Acids and Bases

 

Conjugate Acid-base pairs

 

According to the Brønsted definition, an acid is a substance capable of donating a proton, and a base is a substance capable of accepting a proton.  This means that all Brønsted bases must possess a lone pair of electrons, in order to form a bond to the proton they are accepting. 

 

An extension of this definition is the concept of conjugate acid-base pairs, which are defined as an acid and its conjugate base or a base and its conjugate acid.  They differ from each other by a proton.  For example, when HCl (g) is mixed with water, the following reaction occurs:

The species giving up the proton is HCl, an acid.  The species accepting the proton is water, the base.  The species Cl- is the conjugate base of HCl. They differ only by a proton.   H3O+ is the conjugate acid of H2O. 

 

Another example is the reaction of nitrous acid and water:

 

Acids

 

Some acids are better proton donors than others.  The strength of an acid can be measured by the fraction of the acid molecules that undergoes ionization (loses a proton).  Strong acids are those that ionize completely in water, that is, they give up their protons completely.  In the examples above, HCl is a strong acid.  Its reaction with water goes to completion.  It is not an equilibrium process.  HCl is converted completely to Cl-.  This is because the conjugate base, Cl-, has virtually no tendency to gain a proton, so there is no reverse reaction.  The stronger an acid , the weaker its conjugate base. 

 

Weak acids are those that only partly dissociate in water.  HNO2, shown above, is an example.  In its reaction with water, there is an equilibrium mix of all of the species, HNO2, H2O, NO2- and H3O+.  The conjugate base of this weak acid, NO2- , is a weak base, with some ability to gain protons, so the reverse reaction will proceed to some extent.  The weaker an acid, the stronger its conjugate base.  An equilibrium constant, Ka, can be used to describe this process. 

 

 

It will follow all of the rules that we developed for equilibrium processes (Le Chatelier).  There is a list of the Ka values for a number of weak acids on page 628 of the textbook.  The larger the equilibrium constant, the more complete the dissociation of the acid, the stronger the acid. 

 

The strong acids are HCl, HBr, HI, and the oxyacids, HNO3, HClO4 and H2SO4.  Their conjugate bases, Cl-, Br-, I-, NO3-, ClO4- and HSO4- have negligible activity as bases, no tendency to gain protons. 

 

H3O+ is the strongest acid that can exist in aqueous solutions.  Acids stronger than H3O+ react completely with water to form H3O+ and their conjugate bases.

 

We can think of proton transfer reactions as being governed by the relative ability of two acids to transfer protons.  This can be shown by the reaction between an acid, HA and water.

 

We can compare the strength of acid1 and acid2.  If HA is a stronger acid than H3O+, the HA will transfer its proton to water more effectively than H3O+ will transfer its proton to A-.  The equilibrium will lie far to the right, so far, that it will no longer be considered an equilibrium process.   If HA is a weaker acid than H3O+, the reverse reaction will have a stronger tendency to take place, an equilibrium will be established. 

 

As demonstrated in the examples, above, the H+ ion (proton) released by the acid is hydrated in aqueous solutions.  The reaction between water and H+ is usually represented as:

 

H+ (aq) + H2O (l) H3O+ (aq)

 

The proton may be associated with more than one water molecule.  It can be written as H+, H3O+or H7O4+, to show the high degree of hydrogen bonding.  We will usually refer to it as H+, but writing it as H3O+ demonstrates that water is a Brønsted base. 

 

Bases

 

Shown below is the reaction between ammonia, NH3, and water. 

 

 

 

 

The strongest acid that can exist in aqueous solutions is H3O+.  The strongest base that can exist in aqueous solutions is OH-, the hydroxide ion.  In the reaction between ammonia, NH3 and water, ammonia is a base that accepts a proton from water to form the ammonium ion, NH4+, its conjugate acid.  As shown, this is an equilibrium reaction.  Ammonia is a weaker base than OH-, so the equilibrium will lie to the left. 

 

There are relatively few common strong bases.  The most common strong bases are the soluble ionic hydroxides of the alkali metals (Group I) and the alkaline earth metals (Group II), like NaOH, KOH and Ca(OH)2.   Strongly basic solutions are also created by substances that react with H2O to form OH-.  The most common of these is the oxide ion, O2-..

 

 

O2-  is a stronger base than OH-, and the reaction will proceed completely to the right. 

                            

Water

 

In addition to its other unique properties, water is also interesting because it can act both as a Brønsted acid and base.  In fact, water, itself undergoes ionization, to a small extent.

 

H2O (l) H+ (aq) + OH- (aq)

 

These represent conjugate acid-base pairs.  In studying acid/base reactions in aqueous solutions, an important quantity is the concentration of hydrogen ions (H+ or H3O+).  In pure water, only a small fraction of the water molecules actually exist as ions.  Water is a very weak electrolyte and conducts electricity poorly.  The equilibrium expression for water is given by:

 

 

Because so very little of the water actually dissociates, the [H2O] is constant, this is written as:

 

Kw = [H+] [OH-]

 

This is called the ion-product constant and represents the concentrations of H+ and OH- at a particular temperature.  At 25oC, in pure water, [H+] =[OH-] = 1.0 x 10-7 M. 

Kw = [H+] [OH-] = 1 x 10-14

 

Whenever the [H+] = [OH-], the solution is said to be neutral.  In acidic solutions, there will be an excess of H+ and [H+] > [OH-].  In basic solutions, there will be an excess of OH-, [OH-] > [H+].  We can change the concentration of either of these ions in solution, but we can't change one without changing the other, in aqueous solutions.  This is just another example of Le Chatelier's Principle.  If we have an H+ concentration of 1 x 10-3 M, we can calculate the concentration of OH-. 

 

Kw = 1 x 10-14 = [1 x 10-3 M] [OH-]

[OH-] = 1 x 10-11 M

 

Since Kw is an equilibrium constant, its value will change with temperature.  At 25oC, it will always be 1 x 10-14. 

 

pH Scale

 

Since the concentrations of H+ and OH- are so small, it is often convenient to have another way of expressing their values.  This was introduced by the Danish biochemist, Sorensen, as pH.  It is defined as:

 

pH =  - log [H+]

 

Like the equilibrium constant, K, pH will be unitless.  So, solutions can be described by their H+ concentrations. 

 

 

A scale analogous to the pH scale has been devised for bases, pOH.  It is defined as:

 

pOH = - log [OH-]

Looking again at the ion-product constant for water:

 

[H+] [OH-] = 1.0 x 10-14

 

we can take the negative logarithm of both sides and get:

 

- (log [H+] + log[OH-]) = - log (1.0 x 10-14)

 

pH + pOH = 14.00

 

pH Calculations

 

We can now calculate the pH of solutions of acids or bases.  This is most easily done for the strong acids and bases.  In these cases, the reactions go to completion.  The strong acid will dissociate completely, forming H3O+ and its conjugate base.  If we add 2.00 moles of HCl to 1.00 L of water, we can calculate the pH of the resulting solution as follows:

 

2.00 moles HCl " 2.00 moles  H+ (aq)  since it is a strong acid, and dissociates completely.

 

[H+] = 2.00 mol H+  = 2.00 M

            1.00 L

 

pH = - log [H+] = - log (2.00) = -0.31

 

The pH is negative in this case.  It will be negative whenever the [H+] is greater than 1.0 M.

 

If we add 0.200 moles of HClO4 to 1.00 L of water, what is the pH of the solution?  Again, this is a strong acid, which dissociates completely. 

 

[H+] = 0.200 mol H+ = 0.200 M

             1.00 L

 

pH = - log (0.200) = 0.70

 

If we add 2.00 x 10-4 mol of HNO3 to 1.00 L water, what is the pH?  It is a strong acid.

 

[H+] = 2.00 x 10-4 mol = 2.00 x 10-4 M

            1.00 L

pH = - log (2.00 x 10-4) = 3.70

 

As the concentration of  H+ increases, the pH decreases. 

 

What is the concentration of OH- in each of these aqueous solutions? 

 

To calculate this, use either relationship, pH + pOH = 14, or  Kw = 1 x 10-14 = [H+] [OH-], to calculate pOH or [OH-]. 

 

If the [H+] = 2.00 M, 1 x 10-14 = [2.00] [OH-]  and [OH-] = 5.00 x 10-15 M and pOH = 14.3

 

What is the pH of a solution made by dissolving 2.00 x 10-8 mol of  HBr in 1.00 L of water.  Again, this is a strong acid, which dissociates completely. 

 

[H+] = 2.00 x 10-8 mol H+ = 2.00 x 10-8 M

             1.00 L

 

pH = - log (2.00 x 10-8) = 7.70

 

This result should seem odd to you.  We are adding an strong acid to water, and getting a basic solution?  In fact, this is not the pH of the solution.  At this concentration, HBr provides fewer H+ than the autoionization of water. 

 

1.00 x 10-14 = [ H+] [OH-]

[H+] = 1.00 x 10-7 M

 

So, the [H+] = 1.00 x 10-7M and the pH = 7.0, a neutral solution.