14. Equilibria of weak acids and bases 

pH of weak acids and bases, ion product constant of water, hydrolysis, buffers, titration curve, indicators

Dissociation equilibrium constant for acids:

·               always mol/l

·               always standard conditions

·               AcH ⇌ Ac- + H+

·               or in water: AcH +H2O = Ac- + H3O+

·               both can be used

·       

·               if Ka is large than it is a strong acid

·               if Ka is close to 0 the acid is weak

pH of weak acids and bases

·               we can’t directly calculate it from the initial concentration of the acid/base

·               weak acids and bases dissociate only partially, so there is remaining acid/base in the solvent (water)

·               we have to write down the equilibrium equations and calculate pH from there using KA/Kb

·               for example for acetic acid Ka=10-5 we have c=0,1 mol/l, let’s calculate the pH
                                    AcH                              ⇌Ac-                                          + H+

AcH

Ac-     

H+

i

0,1

0

0

c

-x

+x

+x

e

0,1-x

x

x

            Ka=10-5=x2/0,1-x
            if we solve this for x we get the equilibrium concentration of H+ and we can calculate         the pH from there

·       there is a way to approximate → (x=c*Ka)1/2

·       same is true for weak bases but we get pOH first instead

Ion product constant for water

·       we can do the same thing as before but for water

·       the concentration of water in a liter of water is 55,5 mol/l

o   1l is 1000 cm3, water has a density of 1 g/cm3 so 1000 cm3 is 1000g, a 1000g divided by the molar mass of water (18 g/mol) is 55,5 moles

·       Ka for water is 1,8*10-16 →it is a much weaker acid than acetic acid

            H2O ⇌ H+ + OH-

·       we will use the approximation method to find x=(55,5*1,8*10-16)1/2

·       that means x2 is 10-14 which is the ion product constant for water              

(Kw=10-14=[H+][OH-])

·       this also means that both the pH and the pOH are 7 so their sum is 14

(pH+pOH=14)

·       for solutions with very small concentration (less than 10-7) the protons from the         water itself also counts in the pH calculation

Hydrolysis

·       used to determine the pH of salts

·       e.g. NaCl solution

o   pH=7, according to Arrhenius no additional H+ or OH- is present

o   according to Brönsted the Cl- is a weak base so it does react with some H+ from the water to create some OH-

·       salts from a strong base and a weak acid are basic

o   e.g. NaAc, K2CO3

·       salts from a strong acid and a weak base are acidic

o   e.g. NH4Cl

·       we have some NaAc solution with a concentration of 0,1 M and K=10-5

·       some Ac- picks some protons up: AcH ⇌ Ac- + H+

·       Khydrolysis=KAcH/Kw =[Ac-]/[AcH][OH-], because the proton concentrations cancel each other (Kw==[H+][OH-], KAcH = [Ac-][H+]

·       from here we can write the equation for the hydrolysis (the water reacts in equilibrium with the ion of the weak acid/base) and calculate the pH using KAcH and             Khydrolysis

Buffers

·       weak acids have undissociated protons (since they dissociate in an equilibrium     reaction)

·       these protons can be removed by the addition of base (Le-Chatelier-Braun)

·       the salt of a weak acid + strong base is basic so it has proton affinity (Brönsted)

·       if both the weak acid and its salt are present the pH change from the addition of proton or base will be softened
           

·       the solution where both the weak acid and its salt with a strong base are present are called buffer solutions   

·       The formula to calculate the H+ concentration in a buffer is the following:

o       

·       acid is the measured acid

·       salt is the measured salt but only in case of buffers, since this formula comes           from KAcH:

o     

o       

o       

Limitations:

·       both components need to be present

·       the solution can’t be too dilute


Buffer capacity

1 liter water

pH

pH(+0.1 M HCl)

-

7

1

0.1 M AcH/NaAc

5

2.9

1 M AcH/NaAc

5

4.9

·       The amount (mol) of a strong acid/base needed for a unit of pH change for
1 dm3 buffer solution, considering no change in volume

·       There is a pH range, where upon proton addition or removal the pH change is        very minor (this is related to the dissociation constant of the acid)

o   the higher the concentration of the buffer solution, the stronger the softening power is


Titration curve
            The KAcH formula can also be rearranged to get this ratio:
           
           
            -This means that if KAcH > [H+] → Ac- > HAc → the acid is more present as Ac-
            -also if KAcH < [H+] → Ac- <HAc  → the acid is more present as Hac
            -This relation can be represented on a c-pH graph like this:  (pK= -log10K)
           
            -at pK the concentration of Hac and Ac- is 50%-50%
            -we can use an indicator that has different colors for the pH of Ac- and Hac so the     graph can look like this:
           

            Titration curve for two base acids:
           

            -at pK1 the concentration of H2Ac and HAc- are 50%-50%
            -at pK2 the concentration of HAc- and Ac2- are 50%-50%
            -(Pl=e.g.)

            Titration curve for phosphoric acid(three base acid):
           

Indicators
            -they are used to determine the pH of mixtures
            -indicators have transient regions, they change color in specific pH ranges
            -important pH ranges:


            (just some examples are needed on the exam)
Universal indicator:  

            -a mixture of multiple indicators, made so that each pH unit has its own color
            -the universal indicator needs to have a scale so we can determine what pH the color of it represents
            -it is a mixture of methyl red, phenolphthalein, Bromo-thymol blue, thymolblue