Análisis cualitativo

Tadeusz Górecki Ionic Equilibria

Acid-Base Equilibria

Brønsted-Lowry: an acid is a proton _______, a base is a ______________.++↔ HBaseAcid

________________ (H3PO4, H2O), ______ ( +4NH ) and _____ (H2PO4

-) can allbehave as acids.

Example:++ +↔ HNHNH 34

Substances which can behave both as acids and as bases: ____________, or______________ substances (e.g. H2O, SH-).

baseacidSHSH −+− +↔ 2

acidbaseSHSHH 2↔+ −+

Free protons _________ in any solvent, thus the above reactions are______________. In reality:

++ +↔+ OHNHOHNH 3324

Energy required to dissociate _____ to ____ and __: _____ kcal/mol

Equilibrium constant for _______________:−+ +↔+ AOHOHHA 32

][]][[

HAAHKa

________________:−+ +↔+ OHBHOHB 2

][]][[

BOHBHKb

Relationship between Ka and Kb:

wba KKK =⋅

Lewis: an acid is an ___________________; a base is an _________________.

________________________________________________________________

Strength of acids and bases−+− +↔+ 2

4324 SOOHOHHSO

−+ +↔+ 33232 HCOOHOHCOH

−+ +↔+ CNOHOHHCN 32

1221 baseacidbaseacid +↔+

_______][

243 == −

HSOSOOHKa

_______][

33 ==−+

COHHCOOHKa

______][

]][[ 3 ==−+

HCNCNOHKa

_______ value of __ means that the acid is ________, thus:

______________________

____________ of water:−+ +↔ OHHOH2

Equilibrium constant using __________:

0 −+=

Activity of water is by thermodynamic convention proportional to the _____________ of water in the solution. In dilute solutions it is close to __.

Activity of water can be _____________________:

___][][ == −−

−+ γγ OHHaa OHH

"________________" constant:

wKOHH =−+ ]][[

−+−+

== γγγγ

/00 2w

At 50°C, pKw = ______, and the neutral point is pH = ____. At 25°C in 3 MNaClO4 pKw = _____, and the neutral point is pH = ____.

____________ solvents:−+ +↔+ 2433 NHNHNHNH

At -60°C, the equilibrium constant is:32

24 10]][[ −−+ == NHNHK

Thus, the pH scale (defined as -log[NH4+]) in liquid ammonia ranges from _ to

pH of a strong acid

Initially PH, or "_________________", defined as

PH = -log CH

Today's definition of pH:

)]log([log ++−=−== γHapapH HH

General approach

Example: HCl

Mass balance: ____][ =−ClIon product of water: ____]][[ ==−+

wKOHHCharge balance: ][][][ −−+ += ClOHH

Solution: HAw C

HKH += +

This is a quadratic equation, which applies ________.

When ____________, [H+] = ___ ([OH-] is _______________)

At higher ionic strength, activity coefficient should be used.

Strong base:

Example: NaOH

Mass balance: ___][ =+NaIon product of water: 1410]][[ −−+ == wKOHHCharge balance: _____________________

Solution:][

][ ++ =+

HKCH w

Basic solution, thus ______________, and in general

CKH =+ ][

___________________

____________________________________

Example: pH of 7102 −⋅ M solution of NaOH

0][][ 2 =−+ ++wb KHCH

wbb KCCH

++−=+

LmolH /1014.4][ 8−+ ⋅= pH = _____

Simplified equation: pH = _____

____________________________________

pH of strong acid/base as a function of concentration:

-10-9-8-7-6-5-4-3-2-10

0 2 4 6 8 10 12 14

Clog C(acid) log C(base)

Mixture of a strong acid and a strong base

Example: HCl and NaOH

Mass balance: ___][ =−ClMass balance: ___][ =+NaIon product of water: 1410]][[ −−+ == wKOHHCharge balance: ][][][][ −−++ +=+ OHClNaH

][][ +

+ −=−HKHCC w

When the acid and the base are ____________:

LmolKOHH w /10][][ 7−−+ ===

Titration of Strong Acids and Bases

Volume of the system changes, thus _______ must be taken into mass balancesrather than _______________.

Example: titration of HCl with NaOH:

Mass balance: ________)]([ =+−ba VVCl

Mass balance: ________)]([ =++ba VVNa

Ion product of water: 1410]][[ −−+ == wKOHHCharge balance: ][][][][ −−++ +=+ OHClNaH

][][ +

VVVCH w

At the equivalence point, __________ (1:1 stoichiometry) and ___________

Before the equivalence point, _______________:

VVVCVCH

After the equivalence point, _______________:

VVVCVC

VCVCVVKH

=+ )(][

In the vicinity of the equivalence point (Ca = 0.1 M, Va = 50 mL, Cb = 0.2 M):

24.999 24.9995 25 25.0005 25.001

OH- neglectedFull equationH+ neglected

Plotting the titration curve

__________ titrated with _________:

−++−

]/[][]/[][

HKHCHKHCVV

Titration of ___________ with ___________:

+−−+

]/[][]/[][

HKHCHKHCVV

Example:

Titration curve

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

_______________ titration:

HCl titrated with NaOH

][][][][ −−++ +++=Λ ClOHNaH ClOHNaH λλλλ

Λ - _______ conductance ( ][ 11 −−Ω cmk )Xλ - __________ conductance.

At 25°C, ________ conductances 0λ are:

_____0 =+ λH_____0 =+ λNa_____0 =− λOH_____0 =− λCl

Procedure:

• ______ the values of pH;

• ________ [H+] and [OH-];• calculate V from the ____________ equation;• calculate )/(][ 0VVVCNa b +=+ (from ___________);

• calculate )/(][ 00 VVVCCl a +=− (from ___________).

50 mL 0.1 M HCl titrated with 0.2 M NaOH:

0 10 20 30 40 50

50 mL 0.0001 M HCl titrated with 0.0001 M NaOH:

0.0065

0.0075

0.0085

0.0095

0.0105

40 50 60

Titration error

errorTitration ep −=

Vep - V at ________V' - V at _______________Titration of 50 mL 0.1 M HCl with 0.2 M NaOH:

Enlarged section (end point detected with __________ at pH = 5):

Titration error:

_________25

259963.24100 =−

________________50 mL 0.0001 M HCl titrated with 0.0001 M NaOH:

Titration error:

______50

5040100 =−

Gran plotsTitration of a ___________ with a __________:

][][ +

VVVCH w

Before the equivalence point, ______ is negligibly small, thus:

bbaaba VCVCHVV −=+ + ])[(

or bbaapH

ba VCVCVVf −=+= −10)(1

__ , ___ and __ are _________, thus a plot of f1 as a function of Vb should be a____________ with a slope of _____ intersecting the X axis at the _______________, _____________.Example: 50 mL 0.0001 M HCl titrated with 0.0002 M NaOH:

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

0.0005

22 23 24 25 26 27

Vb [mL]

In the vicinity of the equivalence point:

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0.0001

24.5 24.6 24.7 24.8 24.9 25 25.1 25.2 25.3

Weak monoprotic acids and bases

−+ +↔ AHHA

][]][[

HAAHKa

−+ +↔+ OHBHOHB 2

][]][[

BOHBHK b

wba KKK =⋅

wba pKpKpK =+

NH4+: __________

NH3: __________Dependence of ___ on ___________:

][ ]][[

γγγ

γγγ −+−+

== aa KHA

00 logloglog γγγ −++= −+aa pKpK

Using _______________ and setting bI=0logγ (activity coefficient for an______________________):

IpKa −

+⋅−= '

151.02757.4

where b' is the ________________ (usually 0.2).

Best fit: _______________

Temperature dependence of apK 0 :

Calculating the pH of weak acidKnown: ___________Unknown: ______________________

][]][[

HAAHKa

]][[ −+= OHHK w

Mass balance: ][][ HAACHA += −

Charge balance: ][][][ −−+ += OHAH

−+−

aaHA K

][][][1][]][[][

From ______________:

KHHCHA+

][][][

From ____:

][][ +

− =HKOH w

Substituting ____ and _____ into __________________:

][][][ ++

KHKCH w

0)]([][][ 23 =⋅−+−+ +++wawaHAa KKKKCHKHH

Simplifying assumption: _____ is negligibly small

KHKCH+

0][][ 2 =−+ ++aHAa KCKHH

When ____________:

][][ +

KCH aHA aHAKCH =+ 2][ aHAKCH =+ ][

Flood's diagramFrom ____ and _______________:

][][][

KKHC w

Flood's diagram

00 2 4 6 8

Strong acidpKa=4.75pKa=7.53pKa=10.72

Degree of dissociation

KHKCA+

= +−

KHHCHA+

][][][

Degree of _____________:

== −

−−

][][][][AHA

Degree of ____________:

==− − ][][][][1AHA

Degree of dissociation and formation

0 2 4 6 8 10 12 14

degree of dissociationdegree of formation

Sillén's diagram (______________, ____________________)Acetic acid, 0.01 M, pKa = 4.75

00 2 4 6 8 10 12 14

[OH-] [H+]

1. [H+] is determined from the _______________:

pHH −=+ ]log[

2. [OH-] is determined from _________________:

ww pKpH

HKOH −== +

][log]log[

3. [A-] is determined from ____________ and ___:

KHKCA+

= +−

4. [HA] is determined from ____________ and ___:

KHHCHA+

][][][

pH of a given system can be determined from the _______________:

][][][ −−+ += OHAH

Acidic solution, thus _____ can be neglected

][][ −+ = AH

Solution for the proton condition can be easily found on equilibrium diagramsusing the _______________:

( )][][][log −−+ −− OHAH

Acetic acid, _____ M, pKa = _____

00 2 4 6 8 10 12 14

[OH-] [H+]

Pointer

Acetic acid, ____ M, pKa = ____

00 2 4 6 8 10 12 14

Pointer

[OH-][H+]

[A-][HA]

Plotting equilibrium diagrams

1. [H+] and [OH-]: _______ lines at ________ (slopes of __ and __,respectively)

2. [A-]:

KHKCA+

= +−

for ____________________

][][ +

− ≅H

KCA aHA

pHpKCA aHA +−=− log]log[

1]log[=

for ___________________ HACA ≅− ][

3. [HA]:

KHHCHA+

][][][

for ___________________ HACHA =][

for ___________________

KHCHA ][][

aHA pKpHCHA +−= log]log[

1]log[−=

dpHHAd

4. When __________:

2][][ HACHAA ==−

3.0log2loglog2

log]log[]log[ −=−===−HAHA

HA CCCHAA

What is the pH of 0.001 M NaAc?

][][][ −+ =+ OHHAH

___________, thus _____:

][][ −= OHHA

0 2 4 6 8 10 12 14 -14

What happens when the acid concentration is __________?

0.001 M HF, pKa = 3.17

Proton condition: ][][][ −−+ += OHFH

][][ −+ ≅ FH

00 2 4 6 8 10 12 14

[OH-][H+]

00 2 4 6 8 10 12 14

CPointerpH=3.26

[OH-][H+]

Checking the results:

pH = ____

[OH-] = ______

[HF] = ______

== −

−−−+

26.326.3

101010

][]][[

HFFHKa

Mass balance:

=+=+ −−− 34.326.3 1010][][ HFF

Algebraic solution:

0][][ 2 =−+ ++aHAa KCKHH

=+ ][H

pH = ____

Low concentrations of very weak acids:

5 x 10-5 M HCN, pKa = 9.32

00 2 4 6 8 10 12 14

C[OH-][H+]

[HCN] [CN-]

[CN-]+[OH-]

Mixture of acids

Strong acids represented by ______________.

Strong bases represented by ______________.

Typically ___________ on EquiligrapHs.

Each __________ or _____ represented by the expressions:

KHKCA+

= +−

KHHCBH+

][][][

pH found at the point where _______________.

0.01 M HAc (Ka = 10-4.75) and 0.001 M HFo (Ka = 10-3.75)

00 2 4 6 8 10 12 14

[OH-] [H+]

[Ac-][HAc]

[HFo] [Fo-]

[Ac-]+[Fo-]+[OH-]

Proton condition: _________________________

Pointer function:

00 2 4 6 8 10 12 14

PointerpH=3.3

[OH-] [H+]

[Ac-][HAc]

[HFo] [Fo-]

Assumptions:

______ negligibly small

__________

][][][][ +++

KHKCH w

++= ++

][][][

Iteration:f

ffaa KH

KCHKCH

Circular reference:f

ffaa KH

KCHKCH

Mixture of strong and weak acid:

0.001 M HCl and 0.01 M HAc

][][][][ −−−+ ++= OHClAcH

][][ +

KHKCH w

____________________

]][[][ 2 −++ += ClHKCH aa

Solution: pH = _____

00 2 4 6 8 10 12 14

[OH-] [H+]

[Ac-]+[Cl-]+[OH-]

Salt of a weak acid and a weak base

Two independent ________________ linked by the condition that they have thesame ___________________.

][]][[ 1 HAKAH a=−+

][]][[ 2++ = BHKBH a

wKOHH =−+ ]][[

____ balances: ][][][][ BBHAHAC +=+= +−

______ balance: ][][][][ −−++ +=+ OHAHBH

_______________: ][][][][ BOHHHA +=+ −+

If [H+] and [OH-] _________:

1 ][][][

a KHCK

212][ aa KKH ⋅=+

21][ aa KKH ⋅=+

pH _______________ on C (provided the assumption above is fulfilled)!

Example: pH of 0.01 M NH4Ac (pKa1 = 4.75, pKa2 = 9.25)

=+= )(2/1 21 aa pKpKpH

The value of __ is coincidental.

Equilibrium diagram:

00 2 4 6 8 10 12 14

[OH-] [H+]

[HAc][NH3]

[NH4+]

Pointer function:

00 2 4 6 8 10 12 14

PointerpH=7

[OH-] [H+]

[HAc][NH3]

[NH4+]

Full solution:

][][][

_______ equation in [H+].

The equation is _____________, thus:

Example: Dimethylammonium acetate

pKa1 = 4.75 (___________), pKa2 = 10.76 (__________________)

0 2 4 6 8-log C

pH = 7.755

General equation for the titration curve

____ balance:ba

VVVCAHA+

=+ − ][][

____ balance:ba

VVVCNa+

][]][[

HAHAKa

______ balance: ][][][][ −−++ +=+ OHANaH

][][][ ++

VVVCH w

][ ++ +

VVVCH w

+−⋅=

Titration of a ___________ with a __________:

Simplifying assumptions: before the equivalence point ____________; after theequivalence point ________________

Example: titration of 10 mL 0.1 M HAc with 0.1 M NaOH

0 2 4 6 8 10 12 14Vb

________________

bb VpH

∆∆

≈∂∂

End point determined by the _________ of the ______________. If necessary,________________ can be obtained in the same manner.

________________:

0 2 4 6 8 10 12 14Vb

d(pH)/dVb

____ and ________________:

9.90 9.95 10.00 10.05 10.10

Another way to plot the titration curve: through _____________ Φ :

Substitution to the general equation:

=Φ +++ ][][

Iteration – set ________________ and get the ________________

0 1 2Fraction titrated

_______________ solution:

−−

==Φα

The plot of _____________________ enables easy comparisons of different_______________.

Examples:

• Different _________ of the acid

• Different ___ values

Ka = 1e-6Ka = 1e-5Ka = 1e-4

Ca = Cb = 0.01 M

0 5 10 15 20 25 30 35 40Vb

Va = 10 mLVa = 20 mL

Va = 30 mL

0 5 10 15 20Vb

Ka = 1e-6Ka = 1e-5Ka = 1e-4

Ca = Cb = 0.01 M

• Different __________________________:

Fraction titrated

Ca = 0.0001 M

Ca = 0.001 M

Ca = 0.01M

pKa = 4.75Cb = 0.01 M

• Different concentrations of the _____:

Fraction titrated

Cb = 0.0001 M

Cb = 0.001 M

Cb = 0.01 M

pKa = 4.75Ca = 0.01 M

0 5 10 15Vb

Ca = 0.0001 M Ca = 0.001 M

Ca = 0.01 M

pKa = 4.75Cb = 0.01 M

0 500 1000 1500 2000Vb

Cb = 0.0001 MCb = 0.001 M

Cb = 0.01 M

pKa = 4.75Ca = 0.01 M

Titration of a ___________ with a _________:

][][ +

+ −+ HK

VVVCH w

−−

where +

BHBBH KH

][][α ;

HAA KH

][][α

Strong base Kb = 5

pKa = 4.75pKb = 5Ca = 0.01 M

0 5 10 15 20Vb

Strong base

Kb = 5

pKa = 4.75pKb = 5Ca = 0.01 MVa = 10 mL

Titration error

At the equivalence point ________

aabb VCVC ='

where Vb’ is Vb at the _______________

VCV ='

Titration error:

1111''

'.. −Φ=−=−=−=

−= ep

At the equivalence point and its vicinity:

Also, near the equivalence point, ____________ , thus _____________

KHK ][

+ −≅+

−=−+

=−α

+−=−Φ ++ ][][

)(11 HHK

VCVV w

baep α

baep K

VCVV ][][

=−Φ

baep K

CCCC ][

++ −

+=−Φ

Example: 0.1 M HAc, 0.1 M NaOH, pHep = __ instead of pH = _____ at theequivalence point

=−−=−Φ −

−−−

1010)1010)(20(1ep

Titration of a weak base with a strong acid:

baep H

][][][)(1 ++

+=−Φ

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