to gramschange moles to grams
moles to atomsmoles to atoms
moles to formula unitsmoles to formula units
moles to moleculesmoles to molecules
moles to litersmoles to liters
molecules to atomsmolecules to atomsformula units to atomsformula units to atoms
formula units to ionsformula units to ions
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Moles
Mass
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Moles
MassPT
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Moles
MassVolume PT
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Moles
MassVolume PT22.4 L
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Moles
MassVolume
RepresentativeParticles
PT22.4 L
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Moles
MassVolume
RepresentativeParticles
6.02 x 1023
PT
Atoms
22.4 L
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Moles
MassVolume
RepresentativeParticles
6.02 x 1023
PT
Atoms Ions
22.4 L
Percent CompositionPercent Composition
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Percent CompositionPercent Composition
Like all percentsLike all percents Part x 100 %Part x 100 %
wholewhole
Find the mass of eachFind the mass of each
component,component,
divide by the total mass.divide by the total mass.
ExampleExample
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ExampleExample
Calculate the percentCalculate the percentcomposition of a compoundcomposition of a compound
that is 29.0 g of Ag withthat is 29.0 g of Ag with
4.30 g of S.4.30 g of S.87n1387n13
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ExamplesExamples
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ExamplesExamples
Calculate the percentCalculate the percentcomposittion of Ccomposittion of C22HH44??86n1486n14
Aluminum carbonate.Aluminum carbonate.
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Empirical FormulaEmpirical Formula
From percentage to formulaFrom percentage to formula
The Empirical FormulaThe Empirical Formula
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The Empirical FormulaThe Empirical Formula
The lowest whole number ratio of The lowest whole number ratio of
elements in a compound.elements in a compound. The molecular formula the actual The molecular formula the actual
ratio of elements in a compound.ratio of elements in a compound. The two can be the same. The two can be the same.
CHCH22 empirical formulaempirical formula
CC22HH44 molecular formulamolecular formula
CC33HH66 molecular formulamolecular formula
H O both
Calculating EmpiricalCalculating Empirical
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Calculating EmpiricalCalculating Empirical
Just find the lowest whole number Just find the lowest whole number
ratioratio
CC66HH1212OO66 ---> ?---> ?
CHCH44NNIt is not just the ratio of atoms, it isIt is not just the ratio of atoms, it is
also the ratio of moles of atoms.also the ratio of moles of atoms.
In 1 mole of COIn 1 mole of CO22 there is 1 mole of there is 1 mole of
carbon and 2 moles of oxygen.carbon and 2 moles of oxygen.
In one molecule of COIn one molecule of CO22 there is 1there is 1
Calculating EmpiricalCalculating Empirical
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Calculating EmpiricalCalculating Empirical
Means we can get ratio fromMeans we can get ratio frompercent composition.percent composition.
Assume you have a 100 g.Assume you have a 100 g.
The percentages become The percentages become
grams.grams.
Can turn grams to moles.Can turn grams to moles.
Find lowest whole numberFind lowest whole number
How do we do it?How do we do it?
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How do we do it?How do we do it?
Calculate the empirical formula of aCalculate the empirical formula of acompound composed of 38.67 % C,compound composed of 38.67 % C,
16.22 % H, and 45.11 %N.16.22 % H, and 45.11 %N.
Assume 100 g soAssume 100 g so38.67 g C x 1mol C = 3.22038.67 g C x 1mol C = 3.220
mole Cmole C 12.01 g C12.01 g C
16.22 g H x 1mol H = 16.0916.22 g H x 1mol H = 16.09mole Hmole H 1.01 g H1.01 g H
45.11 g N x 1mol N = 3.219 mole45.11 g N x 1mol N = 3.219 mole
NN 14.01 g N14.01 g N
ExampleExample
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ExampleExample
The ratio is 3.220 mol C = 1 mol C The ratio is 3.220 mol C = 1 mol C3.219 mol N 13.219 mol N 1
mol Nmol N
The ratio is 16.09 mol H = 5 mol H The ratio is 16.09 mol H = 5 mol H
3.219 mol N 13.219 mol N 1
mol Nmol N
1 C : 1 N 5 H : 1 N1 C : 1 N 5 H : 1 N
CC11HH55NN11
ExampleExample
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ExampleExample
i
A compound is 43.64 % PA compound is 43.64 % Pand 56.36 % O. What is theand 56.36 % O. What is the
empirical formula?empirical formula?
iCaffeine is 49.48% C, 5.15%Caffeine is 49.48% C, 5.15%
H, 28.87% N and 16.49% O.H, 28.87% N and 16.49% O.
What is its empirical formula?What is its empirical formula?
Empirical to molecularEmpirical to molecular
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Empirical to molecularEmpirical to molecular
Since the empirical formula is theSince the empirical formula is the
lowest ratio, the actual moleculelowest ratio, the actual molecule
would weigh more.would weigh more.
By a whole number multiple.By a whole number multiple.Divide the actual molar mass byDivide the actual molar mass by
the the mass of one mole of thethe the mass of one mole of the
empirical formula.empirical formula.
Caffeine has a molar mass of 194Caffeine has a molar mass of 194
g what is its molecular mass?g what is its molecular mass?
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ExampleExample
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ExampleExample
What is its molecularWhat is its molecularformula?formula?
E.F. = CHE.F. = CH22ClCl
E.W. = 49.5E.W. = 49.5∴∴M.F. =M.F. = C2H4Cl2
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The effect of adding gas.The effect of adding gas.
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The effect of adding gas.The effect of adding gas.
When we blow up a balloonWhen we blow up a balloonwe are adding gaswe are adding gas
molecules.molecules.
((we can see an increase inwe can see an increase insize of the balloonsize of the balloon))Doubling the the number of
gas particles doubles thepressure.
(given the same volume at
Pressure and the number of Pressure and the number of
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molecules are directly relatedmolecules are directly related
½More molecules meansMore molecules meansmore collisions.more collisions.
½
Fewer molecules meansFewer molecules meansfewer collisions.fewer collisions.
½Gases naturally move fromGases naturally move from
areas of high pressure to lowareas of high pressure to lowpressure because there ispressure because there isempty space to move in.empty space to move in.
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1 atm
If you double the number of If you double the number of moleculesmolecules
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You double the pressure. You double the pressure.2 atm
If you double the number of molecules
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4 atm Assuming theAssuming thepressure outsidepressure outside
is 1 atm.is 1 atm.
As you removeAs you removemolecules from amolecules from a
containercontainer
Patm = 1 atm
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As you removeAs you remove
molecules from amolecules from a
container thecontainer the
pressurepressuredecreasesdecreases
2 atm2 atm
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Molecules naturally move fromMolecules naturally move from
high to low pressurehigh to low pressure
1 atmAs you removemolecules from acontainer the
pressuredecreases until thepressure inside
equals thepressure outside
containercontainer
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containercontainer
½In a smaller container,In a smaller container,molecules have less room tomolecules have less room to
move.move.
½ They hit the sides of the They hit the sides of the
container more often.container more often.
½As volume decreasesAs volume decreases
pressure increases.pressure increases.
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1 atm
4 Liters
As theAs the
pressure onpressure ona gasa gas
increasesincreases
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TemperatureTemperature
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pp
½Raising the temperature of aRaising the temperature of agas increases the pressure if gas increases the pressure if
the volume is held constant.the volume is held constant.
½ The molecules hit the walls The molecules hit the walls
harder.harder.
½ The only way to increase the The only way to increase the
temperature at constanttemperature at constant
ressure is to increase theressure is to increase the
300 K
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1L ; 1 atm
If you start with 1 liter of gas at 1atm pressure and 300 K and heat itto 600 K one of 2 things happens
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For this course we
are going toassume the gases
behave ideally.
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vacuum
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hole
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Effusion
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The term used to
describe the passageof gas through a tiny
orifice into anevacuated chamber
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Ideal Gases don’t existIdeal Gases don’t exist
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½Gas molecules do takeGas molecules do take
up spaceup space
½ There are attractive There are attractive
forces between them,forces between them,
otherwise there would beotherwise there would beno liquidsno liquids
Ideal Gases
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½ There are no gases forwhich this is true. Does notreally exist
½Makes the math easier andis a close approximation.
½Particles have no volume.
½No attractive forces.
Ideal GasesIdeal Gases
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Real gases
behave likeideal gases athigh temperatureand low
GasesGases
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½When the moleculesWhen the molecules
do not take up as bigdo not take up as biga percentage of thea percentage of the
spacespace
½We can ignore theirWe can ignore their
volume.volume.
½When the moleculesare far apart
½ This is at low
pressure
gasesgases
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½When molecules are movingWhen molecules are moving
fast.fast.
½Collisions are harder and faster.Collisions are harder and faster.
½Gas molecules are not next toGas molecules are not next to
each other very long.each other very long.
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PressuresPressures
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½ The total pressure inside a The total pressure inside a
container is equal to thecontainer is equal to the
partial pressure due to eachpartial pressure due to each
gas.gas.
½ The partial pressure of a The partial pressure of a
gas is the contribution bygas is the contribution by
that gas.that gas.
ExamplesExamples
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What is the total pressure in aWhat is the total pressure in a
balloon filled with air if theballoon filled with air if the
pressure of the oxygen is 170 mmpressure of the oxygen is 170 mm
Hg and the pressure of nitrogen isHg and the pressure of nitrogen is620 mm Hg?620 mm Hg?
In a second balloon the totalIn a second balloon the totalpressure is 790 mm Hg. What ispressure is 790 mm Hg. What is
the pressure of oxygen if thethe pressure of oxygen if the
Boyle’s LawBoyle’s Law
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½At a constant temperature,At a constant temperature,
pressure and volume arepressure and volume are
inversely related.inversely related.
½As one goes up the otherAs one goes up the other
goes downgoes down
½P x V =P x V = kk ((k is some constantk is some constant))
½Easier to use PEasier to use P11 x Vx V11 = P= P22 xx
Boyle’s LawBoyle’s Law
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ExamplesExamples
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A balloon is filled with 25 L of A balloon is filled with 25 L of air at 1.0 atm pressure. If theair at 1.0 atm pressure. If the
pressure is change to 1.5 atmpressure is change to 1.5 atm
what is the new volume?what is the new volume?16.6716.67
A balloon is filled with 73 L of A balloon is filled with 73 L of
air at 1.3 atm pressure. Whatair at 1.3 atm pressure. Whatpressure is needed to changepressure is needed to change
to volume to 43 L?to volume to 43 L?2.22.2
Charles’ LawCharles’ Law
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½ The volume of a gas is directly The volume of a gas is directly
proportional to theproportional to the KelvinKelvin
temperature if the pressure istemperature if the pressure is
held constant.held constant.
½V =V = kk xx T T ((k is some constantk is some constant))
½V/T=V/T= kk
½Easier to useEasier to use VV11/T/T11= V= V22/T/T22
Charles’ LawCharles’ Law
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T
ExamplesExamples
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What is the temperature of What is the temperature of a gas that is expanded froma gas that is expanded from
2.5 L at 25ºC to 4.1 L at2.5 L at 25ºC to 4.1 L at
constant pressure.constant pressure.216216
What is the final volume of What is the final volume of
a gas that starts at 8.3 La gas that starts at 8.3 L
and 17ºC and is heated toand 17ºC and is heated to
Gay Lussac’s LawGay Lussac’s Law
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½ The temperature and the The temperature and thepressure of a gas arepressure of a gas are
directly related at constantdirectly related at constantvolume.volume.
½P =P = kk xx T T ((k is somek is some
constantconstant))
½ ==
Gay Lussac’s LawGay Lussac’s Law
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T
ExamplesExamples
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What is the pressure inside aWhat is the pressure inside a
0.250 L can of deodorant that0.250 L can of deodorant that
starts at 25ºC and 1.2 atm if starts at 25ºC and 1.2 atm if
the temperature is raised tothe temperature is raised to
100ºC?100ºC?1.51.5
At what temperature will theAt what temperature will the
can above have a pressure of can above have a pressure of
Combined Gas LawCombined Gas Law
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½Deals with the situationDeals with the situationwhere only the number of where only the number of
molecules stays constant.molecules stays constant.
½(P(P11 x Vx V11)/T)/T11 = (P= (P22 x Vx V22)/T)/T22
½
PP11VV11 T T22 = P= P22VV22 T T11
ExamplesExamples
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A 15 L cylinder of gas at 4.8A 15 L cylinder of gas at 4.8
atm pressure and 25ºC isatm pressure and 25ºC is
heated to 75ºC andheated to 75ºC and
compressed to 17 atm. Whatcompressed to 17 atm. Whatis the new volume?is the new volume?4.954.95
If 6.2 L of gas at 723 mm HgIf 6.2 L of gas at 723 mm Hgat 21ºC is compressed to 2.2at 21ºC is compressed to 2.2
L at 4117 mm Hg, what is theL at 4117 mm Hg, what is the
The combined gas law contains The combined gas law contains
ll th th l !all the other gas laws!
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all the other gas laws!all the other gas laws!
If the temperature remainsIf the temperature remainsconstant.constant.
P1 V1
T1
x = P2 V2
T2
x
Boyle’s Law
The combined gas law contains The combined gas law contains
all the other gas la s!all the other gas laws!
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all the other gas laws!all the other gas laws!
If the pressure remainsIf the pressure remainsconstant.constant.
P1 V1
T1
x = P2 V2
T2
x
Charles’ Law
The combined gas law containsll th th l !
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P1 V1
T1
x = P2 V2
T2
x
Gay-Lussac Law
all the other gas laws!
If the volume remains constant.
Volume and molesVolume and moles
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½Avogadro’s Hypothesis - atAvogadro’s Hypothesis - at
the same temperature andthe same temperature and
pressure equal volumes of pressure equal volumes of
gas have the same numbergas have the same numberof particles.of particles.
½V is proportional to numberV is proportional to number
of molecules at constant Tof molecules at constant Tand P.and P.
½V is ro ortional to molesV is proportional to moles
The Ideal Gas LawThe Ideal Gas Law
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½PP xx V = nV = n xx RR xx T T
½ This time R does not depend This time R does not depend
on anything, it is reallyon anything, it is really
constantconstant
½
R = 0.0821 (L atm)/(mol K)R = 0.0821 (L atm)/(mol K)½R = 8.3145 J/(mol K)R = 8.3145 J/(mol K)
½
The Ideal Gas LawThe Ideal Gas Law
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½We now have a new way toWe now have a new way tocount the number of moles of count the number of moles of
a gas. By measuringa gas. By measuring TT,, PP, and, and
VV. We aren’t. We aren’t restrictedrestricted totoSTPSTP..
½n = PV/RTn = PV/RT
ExamplesExamples
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How many moles of air areHow many moles of air arethere in a 2.0 L bottle at 19 ºCthere in a 2.0 L bottle at 19 ºC
and 747 mm Hg?and 747 mm Hg?0.080.08
What is the pressure exertedWhat is the pressure exerted
by 1.8 g of Hby 1.8 g of H22 gas exert in a 4.3gas exert in a 4.3L balloon at 27 ºC?L balloon at 27 ºC?3918mm5.2atm3918mm5.2atm
Points to Ponder?
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½ The molar mass of a gas can be The molar mass of a gas can be
determined by the density of determined by the density of
the gas.the gas.
½Density = mass/Volume = m/VDensity = mass/Volume = m/V
½Molar mass = mass/moles =Molar mass = mass/moles =
m/nm/n
Points to Ponder?
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½Molar Mass =Molar Mass = mm(PV/RT)(PV/RT)
½Molar mass =Molar mass = m RTm RTV PV P
½
Molar mass =Molar mass = D RTD RTPP
At STPAt STP
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½
At STP determining the amountAt STP determining the amountof gas required or produced isof gas required or produced is
easy.easy.
½For example, how many liters of For example, how many liters of
OO22 at STP areat STP are required torequired to
produce 20.3 g of Hproduce 20.3 g of H22O?O?14.22L14.22L
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Kinetic Molecular Theory of Gases
Th l f th i di id lTh l f th i di id l
PostulatesPostulates
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½ The volume of the individual gas The volume of the individual gas
particles can beparticles can be assumed to beassumed to benegligiblenegligible½ The particles are in The particles are in constantconstant
motionmotion½ The particles are The particles are assumed toassumed to
exertexert nono forcesforces on each otheron each other
½ The The average kinetic energyaverage kinetic energy of of the gas isthe gas is assumed to be directlyassumed to be directlyproportional to the temperatureproportional to the temperature
of the gasof the gas
From the theory
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PV n ∝ T
23 (KE)av
g
From the theory
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PV
n∝
T
From the experiment
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PV
n = RT
combining
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(KE)av
g
RT32
ExampleExample
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It was found out that 1.0 LIt was found out that 1.0 Lof carbon dioxide (COof carbon dioxide (CO22) took) took
3 minutes to effuse through3 minutes to effuse through
a porous filter. How longa porous filter. How long
will it take 1.0 L of methanewill it take 1.0 L of methane
(CH(CH44) to effuse under the) to effuse under thesame conditions?same conditions?
Can we predict the distanceCan we predict the distancetraveled by NHtraveled by NH and HCl?and HCl?
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traveled by NHtraveled by NH33 and HCl?and HCl?
Graham Law
A
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1
2
M
M
2gasof effusionof rate
1gasof effusionof rate=
At constant temperature,the relative rates of effusion of two gases are
given by the inverse ratioof the square roots of
their masses
1
2
M
M2gasof effusionof rate1gasof effusionof rate =
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= 0.55 L /min
2
4
CO
CH
4
2
MM
CHrateCOrate =
2
4
CO
CH
4 MM
MM
CHrate
L/min.0.33 =
44
16
CHrate
L/min.0.33
4
=4416
CHrate
L/min.0.33
4
=
= 1.8 min
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