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    Acid-Base Titrations

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    Titration ofStrong Acid and Strong Base

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    Strong Acid - Strong BaseTitration Curve

    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 0.00 mL of NaOH added, initial point

    [H3O+] = C

    HCl = 0.1000 M

    pH = 1.0000

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 15.00 mL of NaOH added,Va * Ma > V b * Mb

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 15.00 mL of NaOH added,Va * Ma > V b * Mb

    (Va * Ma) - (V b * Mb)[H3O+] = ----------------------------(Va + V b)

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 15.00 mL of NaOH added, Va * Ma > V b * Mb (Va * Ma) - (V b * Mb)[H3O +] = ----------------------------(Va + V b)

    ((35.00mL)*(0.1000M)) - ((15.00mL)*(0.1000M))

    = ------------------------------------------------------------(35.00 + 15.00)mL

    = 4.000x10 -2M pH = 1.3979

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 35.00 mL of NaOH added,Va * Ma = V b * Mb , equivalence point

    at equivalence point of a strong acid - strongbase titrationpH = 7.0000

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 50.00 mL of NaOH added,

    Vb * Mb > V a * Ma , post equvalence point

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 50.00 mL of NaOH added,Vb * Mb > V a * Ma , post equvalence point

    (Vb * Mb) - (V a * Ma)[OH -] = ---------------------------(Va + V b)

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 50.00 mL of NaOH added,Vb * Mb > V a * Ma , post equvalence point

    (Vb * Mb) - (V a * Ma )[OH -] = ---------------------------

    (Va + V

    b)

    ((50.00mL)*(0.1000M)) - ((35.00mL)*(0.1000M))= ------------------------------------------------------------

    (35.00 + 50.00)mL

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000

    M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 50.00 mL of NaOH added, V b * Mb > V a * Ma , post equvalence point

    (Vb * Mb) - (V a * Ma )[OH -] = ---------------------------

    (Va + V b)((50.00mL)*(0.1000M)) - ((35.00mL)*(0.1000M))

    = ------------------------------------------------------------(35.00 + 50.00)mL

    = 1.765x10 -2M pOH = 1.7533

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000M HCl with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    at 50.00 mL of NaOH added, V b * Mb > V a * Ma , postequvalence point

    [OH-

    ] = 1.765x10-2

    M pOH = 1.7533pH = 14.00 - 1.7533 = 12.25

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    Strong Acid - Strong Base Titration

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    p H

    Series1

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    Strong Acid - Strong Base Titration

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    p H

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    Strong Acid - Strong Base Titration

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    p H

    1

    0.1

    0.01

    0.001

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    Titration ofWeak Acid with Strong BaseEXAMPLE: Derive the titration curve for

    the titration of 35.00 mL of 0.1000 MHC 2H3O 2 with 0.00, 15.00, 35.00, and 50.00

    mL of 0.1000 M NaOH.Ka = 1.75 x 10 -5M

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    EXAMPLE: Derive the titration curve forthe titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and 50.00mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 0.00 mL of NaOH added, initial point

    [H3O+] = Ka * C HA

    =

    (1.75e-5 M)*(0.1000 M) = 1.32e-3 MpH = 2.878

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 15.00 mL of NaOH added,Va * Ma > V b * Mb

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 15.00 mL of NaOH added,Va * Ma > V b * Mb

    (Va * Ma) - (V b * Mb)[HC 2H3O 2]excess = ---------------------------

    (Va + V b)

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000

    M HC 2H3O 2 with 0.00, 15.00, 35.00,and 50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 15.00 mL of NaOH added, Va * Ma > V b * Mb (Va * Ma) - (V b * Mb)

    [HC 2H3O 2]excess = ------------------------------(Va + V b)

    ((35.00mL)*(0.1000M)) - ((15.00mL)*(0.1000M))= ------------------------------------------------------------(35.00 + 15.00)mL

    = 4.000x10 -2M

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 15.00 mL of NaOH added, Va * Ma > V b * Mb [HC 2H3O 2]excess = 4.000x10 -2M

    (Vb * Mb)[C2H3O 2-] = -------------

    (Va + V b)(15.00 mL)(0.1000 M)

    = ---------------------------- = 3.000x10 -2M(35.00 + 15.00)mL

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    EXAMPLE: Derive the titration curve forthe titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and 50.00mL of 0.1000 M NaOH.Ka = 1.75 x 10 -5M

    at 15.00 mL of NaOH added, Va * Ma > V b * Mb [HC2H3O 2]excess = 4.000x10 -2M[C2H3O2-] = 3.000x10 -2M

    [HC 2H3O 2]excess [H3O+] = K a * ----------------------

    [C2H3O 2-]4.000x10 -2M

    = 1.75e-5 M * ------------------- = 2.33e-5 M3.000x10 -2M

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 15.00 mL of NaOH added, Va * Ma > V b *Mb

    [HC 2H3O 2]excess = 4.000x10 -2M[C2H3O 2-] = 3.000x10 -2M

    [H3O+] = 2.33e-5 MpH = 4.632

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 35.00 mL of NaOH added,Va * Ma = V b * Mb , equivalence point

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    3535

    0.1x35

    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 35.00 mL of NaOH added,Va * Ma = V b * Mb , equivalence pointpH = (pKw + pKa + log [G])

    pH = (14

    log 1.75x10-5

    + log( ))pH = (14 + 4.76 1.301)pH = 8.728

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 50.00 mL of NaOH added,Vb * Mb > V a * Ma , post equvalence point

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 50.00 mL of NaOH added,Vb * Mb > V a * Ma , post equvalence point

    (Vb * Mb) - (V a * Ma)

    [OH-

    ] = --------------------------(Va + V b)

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    EXAMPLE: Derive the titration curve forthe titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and 50.00mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 50.00 mL of NaOH added, Vb * Mb > V a * Ma (Vb * Mb) - (V a * Ma)[OH -] = --------------------------

    (Va + V b)((50.00mL)*(0.1000M)) - ((35.00mL)*(0.1000M))

    = ------------------------------------------------------------(35.00 + 50.00)mL

    = 1.765x10 -2M

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    EXAMPLE: Derive the titration curvefor the titration of 35.00 mL of 0.1000 M

    HC 2H3O 2 with 0.00, 15.00, 35.00, and50.00 mL of 0.1000 M NaOH.

    Ka = 1.75 x 10 -5M

    at 50.00 mL of NaOH added, Vb * Mb > V a * Ma

    [OH -] = 1.765x10 -2M

    pOH = 1.7533pH = 14.00 - 1.7533 = 12.25

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    Weak Acid - Strong Base Titration

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    p H

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    Weak Acid - Strong Base Titration

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    Titration ofWeak Base with Strong Acid Much the same shape, except the titration

    would start at high pH and decrease as acidis added

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    Weak Base - Strong Acid Titration

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    p H

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    Features of the Titration of aPolyprotic Acid with a Strong Base

    1. The loss of each mole of H + shows up asseparate equivalence point (but only if thetwo pK as are separated by more than 3 pKunits).

    2. The pH at the midpoint of the buffer region

    is equal to the pK a of that acid species.3. The same volume of added base is required

    to remove each mole of H +.

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    Finding the End Point with a pHElectrode

    Titration curve for a weak acid - strong base titration.

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    Finding the End Point with a pH Electrode

    p H / V versu s V

    First derivative of a weak acid- strong base titration

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    Finding the End Point with a pH Electrode

    Second derivative of a weak acid - strong base titration

    (

    pH /

    V) /

    V versus V

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    Indicators

    Indicator BehaviorHIn + H 2O H3O+ + In - acid base

    color color

    [H3O+][In-]Ka = -------------- (1)

    [HIn]

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    Indicators

    Indicator BehaviorIn + H 2O InH + + OH -

    base acid

    color color

    [InH+][OH -]K

    b = --------------- (2)

    [In]

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    Indicators

    Indicator Behaviorrearranging Equation (1) gives

    [In-] Ka ------ = ----------[HIn] [H3O+]

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    Indicators Indicator Behavioracid color shows when [In-] 1 [H 3O+][In-] 1------ ---- ------------- = ---*[H 3O+] = K a [HIn] 10 [HIn] 10

    base color shows when [In-] 10 [H 3O+][In-]------ ---- ------------- = 10*[H 3O+] = K a [HIn] 1 [HIn]

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    Indicators

    Indicator Behavioracid color shows when pH + 1 = pK a

    and base color shows when pH - 1 = pK

    a

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    Indicators

    Indicator BehaviorColor change range is

    pK a = pH + 1 or pH = pK a + 1

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    Choosing the Proper Indicator

    color change range should be in area wheretitration curve is most vertical

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    Strong Acid - Strong Base Titration

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    p H

    phenolphthalein

    bromocresol green3.8

    5.4

    8.0

    9.6

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    Weak Acid - Strong Base Titration

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    9.6

    8.0 phenolphthalein

    3.8

    5.4 bromocresol green