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Weak Acid Equilibrium

When an uncharged weak acid is added to water, a homogeneous equilibrium forms in which aqueous acid molecules, HA(aq), react with liquid water to form aqueous hydronium ions and aqueous anions, A-(aq). The latter are produced when the acid molecules lose H+ ions to water.

HA(aq)  +  H2O(l)   Double arrow   H3O+(aq)  +  A-(aq)

In writing an equilibrium constant expression for this homogeneous equilibrium, we leave out the concentration of the liquid water. The equilibrium constant for this expression is called the acid dissociation constant, Ka.

Image of the general form of the acid dissociation constant expression, Ka equals the H3O+ concentration times the A- concentration divided by the HA concentration 

= acid dissociation constant

When the equilibrium in question occurs in solution, the chemical formulas enclosed in brackets in the equilibrium constant expression represent the molarities of the substances (moles of solute per liter of solution).

Remember that H+ can be used to represent H3O+, thus simplifying our depiction of the reaction between a weak acid and water and its acid dissociation constant expression:

HA(aq)   Double arrow   H+(aq)  +  A-(aq)

Image of the general form of the acid dissociation constant expression, Ka equals the H+ concentration times the A- concentration divided by the HA concentration 

= acid dissociation constant

For example, acetic acid is a weak acid, because when it is added to water, it reacts with the water in a reversible fashion to form hydronium and acetate ions.

HC2H3O2(aq) + H2O(l)   Double arrow   H3O+(aq) + C2H3O2-(aq)

or  HC2H3O2(aq)   Double arrow   H+(aq) + C2H3O2-(aq)

Image of the acid dissociation constant expression for acetic acid, Ka equals the H+ concentration times the C2H3O2- concentration divided by the HC2H3O2 concentration 

= 1.8 × 10-5

 

EXAMPLE 1 - Writing an Acid Dissociation Constant: Write the equation for the reaction between the weak acid nitrous acid and water, and write the expression for its acid dissociation constant.

Solution:

HNO2(aq)  +  H2O(l)   double arrow   H3O+(aq)  +  NO2-(aq)

Image of the the acid dissociation constant expression for nitrous acid, Ka equals the H3O+ concentration times the NO2- concentration divided by the HNO2 concentration

or  HNO2(aq)   Double arrow   H+(aq) + NO2-(aq)

Image of the simpler acid dissociation constant expression for nitrous acid, Ka equals the H+ concentration times the NO2- concentration divided by the HNO2 concentration

 

The table below lists acid dissociation constants for some common weak acids. These Ka values can be used to describe the relative strength of the acids. A stronger acid will generate more hydronium ions in solution. A larger Ka indicates a greater ratio of ions (including hydronium ions) to uncharged acid. Therefore, a larger Ka indicates a stronger acid. For example, the larger Ka for chlorous acid (1.2 × 10-2) compared to acetic acid (1.8 × 10-5) tells us that chlorous acid is stronger than acetic acid.

 

Acid Dissociation Constants, Ka, for Common Weak Acids

 

Weak Acid

Equation

Ka

acetic acid

HC2H3O2   Double arrow   H+  +  C2H3O2-

1.8 × 10-5

benzoic acid

C6H5CO2H  
               Double arrow   H+  +  C6H5CO2-

6.4 × 10-5

chlorous acid

HClO2   Double arrow   H+  +  ClO2-

1.2 × 10-2

formic acid

HCHO2   Double arrow   H+  +  CHO2-

1.8 × 10-4

hydrocyanic acid

HCN   Double arrow   H+  +  CN-

6.2 × 10-10

hydrofluoric acid

HF   Double arrow   H+  +  F-

7.2 × 10-4

hypobromous acid

HOBr   Double arrow   H+  +  OBr-

2 × 10-9

hypochlorous acid

HOCl   Double arrow   H+  +  OCl-

3.5 × 10-8

hypoiodous acid

HOI   Double arrow   H+  +  OI-

2 × 10-11

lactic acid

CH3CH(OH)CO2H  
    Double arrow   H+  +  CH3CH(OH)CO2-

1.38 × 10-4

nitrous acid

HNO2   Double arrow   H+  +  NO2-

4.0 × 10-4

phenol

HOC6H5   Double arrow   H+  +  OC6H5-

1.6 × 10-10

propionic acid

CH3CH2CO2H  
         Double arrow   H+  +  CH3CH2CO2-

1.3 × 10-5

   

The following study sheet describes one procedure for calculating the pH of solutions of weak acids. If you take other chemistry courses, you will find that there are variations on this procedure for some weak acid solutions.

 

Study Sheet - Calculating pH for Weak Acid Solutions

Tip-off - You are given the concentration of a weak acid solution and asked to calculate its pH.

General Steps -

STEP 1 Write the equation for the ionization of the weak acid in water.

HA(aq)   Double arrow   H+(aq) + A-(aq)

STEP 2 Write the Ka expression for the weak acid.

Image of the general form of the acid dissociation constant expression, Ka equals the H+ concentration times the A- concentration divided by the HA concentration

STEP 3 Describe each equilibrium concentration in terms of x.

x = [H+]equilibrium = [A-]equilibrium

[HA]equilibrium = [HA]initial - x

STEP 4 Assume that the initial concentration of weak acid is approximately equal to the equilibrium concentration. (Weak acids are rarely ionized to a large degree. We can most often assume that the initial concentration added, [HA]initial is much larger than x. Thus, the equilibrium concentration is approximately equal to the concentration added. You may learn how to deal with weak acid solutions for which this approximation is not appropriate in other chemistry courses.)

[HA]equilibrium = [HA]initial

STEP 5 Plug the concentrations described in terms of x into the Ka expression, and solve for x.

Image of the general steps for doing weak acid equilibrium problems

 

EXAMPLE 2 - pH Calculations for Weak Acid Solutions: Vinegar is a dilute water solution of acetic acid with small amounts of other components. Calculate the pH of bottled vinegar that is 0.667 M HC2H3O2, assuming that none of the other components affect the acidity of the solution.

HC2H3O2(aq)   Double arrow   H+(aq) + C2H3O2-(aq)

We get the value for the acid dissociation constant for this reaction from the table above.

Image showing the steps of this problem

x2 = 1.2 × 10-5 x = 3.5 × 10-3

[H+] = 3.5 × 10-3 M H+       pH = -log(3.5 × 10-3) = 2.46