chem 101 ch 3,4,5
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Chapter 3. Stoichiometry
3.1. Introduction
3. 2. Atomic Masses
3.3. The Mole
3.4. The Molar Mass
3.5. Percent Composition of Compounds
3.. !eterminin" the #ormula of a compound
3.$. Chemical %&uations
3.'. (alancin" Chemical %&uations
3.). Stoichiometric Calculations
3.1*. Calculations in+ol+in" a limitin" ,eactant and a percent yield
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3. 1. Introduction
Chemical reactions have a profound effect on our live.
- Foods transformed to energy.
- cancer is induced in humans by substances in our environment.
Reactions involved the quantities of materials consumed and produced. Thisarea of study is called chemical stoichiometry.
To understand chemical stoichiometry you must first understand the concept ofrelative masses.
3.2. Atomic Masses
The first quantitative information about atomic masses came from thework of alton! "ay-#ussac! #avoisier! $vogadro and %er&elius.
' mass of 1()1amu*
The modern system of atomic masses is based on carbon twelve 1+C as a
standard in this system. 1+C is assigned a mass of e,actly 1+ atomic massunits 'amu*. The masses of other atoms are given relative to this standard.
Carbon 'C* /./0 1+C 1.110 12C 34.410 15C6
Carbon atomic mass ) 1+.41 amu 'also called average atomic mass*
7nit ) atomic mass unit. amu or dalton.
$bsolute si&es of atoms8
9ass of ( atom) 1.::4;5 , 14-+5g.
article Charge 9ass 'g* 9ass 'amu*
+
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>roton ?1 1.:@+@,14-+5 1.44@2
Aeutron Aeutral 1.:@;4,14-+5 1.44/@
Blectron -1 .14,14-+/ ;.5/: , 14-5
#BA"T( = $A"TRD9 'E* ) 14-14m
Typical atomic dimensions are 1 to ; ,14-14m which corresponds to 1 to ; E.
3.2.1. A+era"e Atomic Mass
Pro-lem
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Aaturally occurring chlorine has two isotopes! 2;1@Cl! 2@1@Cl. The 2;-Cl isotopehas a relative atomic mass of 25.://amu and an abundance of @;.@@0 andthe 2@-Cl isotope has a relative atomic mass of 2:.:;amu and anabundance of +5.+20. Calculate the average atomic mass of Cl.
Solution
$verage $tomic 9ass of Cl ) '4.@;@@,25.:;* ?
'.+5+2,2:.:;*
) 2;.5;+@ umaatom
3.2.2. Molecular Mass
The molecular mass is the summery of the atomic masses of the atoms thatmake up the molecule.
B,ample. The chemical formula for water is CD+
9ass of C ) 1+.41 amu
9ass of D ) 1;. amu
Gts relative molecular mass ) '1+.41* ? +'1;.*
) 52. amu
3.2.3. ,elati+e Atomic Mass
$ relative scale has been developed to compare the relative masses of
atoms. The $TD9GC 9$ of an atom is its relative mass on this scale.
Carbon- 1+ '1+C* has been set as the standard and assigned a
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The relative molecular mass is the sum of the relative atomic masses ofthe atoms that make up the molecule.
B,ample! the chemical formula for water is (+D
Gts relative molecular mass
) + '1.44@5* ? 1;.5 ) 1/.41;2
3.3. The Mole
$ mole has been defined as a unit containing :.4++12@ , 14 +2 ! $vogadroHsnumber! atoms or molecules. Dne mole of any atom or molecule contains thesame number of atoms or molecules.
$vogadroIs Aumber
$vogadroIs number8 the number of atoms in e,actly 1+ g of 1+C.
Ao) :.4++12@ , 14+2
1mole 1+C weigts 1+g and contains A4atoms.
odium 'Aa* has a relative atomic mass of ++./@@
Gf Aoatoms of 1+C have a mass of 1+g then! the mass of Ao atoms of sodiummust be '++./@@*1+ ,1+g ) ++./@@ g
1mole of sodium weigts ++./@@g
The mass! in grams! of Aoatoms of $AJ element is numerically equal to the
relative atomic mass of that element.
ame applies to molecules.
ince the relative molecular mass of water is 1/.41;+! the mass of A owatermolecules is 1/.41;+g.
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%ercise 1. Calculating number of atom
$ silicon chip used in an integrated circuit of a microcomposer has a mass of;.:/mg how many silicon 'i* atoms are present in the chipK
9olar mass of silicon ) 9i) +/.4g
olution
The strategy for doing this problem is to convert from milligrams of silicon tograms of silicon then to moles of silicon and finally to atom of silicon.
%ercise 2.
How many moles and atoms of Fe are there in 8.232 g of Fe? (M Fe=
55.85g.mol-1)
olution
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%ercise 3.
(ow many grams of water are there in 4.+444 moles of waterK '9(+D)1/.41;g.mol-1*
olution
4.+444 mol (+D , 1/.41; g.mol-1(+D ) 2.:42 g (+D
3.4. The Molar Mass
The 9olar 9ass is the mass! in grams! of one mole of atoms or molecules isnumerically equal to relative atomic or molecular masses.
(ence 1 mole of Aa weighs ++.// g! 1 mole of (+D weighs 1/.41;2 g org.mol-1.
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Mass percent of an element/
For iron in iron 'GGG* o,ide! 'Fe+D2*
%mpirical #ormulas
The simplest! whole-number ratio of atoms in a molecule is called the'empirical formula*.
Can be determined from percent composition or combiningmasses.
The molecular formula is a multiple of the empirical formula.
molecular formula ) 'empirical formula*n n ) integer6
molecular formula ) C:(: ) 'C(*:
empirical formula ) C(
B,amples
(ydrogen >ero,ide
9olecular formula ) (+D+
Bmpirical formula ) (D
%en&ene
massmassof element incompound
massofcompound% = 100
mass Fe% .
..= =
11169
15969100% 6994
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9olecular formula ) C:(:
Bmpirical formula ) C(
"lucose
9olecular formula ) C:(1+D:
Bmpirical formula ) C(+D
%mpirical #ormula !etermination
ince mass percentage gives thenumber of grams of a particular element per 144g of compound! basethe calculation on 144g of compound! each percent will then representthe mass in grams of that element.
etermine the number of mole of each element present in 144g ofcompound using the atomic masses of the elements present.
ivide each value of the number of moles by the smallest of the values
Gf the numbers obtained in the previous step are not whole numbers!multiply each number by an integer so that the results are all wholenumbers
%ample/
Find the empirical formula of aspirin with the given mass percent composition.
Lrite down the given quantity and its units.
"iven8 C ) :4.440
( ) 5.5/0
D ) 2;.;20
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Therefore! in 144 g of aspirin there are :4.44 g C! 5.5/ g (! and 2;.;2 gD.
Gnformation8
"iven8 :4.44 g C! 5.5/ g (! 2;.;2 g D
Lrite down the quantity to find andor its units.
Find8 empirical formula! C(yD!
Collect needed conversion factors8
1 mole C ) 1+.41 g C
1 mole ( ) 1.41 g (1 mole D ) 1:.44 g D
Lrite a solution map8
$pply the solution map8
Calculate the moles of each element.
$pply the solution map8
11
Cmol.Cg12.01
Cmol1Cg. 99640060 =
Hmol.Hg1.01Hmol1Hg.48 4444 =
Omol.Og16.00
Omol1Og5.53 22123 =
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Lrite a pseudoformula.
$pply the solution map8
Find the mole ratio by dividing by the smallest number of moles.
122.25
2.221
2.221
2.221
4.44
2.221
4.996
OHC
OHC
Molecular #ormulas
The molecular formula is a multiple of the empirical formula.
To determine the molecular formula! you need to know the empiricalformula and the molar mass of the compound.
3.. Chemical %&uations
1+
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3..1. Chemical reaction
Chemical reaction is a chemical change involves a reorgani&ation of the
atoms in one or more substances.$ representation of a chemical reaction8
C+(;D( 'l* ? 2D+'g* +CD+'g* ? 2(+D 'l*
reactants products
A(2'g* ? D+'g* M AD'g* ? (+D'g*
Aotes that the atoms have been reorgani&ed %onds have been broken! and
new ones have been formed!
Gn a chemical reaction! atoms are neither created nor destroyed! all atomspresent in reactants are present in the products.
3.$. (alancin" Chemical %&uations
C+(;D( ? 2D+ +CD+ ? 2(+D
1 mole of ethanol reacts with 2 moles of o,ygen to produce + moles ofcarbon dio,ide and 2 moles of water
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The identities of the reactants and products must not be changed. Theformulas of the compounds must not be changed in balancing a chemicalequqtion.
%amples
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1. NNAaCl ? NN%eF+--O NNAaF ? NN%eCl+
+. NNFeCl2? NN%e2'>D5*+--O NN%eCl+? NNFe>D5
2. NN$gAD2? NN#iD( --O NN$gD( ? NN#iAD2
5. NNC(5? NND+--O NNCD+? NN(+D
;. NN9g ? NN9n+D2--O NN9gD ? NN9n
Solutions for the eamples
1. + AaCl ? 1 %eF+--O + AaF ? 1 %eCl+
+. + FeCl2? 1 %e2'>D5*+--O 2 %eCl+? + Fe>D5
2. 1 $gAD2? 1 #iD( --O 1 $gD( ? 1 #iAD2
5. 1 C(5? + D+--O 1 CD+? + (+D
;. 2 9g ? 1 9n+D2--O 2 9gD ? + 9n
3. '. Stoichiometric Calculations
1. %alance the equqtion for the reaction.
+. Convert the known mass of the reactant or product to moles of thatsubstance.
2. 7se the balanced equation to set up the appropriate molar ratios.
5. 7se the appropriate molar ratios to calculate the number of mole ofthe desired reactant or product.
;. Convert from moles back to grams if required by the problem.
Calculatin" Mass of ,eactants and Products
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3.). Calculations In+ol+in" a 0imitin" ,eactant
The limiting reactant is the reactant that is consumed first! limiting theamounts of products formed.
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Chapter 4 Types of Chemical ,eactions and
Solution Chemistry
4.1. ater the common sol+ent.
4.2. The ature of A&ueous Solutions/ Stron" and ea electrolytes.
4.3. The Composition of Solutions.
4.4. Types of Chemical ,eactions.
4.5. Precipitation ,eactions.
4.. !escri-in" ,eactions in Solutions
4.$. Stoichiometry of Precipitation ,eactions
4.'. Acid(ase Titrations.
4.). 6idation,eduction ,eactions.
4.1*. (alancin" 6idation,eduction ,eactions.
4.1. ater the common sol+ent
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Later is one of the most important substances on earth
Dne of the most valuable properties of water is its ability to dissolvemany different substances.
Later is a dissolving medium! or a solvent.
issolved substance is a solute such as salt 'AaCl! 9gF+! PAD2! Q* in
weak amount
Lhen ionic substances dissolve in water they break up into individualcations and aninons
Later is bentS or
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>olar water molecules interact with positive and negative ions of a saltassisting in the dissolving process.
Bthanol is very soluble in water because of the presence of similar polar D-(bond in the tow compounds.
4.2. The ature of A&ueous Solutions/ Stron" and ea electrolytes.
Dne useful property for characteri&ing a solution is its electricalconductivity.
ame aqueous solutions conduct current +ery efficiently theycontain stron" electrolytes.
Dther solutions conduct only a small current7they contain8eaelectrolytes.
ame solution permit no current flo8 they are non electrolytes.
++
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hen aCl dissol+es in 8ater the Cl ions and Sodium ions a9
spread randomly. The solution conducts electricity/ The solutioncontains electrolytes
'a*trong electrolytes8 ubstances completely ioni&ed in water
'b*Leak electrolytes 8 ubstances partially ioni&ed in water or contain fewions
'c*Aon electrolytes 8substances contain no ions
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Stron" electrolytes
Salts / Totally ioni&ed in water to give cations and anoins
Stron" acids8 Totally ioni&ed in water to give (?
:Cl ::Cl :99;a&< 9 Cl;a&< 9 Cl;a&
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4.3. The composition of Solutions
Chemical reaction often take place when two solutions are mi,ed.
$ solution is generally composed by8
A Solute
dissolves in water 'or other solventS*
changes phase 'if different from the solvent*
is present in lesser amount 'if the same phase as the solvent*
Sol+ent
retains its phase 'if different from the solute*
is present in greater amount 'if the same phase as the solute*
The concentration of a solution can be described in many differentways. Le limit on the morality
Molarity
9olarity 'M* 8 moles of solute per volume of solution in liters
7nits8 mol.#-1
Common Terms of Solution Concentration
tandard olution8 a solution of e,act known concentration! prepared bydissolving a definite weight of solute in a volumetric flask
tock 8 routinely used solutions prepared in concentrated form.
Concentrated 8 relati"elylarge ratio of solute to solvent. ';.4 MAaCl*
ilute8 relati"elysmall ratio of solute to solvent. '4.41 MAaCl*
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teps involved in the preparation of a standard aqueous solution
a* >ut a weighted amount of substances 'solute*
b* issolve the solid in water by gently swirling the flask
c* $dd more water until the level of the solution ust reaches the marketched on the neck of the flask.
!ilution /
$ddition of water 'solvent* to a concentrated solution to get a lessconcentrated one
#aw of ilution 8
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4.4. Types of Chemical ,eactions
>recipitation reactions
$gAD2'a#* ? AaCl'a#* A"Cl's* ? AaAD2'a#*
$cid-base reactions
AaD('a#* ? (Cl'a#* AaCl'a#* ? (+D'l*
D,idation-reduction reactions
Fe+D2's* ? $l's* Fe'l* ? $l+D2's*
4.5. Precipitation ,eactions
Lhen two solutions are mi,ed! an insolu-lesubstance sometimesforms. uch a reaction is called a precipitation reaction! and the solidthat forms is called a precipitate.
%ample 1/
+/
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Lhen >otassium Chromate P+CrD5 is added to a solution of %ariumAitrate %a'AD2*+! a yellow precipitate of %arium Chromate %aCrD5isformed.
P+CrD5'aq*? %a'AD2*+'aq* PAD2'aq*? (aCr64;sotassiumchloride PCl! a white precipitate of ilver chloride is formed $gCl.
Simple ,ules for Solu-ility
+
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1. 9ost nitrate 'AD-2* salts are soluble.
+. 9ost alkali 'group 1$* salts and A(5?are soluble.
2. 9ost Cl-! %r-! and G- salts are soluble.
'ADT $g?! >b+?! (g++?*
5. 9ost sulfate salts are soluble.
'ADT %aD5! >bD5! (gD5! CaD5*
;. 9ost D(-salts are only slightly soluble 'AaD(! PD( are soluble!%a'D(*+! Ca'D(*+are marginally soluble.
:. 9ost
+-
! CD2+-
! CrD5+-
! >D52-
salts are only slightly soluble.4.. !escri-in" ,eactions in Solutions
1. 9olecular equation gives the overall reaction stoichiometry but notnecessarily the actual forms of the reactants and products in solution.
$gAD2'a#* ? AaCl'a#* $gCl's* ? AaAD2'a#*
+. Complete ionic equation 'all reactants and products are strong
electrolytes*$g?'a#* ? AD2-'a#* ? Aa?'a#* ? Cl-'a#* $gCl's* ? Aa?'a#* ? AD2-'a#*
2. Aet ionic equation 'show only ions that actually react*
$g?'a#* ? Cl-'a#* $gCl's*
Aa?and AD2-are spectator ions.
4.$. Stoichiometry of Precipitation ,eactions
!eterminin" of the mass of product formed
Calculate the mass of solid AaCl that must be added to 1.;4# of a4.1449 $gAD2solution to precipitate all the $g?ions in the form of$gCl.
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Solution
Lhen added to $gAD2 solution 'which contains $g? and AD2- ions*!the solid AaCl dissolves to yield Aa? and Cl- ions. Thus the mi,ed
solution contains the ions$g? AD2- Aa? Cl-
Aotes that AaAD2 is soluble and $gCl is insoluble. Therefore $gClforms according to the following net ionic equation.
$g? ? Cl- $gCl's*
Gn this case we must add enough Cl- ions to react with $g? ionspresent. Thus we must calculate the moles of $g?present in 1.; # of4.1449 $gAD2solution.
1.;4# , 4.144 mol $g?# ) 4.41; mol $g?
%ecause $g?and Cl-react in a 181 ratio! 4.1;4 mol Cl -ions AaCl arerequired. Le calculate the mass of AaCl requied as follows.
4.'. Acid(ase Titrations
%rVnsted '1/@-15@*
Acid/ a chemical entity that gives proton (?
(ase/ a chemical entity that accept proton (?
(Cl'aq*? AaD('aq* (+D'aq*? AaCl'aq*
'(?'aq*? Cl-'aq*?* ? 'Aa?'aq*? D(-'aq** (+D'aq*? Cl-'aq*? Aa?'aq*
(?'aq*? D(-'aq* (+D'l*
Performin" Calculations for Acid(ase ,eactions
1.#ist initial species in the combined solution before any reaction occur.
+.Lrite balanced net ionic equation for this reaction.
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2.Calculate moles of reactants. 7se the volume of the original solutionsand their molarities.
5.etermine the limiting reactant.
;.Calculate moles of required reactant or product.
:.Convert to grams or volume! as required.
Lhen a ust enough base is added to react e,actly with the acid in asolution we say the acid has been neutrali&ed.
Acid(ase Titrations
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The indicator is a weak organic acid or organic base! its color dependson acidic or basic nature of the analyte during the titration process
>henolphthaline 8 is colorless in acidic medium and pink in base
medium while 9ethyl Drange is orange in a base medium and red inacidic medium.
4.). 6idation,eduction ,eactions
2a;s< 9 Cl2;"< 2aCl ;slanckIs constant! :.:+: , 14-25
X,s-1) kg m+s-1 m) mass! in kg ) frequency! in s-1
5. 3. Atomic Spectrum of :ydro"en
Continuous spectrum8 Contains all the wavelengths of light.
#ine 'discrete* spectrum8 Contains only some of the wavelengths oflight.
The hydrogen spectrum indicates that only certain energy are allowedfor the electron in the hydrogen atom. The energy of the electron in thehydrogen atom is quanti&ed. Changes in energy between discreteenergy levels in hydrogen will produce only certain wavelengths ofemitted light.
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For n) 1! the electron has more negative energy than it does for n ): meansthat the electron is more ti"htly -ound in the smallest allowed orbit.
The change in energy *% when the ele$tron falls from n=+ to n=1
is *% ) %final state - %initial state
) B1 - B:
0imits of the (ohr>s model
%ohrIs model appeared to be very promising.
The energy levels calculated by %ohr closely agreed with the values
obtained from the hydrogen emission spectrum.
Lhen %ohrIs model was applied to atoms other than hydrogen it
5:
=hc
E
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did not work at all.
Blectrons do not move around the nucleus in circular orbits with
quantified energy.
5.5. The ?uantum Mechanical model of the atom
The new approach for the atoms is given by the quantum mechanics
%ased on the wave properties of the electron
$t each electron is associated a function wave .
hrVdungerIs equation
) The wave function is a function of the coordinates ',! y! &* of the
electron position in 2 space
) mathematical operator
%) total energy of the atom
$ specific wave function is often called an orbital characteri&ing its
properties.
There is a fundamental limitation to ust how precisely we can know both theposition and the momentum 'mv* of a particle at a given time.
(eisenberg 7ncertainty >rinciple
Lhere , ) position m") momentum h) >lanckIs constant
The more accurately we know a particleIs position! the less accuratelywe can know its momentum.
Pro-a-ility !istri-ution
5@
H E =
x mv ( ) 4
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quare of the wave function probability of finding an electron at a givenposition Radial probability distribution is the probability distribution ineach spherical shell.
Cross ection of the (ydrogen 1s Drbital >robability istributionivided into uccessive Thin pherical hells 'b* The Radial >robabilityistribution
5. . ?uantum um-ers ;?
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=alue of
l* 1 2 3
0etter
useds p d f
Ma"netic &uantum num-er ml
has integral values between =l and l 'ml) l to -l* relates to orientation ofthe orbital in space relative to others orbitals.
5.$. 6r-ital shapes and ener"ies
The orbital means a probability distribution
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T8o ,epresentations of the :ydro"en 1s 2s and 3s 6r-itals
aThe Blectron >robability istribution
- The urface Contains 40 of the Total Blectron >robability 'thei&e of the Dribital! by efinition*
Representation of the +p orbitals
'a* The Blectron >robability istribution for a +p oribtals.
'b*The %oundary urface Representations of all Three +porbitals.
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Representation of the 2d Drbitals'a* Blectron ensity >lots of elected 2d Drbitals
'b* The %oundary urfaces of $ll of the 2d Drbitals
Representation of the 5f Drbitals in Terms of Their %oundary urfaces
5.'. %lectron spin and the Pauli Principle
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Gn a given atom! electrons must be differentiated one from other .
two electrons can have the same set of quantum numbers 'n! l! ml*.
Therefore! an orbital can hold only two electrons! and they must havedifferent quantum numbers.
The solution is given by the electron spin quantum number
%lectron Spin &uantum num-er ms
'ms) ?1+!-1+* relates to the spin states of the electrons.
A Picture of the Spinnin" %lectron
The Pauli Principle
two electrons can not have the same set of quantum numbers 'n! l! ml ms *.
:und>s ,ule
The lowest energy configuration for an atom is the one having the ma,imumnumber of unpaired electrons allowed by the >auli principle in a particular set
of degenerate orbitals.
5.). Polyelectronic atoms
;+
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The quantum mechanical model is suitable for the hydrogen atom but notvery useful for the other atoms.
The quantum mechanical model not consider the attraction and the repulsion
between electrons in polyelectronic atoms.Dne especially important difference between polyelectronic atoms and thehydrogen atom is that a given principal quantum level have the same energy'degenerate*.
For polyelectronic atoms! we find for a given principal quantum level theorbitals vary in energy as follows
Bns3 Bn,3Bnd3Bnf
Lhen electron are placed in a particular quantum level! they prefer theorbitals in the order s! p! d and then f 'lower energies*.
Drbital Bnergy #evels for the (ydrogen $tom
5. 1*. the history of the periodic ta-le
The periodic table was originally constructed to present the patternsobserved in the chemical properties of the elements
$s chemistry progressed during 1/thand 1thcenturies! it becameevident that the earth is composed of a great many elements with verydifferent properties.
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The Blectron Configurations in the Type of Drbital Dccupied #ast for theFirst 1/ Blements
%amples/ electronic confi"uration
)#/ 1s22s22p5
15P / 1s22s22p3s23p3
Blectron Configurations for >otassium Through Prypton
The Drbitals %eing Filled for Blements in arts of the >eriodic Table
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The >eriodic Table with $tomic ymbols! $tomic Aumbers! and >artial
Blectron
Configurations.
The >osition of the Blements
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$l'g* $l?'g* ? e- G1 ) ;/4PX.mol-1
$l?'g* $l+?'g* ? e- G+ ) 1/1; P.mol-1
$l+?'g* $l2?'g* ? e- G2 ) +@54 PX.mol-1
$l2?'g* $l5?'g* ? e- G5 ) 11:44 k.mol-1
#irst ioni@ation ener"y I1/
increases from left to right across a period
decreases going down a group
%lectron affinity %a
The energy change associated with the addition of an electron to a gaseousatom.
W'g* ? e- W-'g*
Atomic ,adii
decrease going from left to right across a period
increase going down a group.
Information Contained in the Periodic Ta-le
Bach group member has the same valence electron configuration'these electrons primarily determine an atomIs chemistry*.
The electron configuration of any representative element.
Certain groups have special names 'alkali metals! halogens! etc*.
9etals and nonmetals are characteri&ed by their chemical and physicalproperties.
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