Chapter 16
Acid-Base Titration and pH

  1. Aqueous Solutions and the Concept of pH

    1. Hydronium Ions and Hydroxide Ions
      Water can form both hydronium and hydroxide ions.

      1. Self Ionization of Water
        Water conducts but very little - pure water i.e. distilled water
        Reason is self ionization
        Figure 16-1 page 481
        Self ionization - definition

        H2O (l) + H2O (l) = H3O+1 (aq) + OH-1 (aq)
        The concentration of the hydronium and the concentration of the hydroxide is

        1.0 x 10 -7 mol/L of water at 25oC

        use brackets, [], around formula to indicate “concentration in moles per liter”, which is the same as molarity.

        [H3O+1] x [OH-1] = 1 x 10-14 M since [H3O+1] = 1 x 10-7 and
        [OH-1]= 1 x 10-7

        note that 10-7 is equivalent to 1 x 10-7

        The 10-14 is a constant in water and also dilute aqueous solutions at constant temperature. That means that the [H3O+1] times the
        [OH-1] must always equal 10-14 if you have pure water or if you have a solution in which water is the solvent e.g. acids, etc.

        ionization constant of water is

        Kw = [H3O+1] x [OH-1] = 1 x 10-14 M2 = (1.0 x 10-7M ) (1.0 x 10-7 M)

        As temp increases the ionization of water increases and so does Kw.

        Table 16-1 page 482

      2. Neutral, Acidic, and Basic Solutions

        Since [H3O+1] = [OH-1] in pure water, pure water is neutral.

        If [H3O+1] were > [OH-1] then the solution would be acidic. The reverse situation would yield a basic (alkaline) solution.

        Note: If the [OH-1] were greater than 10-7 the solution would be basic or alkaline i.e. values such as 10-6, or 10-5.

      3. Calculating the Concentration of Hydronium and Hydroxide Ions

        Table 16-2 page 483

        Example: The dissociation of NaOH can be represented as

        NaOH(s) ---> Na+(aq) + OH-(aq)

        i.e. one mole of sodium hydroxide yields one mole of sodium ions and one mole of hydroxide ions.

        If you had a solution of NaOH whose concentration was 1.0 x 10-2 M you would have 1.0 x 10-2 moles of sodium ions in solution and 1.0 x 10-2 moles of hydroxide ions in solution.

        Kw = [H3O+1] x [OH-1]

        Kw has a value of 1 x 10-14 M2 for aqueous solutions. That means we know two of the three variables in the above equation.

        1 x 10-14 M2 = [H3O+1] x (1.0 x 10-2 M)

        1 x 10-14 M2 / 1.0 x 10-2 M = [H3O+1]

        [H3O+1] = 1 x 10-12 M

        Note: Review rules for doing arithmetic operations using scientific notation.

        Example: Determine the hydronium and hydroxide ion concentrations in a solution that is 1.0 x 10-4 M Ca(OH)2.
        Need to write the equation to indicate what ions are produced in solution:

        Ca(OH)2 ---> Ca+2 + 2OH-1 i.e. one mole of Ca(OH)2 produces one mole of Ca+2 ions and 2 moles of OH-1 ions.

        The concentration of the solution is 1.0 x 10-4 M which means that the concentration of the Ca+2 ions is the same or 1.0 x 10-4 M and the concentration of the OH-1 ions is twice that amount or
        2(1.0 x 10-4) M.

        Kw = [H3O+1] x [OH-1]

        We know that Kw = 1.0 x 10-14 M2 and from above we indicated that the [OH-1] = 2(1.0 x 10-4) M

        Substituting into the formula we have

        1.0 x 10-14 M2 = [H3O+1] x 2(1.0 x 10-4M)

        1.0 x 10-14 M2 / 2(1.0 x 10-4 M) = [H3O+1]

        1.0 x 10-14 M2 / 2.0 x 10-4 M = [H3O+1]

        0.5 x 10-10 M = [H3O+1]

        5.0 x 10-11 M = [H3O+1]

        Homework: 16.1

    2. The pH Scale

      Way of expressing acidity/alkalinity of a solution.

      pouvoir hydrogene - hydrogen power

      pH - definition

      formula: pH = -log [H3O+1]

      common log v natural log
      purpose of logs

      power to which 10 must be raised to equal a number i.e. a log is an exponent

      e.g. if the [H3O+1] = 1.0 x 10-7 M as it does in pur water then the pH would be

      pH = -log [H3O+1] = -log (1.0 x 10-7) = -(-7) = 7 Note that the pH is the same as the exponent of 10 when the number before the x 10 is 1.

      Scale: 1--->7--->14

      figure 16-3 page 485

      pOH - definition

      pOH = -log [OH-1]

      pH + pOH = 14

      table 16-3 page 486

      Example: Calculate the pH of a solution whose [H3O+1] = 1.0 x 10-6 M.

      pH = -log [H3O+1] = -log (1.0 x 10-6) = -(-6 M) = 6

      table 16-4 page 486

      if [H3O+1] > [OH-1] then solution is acidic

      if [H3O+1] < [OH-1] then solution is basic or alkaline

      if [H3O+1] = [OH-1] then solution is neutral

      Kw is temperature dependent.

    3. Calculations Involving pH

      If either [H3O+1] or pH is known we can calculate the other.
      pH has unique significant figure
      pH is a logarithm or an exponent.

      Because of this the number to the left of the decimal only locates the decimal point. It is not included when counting significant figures. So there must be a many significant figures to the right of the decimal as there are in the number whose logarithm was fund.

      1 x 10-7 has one significant figure thus the pH must have one digit to the right of the decimal. pH = 7.0 correctly indicates the proper number of significant figures.

      Homework 16.2

      1. Calculating pH from [H3O+1]

        Sample Problem 16-2 page 487

        What is the pH of a 1.0 x 10-3 M NaOH solution?

        Given: pH = 1.0 x 10-3 M; NaOH solution; pH = ?

        [H3O+1] [OH-1] = Kw

        [H3O+1] = Kw / [OH-1]

        [H3O+1] = 1.0 x 10-14 M2 / 1.0 x 10-3M

        [H3O+1] = 1.0 x 10-11 M

        pH = -log [H3O+1]

        pH = - log (1.0 x 10-11 M)

        pH = 11.00

        since pH > 7 the solution is basic or alkaline

        Sample Problem 16-3 page 488

        What is the pH of a solution if the [H3O+1] is 3.4 x 10-5 M?

        Given: pH = ?; [H3O+1] = 3.4 x 1-5 M

        pH = - log [H3O+1]

        pH = - log (3.4 x 10-5 M)

        pH = - log (3.4) + - log(10-5)

        pH = - .53 + 5

        pH = 4.47

        Homework: 16.3

      2. Calculating [H3O+1] and [OH-1] from pH

        Given pH calculate either [H3O+1] or [OH-1]

        Note that the base of common logs is 10. Thus the antilog of a common log is 10 raised to that number.

        pH = - log[H3O+1]

        log[H3O+1] = -pH

        [H3O+1] = antilog (-pH)

        [H3O+1] = 10-pH

        e.g. if the pH = 2 then [H3O+1] = 10-2 M

        e.g. if pH = 0 then [H3O+1] = 1 since 100 = 1

        Sample Problem 16-4 page 489

        Determine the hydronium ion concentration of a aqueous solution that has a pH of 4.0.

        Given: [H3O+1] = ?; aqueous solution; pH = 4.0

        pH = - log [H3O+1]

        log [H3O+1] = - pH

        [H3O+1] = antilog (-pH)

        if your calculator does not do antilogs use
        [H3O+1] = 1 x 10-pH

        [H3O+1] = 1 x 10-pH

        [H3O+1] = 1 x 10-4 M

        Since pH is less than 7 the solution is acidic.

        Sample Problem 16-5 page 490

        The pH of a solution is measured and determined to be 7.52.
        a) What is the hydronium ion concentration?
        b) What is the hydroxide ion concentration?
        c) Is the solution acidic or basic?

        Given: pH = 7.52; [H3O+1] =?; [OH-1] = ?; acidic or basic?

        pH = - log [H3O+1]

        log [H3O+1] = -pH

        [H3O+1] = antilog (-pH) = antilog (-7.52)
        if your calculator does not do antilogs use
        1.0 x 10-7.52 =

        3.0 x 10-8 M H3O+1

        [H3O+1] [OH-1] = Kw = 1.0 x 10-14
        [OH-1] = 1.0 x 10-14 / [H3O+1]
        [OH-1] = 1.0 x 10-14 / 3.0 x 10-8 M
        [OH-1] = 3.3 x 10-7 M OH-1

        pH given as 7.52 which is greater than 7, thus the solution is basic.

        Homework: 16.4

      3. pH Calculations and the Strength of Acids and Bases

        Table 16.5 page 491

        Strong acid v weak acid

        strong base v weak base

        For weak species, you cannot use Molarity to determine the pH since not all of the particles form ions when in solution. Need to measure the pH using instruments.

        From the data in the table determine the strong species and the weak species.

        Homework 16.5

  2. Determining pH and Titrations

    1. Indicators and pH Meters

      Acid Base indicators - definition

      Used to get approximate pH of a solution.

      Color change comes from the indicator acting as either a weak acid or a weak base:

      HIn = H+1 + In-1

      The H+1 is the weak acid part and In-1 is the anion part of the indicator.
      The HIn and the ions on the right of the equation are different colors.

      The In ion accepts the H+1 from the acid and forms HIn and has its acid color e.g. for litmus is red.

      In basic solutions, the OH-1 ions combine with the H+1 ions of the indicator which leaves mainly In-1 ions in solution and this produces the base color which for litmus is blue.

      Figure 16-4 page 493

      Figure 16-5 page 494

      pH paper - paper soaked in a mixture of indicators.

      Many different indicators.

      pH range of color change for each is different.

      Transition interval - definition.

      Table 16-6 page 495

      Indicators that change color below 7 are stronger acids than the other types of indicators. e.g. methyl orange

      pH meter - definition

      Figure 16-6 page 494

    2. Titration

      A neutralization reaction is a reaction between an acid and a base. The acid provides the hydronium ion and the base provides the hydroxide ion.

      Summarized by
      H3O+1 (aq) + OH-1 (aq) ---> 2 H2O (l)

      Note: one hydronium ion combines with one hydroxide ion. When equal amounts of hydronium and hydroxide ions are mixed from an acid and a base, the resulting solution is neutral.

      One liter of 0.10 M HCl contains 0.10 mol of hydronium ions.

      One liter of 0.10 M NaOH contains 0.10 mol of hydroxide ions.

      Mix the one liter of each and you get a neutralization reaction in which the products are NaCl + H2O. This solution is neutral.

      The progressive addition of an acid to a base (or visa versa) can be used to compare the concentrations of the acid and the base.

      Titration - definition

      Used to determine the chemical equivalent volumes of acidic and basic solutions.

      Figure 16-7 page 497

      Burets are used to carry out a titration.

      1. Equivalence Point

        Equivalence point - definition

        Use either indicators (most common) or pH meters (most accurate) to determine.

        pH meter shows large voltage change at equivalence point.

        Indicator permanently changes color.

        Figure 16-8 page 498

        End point - definition

        Different indicators change colors at different pH’s.

        Table 16-6 page 495 -- note pH (black horizontal line) for each indicator and strength of both acid and base.

        No good indicator for weak acid/weak base because the relative strengths of the reactants may vary greatly.

        Usually add base to acid i.e. going from low pH to higher pH.

        Change in pH is slow then rapid through the equivalence point then slowly after that.

        Figure 16-9 page 499

    3. Molarity and Titration

      Note: We use only one buret at our locker and use one buret from the side table -- saves solution and possible contamination.

      Note: We never use an eye dropper to add phenolphthalein -- bottles are special dropper bottles -- never put anything into these bottles.

      For our purposes, the buret at our place contains the solution of known concentration -- the standard solution.

      Standard solution - definition.

      Usually carry out a titration until you have three results that agree within 0.05 mL.

      Need to fill buret to approximately ( not above) the zero mark with the base.

      Fill tip with solution.

      Read volume of buret.

      Record as initial volume of solution.

      To a clean dry flask add measured amount of acid from side table (need initial reading and then final reading to get accurate volume).

      Take flask to your place and add indicator.

      Add base from your buret to flask, with swirling, slowly, until a permanent color change takes place. You know you are getting close to the permanent color change when you see a color change but continued swirling makes the color disappear.

      Take a final reading from your buret. Subtracting the initial and final reading tells you the exact volume of base you used.

      Do the calculations.

      Sample Problem 16-6 page 502

      In a titration, 27.4 mL of a 0.0154 M Ba(OH)2 is added to a 20.0 mL sample of HCl solution of unknown concentration. what is the molarity of the acid solution?

      Given: 27.4 mL base; 0.0154 M Ba(OH)2; 20.0 mL of HCl used; M of HCl = ?

      Balanced equation:

      Ba(OH)2 + 2HCl ---> BaCl2 + 2 H2O
      1 mol + 2 mol ---> 1 mol + 2 mol

      a) for Barium hydroxide: (molarity) x (volume) x (1 L / 1000 mL) = mol
      (0.0154 mol Ba(OH)2 / L) x (27.4 mL Ba(OH)2) x (1 L / 1000 mL) = 4.22 x 10-4 mol Ba(OH)2

      b) (molar ratio from balanced equation) x (mol Ba(OH)2 from a)) = mol HCl
      (2 mol HCl / 1 mol Ba(OH)2) x (4.22 x 10-4 mol Ba(OH)2) = 8.44 x 10-4 mol HCl

      c) (mol HCl / vol HCl) x (1000 mL / 1 L) = (mol HCl / 1 L) = M
      (8.44 x 10-4 mol HCl / 20.0 mL) x (1000 mL / 1 L) = (4.22 x 10-2 mol HCl / 1 L) = 4.22 x 10-2 M HCl

      Homework: 16.6

      end of notes

      Titration is the controlled addition and measurement of the amount of a solution of known concentration required to react completely with a measured amount of a solution of unknown concentration.

    Equivalence point is the point at which the two solutions used in a titration are present in chemically equivalent amounts .

    End point of an indicator is the point in a titration at which an indicator changes color.

    Standard solution is the solution that contains the precisely known concentration of a solute.

    Self ionization of water involves the transfer of a proton (H+1) from one water molecule to another to form hydronium ion and a hydroxide ion.

    pH of a solution is defined as the negative of the common logarithm of the hydronium ion concentration.

    pOH of a solution is defined as the negative of the common logarithm of the hydroxide ion concentration.

    Acid base indicators are compounds whose colors are sensitive to pH.

    The transition interval is the pH range over which an indicator changed color.

    pH meter determines the pH of a solution by measuring the voltage between the two electrodes that are placed in the solution.