12-Lecture 12 (2015-07-22) (student version)(1).ppt

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    1

    Housekeeping for Wed. 7/22/15- Endgame for rest of the B term…

      - cover h. 1! toda" and tomorro#$ finish #/ h. 1% tomorro#

      - take-home &uestions for E'am ( handed out/posted to B)ack*oard and

    +oog)e ,rive

      - due in c)ass ne't Monday (7/27)

      - ptiona)0 cumu)ative fina) Wednesda" 3)) have grades #orked up

      *" end of 4onda" night

    - HW 1( e)ectrochemistr" and so)3ns posted to B)ack*oard and +oog)e,rive

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    Weak acids and *ases have sp)it6 persona)ities

    2

    H"de and Hare60 1!550

    Warner Bros.

    http//*it.)"/18B9:!1

    http://bit.ly/1LBjP91http://bit.ly/1LBjP91

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    0

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    0 100 200 300 400

    Vol. NaOH (mL)

         p       H

    Ha)f-e&uiva)ence

     point

    ;t ha)f-e&uiva)ance point0

    p? a

    Buffering region is p? a @/- 1.

    Buffering region

    A

    ; )itt)e more a*out *uffers…

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    0

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    Vol. NaOH (mL)

         p       H

    Ha)f-e&uiva)ence

     point

    he p? a of a *uffer therefore

    represents the pH #here #e have

    equal  concentrations of acid and

    con9ugate *ase or *ase and

    con9ugate acid.

    Cor a weak acid …

     pH D p? a0

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    0

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    Vol. NaOH (mL)

         p       H

    Ha)f-e&uiva)ence

     point

    5

    ; )itt)e more a*out *uffers…

     pH p? a…

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    0

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    0 100 200 300 400

    Vol. HCl (mL)

         p       H

    F

    itration of GHA #ith H) #eak *ase/strong acid

    Ha)f-e&uiva)ence point

     GHA @ H2 >>D GH(@

     @ H-

    Buffering region

    r…

     GH(@ @ H2 >>D GHA @ HA

    @

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    0

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    0 100 200 300 400

    Vol. HCl (mL)

         p       H

    7

    itration of GHA #ith H) #eak *ase/strong acid

    Ha)f-e&uiva)ence point

     pH D p? a…

    D GHA @ HA

    @

     pH > p? a @ )og

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    hinking a*out p?a

    %

    he p?a is the pH #here #e #i)) have equal  amounts of acid and

    con9ugate *ase or *ase and con9ugate acid.

     So0 if #e kno# the pH and p?a0 #e can determine the re)ative

     proportions of acid/con9ugate *ase or *ase/con9ugate acid.

    ;s a ru)e of thum*…

     pH D p?a… the more base component dominates *ase or con9. *ase

     pH p?a… the more acid  component dominates acid or con9. acid

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    onsider the acetic acid/acetate *uffer s"stem.

    he p? a of acetic acid is (.7(.

    What is the e&ui)i*rium for acetic acid in #aterI

    What is the re)ative concentration of acetate at pH 5.7(I +reater than0

    )ess than0 or e&ua) to acetic acidI

    What is the re)ative concentration of acetic acid at pH A.7AI +reater

    than0 )ess than0 or e&ua) to acetateI

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    Ho# a*out the ammonia/ammonium *uffer s"stemI

    he p?  * of ammonia is (.7(. Hint #hat3s the p? aI

    What is the e&ui)i*rium of ammonia in #aterI

    What is the re)ative concentration of ammonia at pH 1J.2FI +reater

    than0 )ess than0 or e&ua) to ammoniumI

    What is the re)ative concentration of ammonium at pH %.2FI +reater

    than0 )ess than0 or e&ua) to ammoniaI

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    h. 1! E)ectrochemistr"

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    1A

    'idation and reduction redo' redu'

    'idation > loss of e)ectrons eduction > gain of e)ectrons

     LEO says GER

     Loss of e)ectrons > o'idation

    G ain of e)ectrons > r eduction

    Oil Rig 

    O'idation > l oss

     Reduction > g ainf "ou3re in oi) countr".

    *Oida!ion and reduc!ion always occur !oge!"er#* 

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    C)aming +ummi Bear http//*it.)"/FLAv

    2?)A s→ 2?) s @ A2 g

    12H2211 s @ A2 g→ ! s @ A2 g @ 11H2 g

    http://bit.ly/6V3Ovhttp://bit.ly/6V3Ov

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    edo' #ithout om*ustion

    2 Ga s @ )2 g → 2 Ga) s

    2 Ga → 2 Ga@ @ 2 e−

    )2 @ 2 e−

     → 2 )−

     

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    E)ectron Bookkeeping

    M for reactions that are not meta) @ nonmeta)0 or do

    not invo)ve 20 #e need a method for determiningho# the e)ectrons are transferred

    M chemists assign a num*er to each e)ement in a

    reaction ca))ed an oxidation state that a))o#s themto determine the e)ectron f)o# in the reaction

     N  even though the" )ook )ike them0 oxidation states are

    not ion charges!

    M oxidation states are imaginar" charges assigned *ased on a set of ru)es sorr"0 more ru)es

    M ion charges are rea)0 measura*)e charges

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     $n general 0 o'idation num*ers for monoatomic ions are

    the same as the charges for monoatomic ions. E'cept#here noted a*ove.

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    elements of Group 2A

    have a +2 charge

    elements of

    Group 5A have a

    3 charge

    elements of

    Group 6A have a

    2 charge

    elements of

    Group !A have a

    1 charge

     

    F.2

    he charge on an ion can *e predicted from its position in the periodic

    ta*)e.

    elements of

    Group 1A have a

    +1 charge

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    :ractice N ;ssign o'idation num*ers to each

    e)ement in the fo))o#ing compounds

    M 2

    M H2O(

    M ? A;s(

    M 4n(-

    M 2(2-

    M  Ga22

    M  GH(@

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    'idation and eduction ;nother ,efinition

    - o'idation occurs #hen an atom3s o'idation state increases during a reaction- reduction occurs #hen an atom3s o'idation state decreases during a reaction

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    'idation and eduction ;nother ,efinition

    H(  @ 2 2 Q 2 @ 2 H2-( @1 J  @( N2 @1 -2

    Based on the changes in o'idation num*ers0 #hich e)ement

    undergoes o'idationI eductionI

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    'idationNeductionM o'idation and reduction must occur simultaneously 

     N  if an atom )oses e)ectrons another atom must take them

    M the reactant that reduces an e)ement in another reactant is ca))ed

    the reducing agent

     N  the reducing agent contains the e)ement that is o'idiSed

    M the reactant that o'idiSes an e)ement in another reactant is ca))edthe oxidizing agent

     N  the o'idiSing agent contains the e)ement that is reduced

    2 Ga s @ )2 g  Q 2 Ga@) N  s

     Ga is o'idiSed0 ) is reduced

     Ga is the reducing agent0 )2 is the o'idiSing agent

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    dentif" the 'idiSing and educing

    ;gents in Each of the Co))o#ing

    2H2 g @ 2 g→ 2H2 g

    Tn s @ H2O( a&→ TnO( a& @ H2 g

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    ne more e'amp)e

    Lesuvius fire @ :haraoh3s serpent demonstration

    http//*it.)"/1A2Ur"

    http://bit.ly/132XCryhttp://bit.ly/132XCry

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    Lesuvius Cire / :haraoh3s Oerpent reactions

    Lesuvius Cire6 decomposition of ammonium dichromate

    GH(2r 27 Q r 2A @ G2 @ (H2

    :haraoh3s Oerpent6 decomposition of HgOG2

    2HgOG2 Q 2HgO @ O2 @ A G(

    HgO @ 2 Q Hg @ O2

    O2 @ A2 Q 2 @ 2O2A G( Q AG2 @ G2

    his is the snake6.

    ,ecomposition gas

     products cause the

    snake to gro#6.

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    Lesuvius Cire is a redo' reaction

    Lesuvius Cire6 decomposition of ammonium dichromate

    GH(2r 27 Q r 2A @ G2 @ (H2

    Which atom is o'idiSedI Which atom is reducedI

    educing agentI 'idiSing agentI

    -A @F @A J

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    2%

    +a)vanic aka Lo)taic eactions

    M ;re spontaneous redo' reactions$ no energeticinput re&uired

    M e)ease energ" as heat if no resistance is met

    M 4a" *e separated into compartments to harnessenerg" as a *atter"

    us @ ;g@

    a& Q u2@

    a& @ ;gs

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    2!

    +a)vanic aka Lo)taic eactions0 cont.

    us @ ;g@a& Q u2@a& @ ;gs

    Oince this is a redo' reaction0 e)ectrons are transferred *et#eencopper and si)ver. here are t#o issues #e need to dea) #ith

     - #hat is the o&erall  reactionI

     - ho# can #e harness the transfer of e)ectrons to do #ork for usI

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    AJ

    Ba)ancing redo' e&uations

    us @ ;g@a& Q u2@a& @ ;gs

    he on)" difference *et#een *a)ancing redo' e&uations and non-redo' e&uations is that #e have to *a)ance mass and  charge in a

    redo' e&uation.

    Cor this e'amp)e0 mass is *a)anced0 *ut charge isn3t. Here3s ho##e go a*out *a)ancing charge…

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    A1

    +a)vanic aka Lo)taic eactions0 cont.

    orrect e&uation us @ 2;g@a& Q u2@a& @ 2;gs

    n this e'amp)e0 e)ectrons are transferred direc!ly *et#een thecopper and si)ver. hat is0 *oth ha)f-reactions occur in the same

    space. Ho# can #e harness the transfer of e)ectrons to do #ork

    for usI

    S i f h )f i i h )f )) ))

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    A2

     Se'ara!ion of ha)f-reactions into ha)f-ce))s a))o#s us to

    harness transfer of e)ectrons

    eduction ha)f-ce)) 'idation ha)f-ce))

     Red uction >ca! hode  node >o idation

     Elec!rons low ro anode !o ca!"ode#

    e-e-

    ) f ) * id

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    AA

    o)e of sa)t *ridge

    Oa)t *ridge a))o#s us to comp)ete circuit *et#een the individua)

    ha)f-ce))s *" a))o#ing coun!erions to f)o# to the appropriate ha)f-

    ce)). ther#ise0 #e *ui)d up im*a)ance of charge in each ha)f-ce)).

    ) f )t * id t

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    A(

    o)e of sa)t *ridge0 cont.

    ) f )t * id t

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    A5

    o)e of sa)t *ridge0 cont.

    ;nother #a" to )ook at it…- at cathode0 reduction of ;g@a& to ;gs resu)ts in deficienc" of

     positive charge$ in other #ords0 *ui)d up of negative charge- at anode0 o'idation of us to u2@a& resu)ts in *ui)d up of

     positive charge

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    ) f )t * id t

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    A7

    o)e of sa)t *ridge0 cont.

    f #e use a so)ution of ?GA0 ? @ cations #i)) migrate to#ards thecathode to make up for the )oss of ;g@ cations.

     GA

    - anions #i)) migrate to#ards the anode to counter the *ui)d

    up of u2@ cations.

    +"e sal! bridge allows or !"e igra!ion o bo!" ions,

    ? @  GA-

    *+i'- anion Q

    anode* 

    *+i'- ca! ion Q

    ca!"ode* 

    Ot d d )) G t ti 8i )) G t ti

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    A%

    Otandard e)) Gotation 8ine e)) Gotation

    M e)) reactions separated *" VV that represents the sa)t *ridge

    M E)ectrodes appear at the outsides

    M eaction e)ectro)"tes in inner section

    M :hases separated #ith V

    M Opecies in the same state separated #ith 0

    M oncentrations sho#n in

    Ot d d )) G t ti 8i )) G t ti

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    A!

    Otandard e)) Gotation 8ine e)) Gotation

    ,ra# a diagram that corresponds #ith the fo))o#ing standard ce))

    notation

    4ns V 4n2@a& VV Gi2@a& V Gis

    ;ssume ?GA is the e)ectro)"te so)ution.

    n the diagram…

    - identif" the anode and cathode ce))s$

    - the direction of e)ectron f)o# *et#een the anode and  cathode$

    - direction of ion movement from the e)ectro)"te so)ution

    Ot d d )) G t ti 8i )) G t ti

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    (J

    Otandard e)) Gotation 8ine e)) Gotation

    Cor the fo))o#ing e)ectrochemica) ce))0

    4ns V 4n2@a& VV Gi2@a& V Gis

    - Write the corresponding ha)f-reactions- the format of the )ine notation gives us a hint at the e&uation

    for the ha)f-reaction at each e)ectrode

    - Write the overa))0 *a)anced reaction

    'idation at the anode

    4ns Q 4n2@ a& @ 2e-

    eduction at the cathode

     Gi2@ a& @ 2e- Q Gis

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    (1

    E)ectrica) :otentia)

    M Ever" su*stance has the potentia) to gaine)ectrons0 or *e reduced  in o'idation state

    M he re)ative ease of gaining e)ectrons is termed the

    reduc!ion 'o!en!ial 0 and is s"m*o)iSed E red 

    M f the matter *eing o*served is in standard state

    then E  is termed the s!andard reduc!ion 'o!en!ial  

    and is s"m*o)iSed as E. red 

    M nits are Lo)t 1 L > 1 X -1

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    (2

    Otandard eduction :otentia)s  E Yred

    M  E Yred are ta*u)ated for near)" ever"kno#n su*stance

    M ; high va)ue of E Yred  E Yred  D J

    means that the su*stance is easi)"

    reduced

    M  E Yred is a re)ative num*er0ar*itrari)" determined

    M ;)) su*stances are compared toH@0 #hich has a E Yred of J.JJ L

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    (A

    e)) :otentia)s

    M he standard ce)) potentia) is ca)cu)ated as E Yce)) > E Ycathode - E Yanode

    M f the ce)) is non-standard

     E ce)) > E cathode - E anode

    M n spontaneous redo' reactions0 the cathode

     portion of the reaction has a higher )ess

    negative reduction potentia) than that of theanode  E cathode D E anode

    M Cor a spontaneous redo' reaction0 Ece)) D J

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    easie

    rto

    redu

    ce

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    harder

    to

    red

    uce$

    easierto

     o          i       d       i       /     e    

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    eduction potentia) ref)ects ease of reduction

    Ho# can #e use e)ectronic structure to e'p)ain #h" f)uorine is the

    easiest to reduce and #h" )ithium is the easiest to o'idiSeI

    Which is the *etter o'idiSing agentI Which is the *etter reducing

    agentI

    a)cu)ating ce)) potentia)

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    (7

    a)cu)ating ce)) potentia)

    ,etermine the ce)) potentia) for the fo))o#ing e)ectrochemica) ce))0

    4ns V 4n2@a& VV Gi2@a& V Gis

    s the reaction spontaneousI

    a)cu)ating ce)) potentia)

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    (%

    a)cu)ating ce)) potentia)

    What if #e reverse the po)arit"I

     Gis V Gi2@a& VV 4n2@a& V 4ns

    What is the ce)) potentia)I s the reaction spontaneousI

    C d f th ht

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    Cood for thought…

    Which ga)vanic ce)) #ou)d "ou e'pect to have the )arger ce)) potentia)I

    8is V 8i2@a& VV C-a& V C2:*s V :*2@a& VV H2Og V Os @ 2H

    @ @ 2e-

    e)) potentia)s e'p)ain activit" series for

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    5J

    4ore active

    meta)s #i))disp)ace )ess

    active meta)s

    e)) potentia)s e'p)ain activit" series for

    sing)e-disp)acement reactions

    4 ti t ) i)) di ) ) ti t )

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    4ore active meta)s #i)) disp)ace )ess active meta)s

    u s @ ;gGA a& Q uGA a& @ ;g s

    e)) notation us V u

    2@

    a& VV ;g

    @

    a& V ;gs

    Ece)) > I s this reaction spontaneous or nonspontaneousI s

    this consistent #ith the ce)) potentia) as #e)) as the prediction

    from the re)ative activitiesI

    Ba)ancing redo' e&uations and #orking out E ))

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    Ba)ancing redo' e&uations and #orking out Ece))

    us Q u2@a& @ 2e-

    ;g@ @ e-  Q ;gs

    -----------------------------

    us Q u2@a& @ 2e-

    2;g@ @ e-  Q ;gs

    -----------------------------

    us Q u2@a& @ 2e-

    2;g@ @ 2e-  Q 2;gs

    -----------------------------

    us @ 2;g@a& Q

    u2@a& @ 2;gs

    his is e'act)" the same as the #a" #e

     *a)anced the redo' e&uation *et#een copper

    and si)ver ear)ier on. he &uestion no# is#hat a*out the potentia)sI Ohou)d #e

    mu)tip)" the potentia) for si)ver *" 2 since #e

    did that to *a)ance the overa)) e&uationI

    *0O,*  he reason #h" #e don1!  is *ecause potentia)s are in!ensi&e$ the"3re independent

    of the amount of su*stance. he rea) reason

    #h" is *ecause potentia) is defined as a ra!io 

    of energ" to charge. he ratio sta"s the same

    regard)ess of ho# much su*stance "ou have.

    +ake"oe essage use the potentia)s as

    !"ey are #hen "ou ca)cu)ate Ece)). ,on3t ad9ust

    them

    8et3s consider the opposite

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    8et s consider the opposite…

    ;gs V ;g@a& VV u2@a& V us

    Ece)) > I s this reaction spontaneous or nonspontaneousI s

    this consistent #ith the ce)) potentia) as #e)) as the prediction

    from the re)ative activitiesI

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    Oo)utions to e'ercises

    ; )itt)e more a*out *uffers…

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    55

    ; )itt)e more a*out *uffers…

    onsider the acetic acid/acetate *uffer s"stem.

    he p? a of acetic acid is (.7(.

    What is the re)ative concentration of acetate at pH 5.7(I +reater than0

    )ess than0 or e&ua) to acetic acidI

    ! '3 4,756 we1re abo&e !"e ' a , 8ce!a!e9 : 8ce!ic acid9 

    What is the re)ative concentration of acetic acid at pH A.7AI +reater

    than0 )ess than0 or e&ua) to acetateI

    ! '3 ;,756 we1re below !"e ' a , 8ce!ic acid9 : 8ce!a!e9 

    ; )itt)e more a*out *uffers…

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    5F

    Ho# a*out the ammonia/ammonium *uffer s"stemI

    he p?  * of ammonia is (.7(. Hint #hat3s the p? aI

     $ ' b < 5,756  b < an!ilog(5,75) < =>5,75 < =,? => 4 ,

      a <  w /  b < =,> =>=5 / (=,? => 4 ) < 4,@ => =>

     ' a < log (4,@ => => ) < A,2@ 

    What is the re)ative concentration of ammonia at pH 1J.2FI +reater

    than0 )ess than0 or e&ua) to ammoniumI

    ! '3 =>,2@6 we1re abo&e !"e ' a , 8onia9 : 8oniu9 

    What is the re)ative concentration of ammonium at pH %.7FI +reater

    than0 )ess than0 or e&ua) to ammoniaI

    ! '3 ?,2@6 we1re below !"e ' a , 8oniu9 : 8onia9 

    :ractice N ;ssign o'idation num*ers to each

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    :ractice ;ssign o'idation num*ers to each

    e)ement in the fo))o#ing compounds

    M 2

    M H2O(

    M? 

    A

    ;s(

    M 4n(-

    M 2(2-

    M  Ga22

    M  GH(@

    @($ -2

    H @1$ O @F$ -2

    ? @1$ ;s @5$ -2

    4n @7$ -2

    @A$ -2

     Ga @1$ -1 G -A$ H @1

    id ti d d ti ; th , fi iti

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    'idation and eduction ;nother ,efinition

    H(  @ 2 2 Q 2 @ 2 H2-( @1 J  @( N2 @1 -2

    o'idation

    reduction

    Based on the changes in o'idation num*ers0 #hich e)ement

    undergoes o'idationI eductionI

    dentif" the 'idiSing and educing

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    dentif" the 'idiSing and educing

    ;gents in Each of the Co))o#ing

    2H2 g @ 2 g→ 2H2 g

    Tn s @ H2O( a&→ TnO( a& @ H2 g

      J J @1 -2

      J @1 @F -2 @2 @F -2 J

    o'idation

    reduction

    o'idation

    reduction

    H2 is reducing  agent

    2 is oidiing  agent

    Tn is reducing  agent

    H2 is oidiing  agent

    Ba)ancing redo' e&uations

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    FJ

    Ba)ancing redo' e&uations

    us @ ;g@a& Q u2@a& @ ;gs

    - Op)it the reaction into ha)f-reactions there #i)) a)#a"s *e ano'idation ha)f-reaction and a reduction ha)f-reaction

    - se o'idation num*ers

    us @ ;g@a& Q u2@a& @ ;gs

    J @1 @2 J

    u is o'idiSed

    ;g is reduced

    Ba)ancing redo' e&uations

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    F1

    Ba)ancing redo' e&uations

    us @ ;g@a& Q u2@a& @ ;gs

    - Write each ha)f-reaction separate)"- Ba)ance each ha)f-reaction *" mass and charge

    'idation ha)f-reaction

    us Q u 2@a& mass is *a)anced

    charge is not

    us Q u 2@a& @ 2e-

    'idation ha)f-reaction is fu))"

     *a)anced

    eduction ha)f-reaction

    ;g@a& Q ;gs mass is *a)anced

    charge is not

    ;g@a& @ e- Q ;gs

    eduction ha)f-reaction is fu))"

     *a)anced

    Ba)ancing redo' e&uations

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    F2

    g &

    us @ ;g@a& Q u2@a& @ ;gs

    - 8ine up ha)f-reactions and prepare to add6 them to o*tain overa))

    reaction

    us Q u2@a& @ 2e- P of e- gained and )ost

    ;g@ @ e-  Q ;gs must *e the same

    -----------------------------

    us Q u2@a& @ 2e-

    2;g@ @ e-  Q ;gs

    -----------------------------

    us Q u2@a& @ 2e-

    2;g@ @ 2e-  Q 2;gs

    -----------------------------

    us @ 2;g@a& Q u2@a& @ 2;gs

    4ass and charge are fu))"

     *a)anced

    Otandard e)) Gotation 8ine e)) Gotation

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    FA

    Otandard e)) Gotation 8ine e)) Gotation

    ? @ from ?GA 

    e)ectro)"te so)3n

    f)o#s to#ards

    cathode.

     GA- f)o#s

    to#ards anode.

    eduction potentia) ref)ects ease of reduction

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    p

    Which is the *etter o'idiSing agentI Which is the *etter reducing

    agentI

    Bluorine has the )arger reduction potentia). t #ants to *e

    reduced . Higher reduction potentia)0 easier to reduce. herefore0

    it #i)) *e a strong oidiing agen! .

     Li!"iu has the )o#er reduction potentia). t #ants to *e oidied .

    8o#er reduction potentia)0 easier to o'idiSe. herefore0 it #i)) *e

    a strong reducing agen! .

    a)cu)ating ce)) potentia)

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    F5

    a)cu)ating ce)) potentia)

    ,etermine the ce)) potentia) for the fo))o#ing e)ectrochemica) ce))0

    4ns V 4n2@a& VV Gi2@a& V Gis

    Ece)) > Ecathode - Eanode

    Crom the ce)) notation… the anode is the o'idation of 4n to 4n2@

      the cathode is the reduction of Gi2@ to Gi

    Ecathode > -J.25 L

    Eanode > -1.FF L

    Ece)) > Ecathode - Eanode  > -J.25 L - -1.FF L

      > @1.(1 L$ Ece)) D J… the reaction is s'on!aneous

    a)cu)ating ce)) potentia)

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    FF

    g p

    ,etermine the ce)) potentia) for the fo))o#ing e)ectrochemica) ce))0

     Gis V Gi2@a& VV 4n2@a& V 4ns

    Ece)) > Ecathode - Eanode

    Crom the ce)) notation… the anode is the o'idation of Gi to Gi2@

      the cathode is the reduction of 4n2@ to 4n

    Ecathode > -1.FF L

    Eanode > -J.25 L

    Ece)) > Ecathode - Eanode  > -1.FF L - -J.25 L

      > -1.(1 L$ Ece))  J… the reaction is no!  spontaneous

    Cood for thought…

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    8is V 8i2@a& VV C-a& V C2 Ece)) > 2.%7 L - -A.J5 L > @ 5.!2 L

    :*s V :*2@a& VV H2Og V Os @ 2H@ @ 2e- Ece)) > J.1( L - -J.1A L

     > @ J.27 L

    * +"e ar!"er a'ar! !"e anode and ca!"ode 'o!en!ials are ro eac"

    o!"er6 !"e larger !"e cell 'o!en!ial, * 

    4ore active meta)s #i)) disp)ace )ess active meta)s

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    4ore active meta)s #i)) disp)ace )ess active meta)s

    u s @ ;gGA a& Q uGA a& @ ;g s

    e)) notation us V u2@a& VV ;g@a& V ;gs

    Ecathode > J.%J L$ Eanode > J.A( L

    Ece)) > Ecathode - Eanode > J.%J L - J.A( L > @J.(F L

    Ece)) DJ$ process is spontaneous. onsistent #ith the fact that

    u is more active than ; .

    8et3s consider the opposite…

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    8et s consider the opposite…

    ;gs V ;g@a& VV u2@a& V us

    Ece)) > I s this reaction spontaneous or nonspontaneousI s

    this consistent #ith the ce)) potentia) as #e)) as the prediction

    from the re)ative activitiesI

    Ecathode > J.A( L$ Eanode > J.%J LEce)) > Ecathode - Eanode > J.A( L - J.%J L > -J.(F L

    Ece))  J… nons'on!aneous#

    onsistent #ith the fact that ;g is less active than u.