- at 25^oC,  [H₃O⁺] =  [OH^-] = 1.0 x 10^-7 M

Animation: Self-ionization of water

  C.     pH & pOH scales- measures the relative strength of an acid or base based on hydrogen ion concentrations.  pH scale was derived by Soren Sorensen

            Paper by S.P.L. Sorenson, Biochemische Zeitschrift (1909)

    1. Identifying pH and pOH       

           pH = -log [H₃O⁺]      and     pOH = -log [OH^-]

       - In any solution, the concentrations of  [H₃O⁺] &  [OH^-] are inversely proportional

Animation:  Relating pH to [H⁺]

Practice: Assessing pH of common materials

    2. Measuring pH & Acid/Base Indicators

      a. pH meters- utilize electrical potentials within a solution to measure pH. 

      b. Indicators:  Acid-Base indicators are dyes that are themselves weak acids and bases.  However, the conjugate 

          acid-base forms of the dye have different colors.  The actual chemical structures of the dyes is often quite complex; 

          however, we can use the generic symbol for the indicator as HIn.  The Bronsted-Lowry equation for the indicator is:

         -Adding acid (increasing [H₃O⁺]) would shift the equilibrium back to HIn 

         -Adding base (decreasing [H₃O⁺]) would shift the equilibrium to In^-

Image: Indicators & their color changes

Activity: Making your own pH indicator from cabbage. Anthocyanins in cabbage produces the purple color

  D. Strength of Acid or Base

      Dissociation constants (K_a & K_b)- measures the amount of ionization of an acid or base.

    1. For strong electrolytes: ( like strong acids)

             ex. 

             So    >> 1 (much larger than one)

            This says that in solution, the prevalent forms are  H₃O⁺  and Cl^-

       a. Calculating pH.  Strong acids are defined as those that completely ionize (or nearly).

          The [ H₃O⁺ ] is invariably equal to [ HA ].

          So if pH = -log [ H₃O⁺ ] then for a strong acid the pH = -log [ HA ]

          ex. Find the pH of a 0.015 M HCl solution

             pH = -log [ H₃O⁺ ]  =  -log [ HCl ]  =  -log (0.015)  =  1.82

          ** The number of sig. figs. in the concentration is equal to the number of decimal places right of the decimal

practice: Finding pH of strong acids/bases -- answers

   2. Weak Electrolytes.  Do they strongly dissociate?

          ex.  Acetic Acid:      CH₃COOH  +  H₂O   --> CH₃COO^-    +  H₃O⁺

           but with weak electrolytes, [H₂O] remains very large and almost unchanged. IGNORE IT

                K_eq  [H₂O]   =      =    1.74 x 10^-5 at 25^oC

         a. Calculating pH. Weak acids only partially ionize so [ H₃O⁺ ] is not equal to [ HA ].

           -To calculate the pH of weak acid or base, you must consider the K_a for the acid & K_b for the base

table: Strength of Acids/Bases with conjugates.

table: K_a & K_b values for common acids & bases

          ex. Calculate the pH of 0.015 M Acetic Acid (CH₃COOH). Construct a table to include concentrations at two

            points: initial (pre-ionization, [ ]_o) and final (post-ionization, [ ]_i) along with changes in concentrations

           Solution:   K_a  =  [CH₃COO^-] [H₃O⁺]       ===>     1.74 x 10^-5 =    (x  *  x)            

                                         [CH₃COOH]                                                   (0.015 - x)

           --If the K_a << 1, assume the change in initial acid concentration is not significant, so  (0.015 - x)   ~ 0.015

             so  1.74 x 10^-5 =    (x  *  x)     ===>   (1.74 x 10^-5) (0.015)  =  x²   ===>  x = 5.11 x 10^-4 M

                                                0.015                          

             pH  =  -log (5.11 x 10^-4)  =  3.29

       b. 5% Rule- As long as a weak acid or base is less than 5% ionized, then the change in initial acid/base concentration can be

            ignored.  If the ionization is greater than 5%, then the change in initial acid/base concentration must be included.

       c. Henderson-Hasselbalch Equation.

        -re:  K_a is an equilibrium expression which relates the concentrations of unionized acid with concentrations of the conjugate

               base and hydronium.  This expression can be modified to calculate the pH of any acid/base solution knowing the

               concentrations of acid and conjugate base.

practice: pH including weak acids worksheet -- answers

 3. Factors that affect the strength of an acid. Resource

     a. Polarity and strength of H-A bond.

A more polar and/or weaker H-A bond creates greater acidic properties.

Greater polarity creates larger positive charge on the hydrogen and thus more likely the H⁺ is willing to be pulled away by bases/electron donors.

b. Conjugate base stability

An anion that is stable in water (doesn't pull H⁺ back due to weak or highly polar H-A bond) is a neglible base, therefore has a strong conjugate acid.

Low charge density can increase the stability of a conjugate base, commonly due to size of the anion or resonance of charge within a polyatomic anion.

c. For oxyacids, a central atom that has a larger electronegativity or a higher oxidation state creates a stronger acid. See Table of Acid/Base strengths

d. For carboxylic acids, peripheral atoms with high electronegativity can affect the -COO-H bond strength. This is called inductive effect.

E. Acid/base neutralization

  1. Acid/base neutralization reactions are double replacement reactions (metathesis) that are driven by the production of water. A soluble salt is the

      other common product.

    Ex. HCl_(aq)  +  NaOH_(aq) --> H₂O_(l)  +  NaCl_(aq)

         acid            base                water        salt

    Note: An acid neutralizes a base and vice versa but the result isn't necessarily a neutral solution. The strength of the acid/base can affect the equilibrium

             and consequently affect the pH of the solution.

 2.  Acid-Base properties of salts

The identify of the cation (conjugate of base) and anion (conjugate of acid) can determine the acidic/basic properties of a salt solution.

a. Neutral salts are formed from cations and anions that don't affect the equilibrium of water, thus are negligible in their acidic/basic characters.

b. Basic salts contain anions that are conjugates of weak acids, therefore as weak bases will affect the equilibrium of water by binding with H⁺.

c. Acidic salts commonly contain cations that increase H₃O⁺ in solution.

    Ex. NH₄Cl(aq) is an acidic salt due to the ammonium being a conjugate of a weak base.

    Ex. FeCl₃(aq) is an acidic salt due to the ferric ion forming a complex ion with water.

  3. Titrations

    An acid/base titration is a procedure used to find the concentration of an unknown acid or base. This involves three basic steps

        1. Start with a specific volume of an acid or base with an unknown concentration

        2. Add a acid/base indicator to the solution with the unknown concentration

        3. Add the corresponding acid/base in a drop-wise fashion until a color change occurs. This represents the inflection point of a titration curve, which

            is the endpoint. At this point, the moles of acid equals the moles of base.

practice: Buffers worksheet -- answers