Chemistry Honors/AP

WebLecture

## Acids and Bases, Round 2

#### Outline

The theoretical side of physical chemistry is and will probably remain the dominant one; it is by this peculiarity that it has exerted such a great influence upon the neighboring sciences, pure and applied, and on this ground physical chemistry may be regarded as an excellent school of exact reasoning for all students of the natural sciences.

Svante Arrhenius, Theories of Solutions 1912

### Acids and Bases

#### Characteristics of acids and bases

Long before Arrhenius identified acids as increasing the count ofH+ ions, chemists identified certain substances as "acid" if, when dissolved in water, they produced a solution that tasted sour, and reacted with bases or certain metals to form salts. Bases, on the other hand, were bitter rather than sour, but when mixed with fats would make soap. Of particular interest to alchemists during the Renaissance was "Aqua Regia", a mixture of nitric and hydrochloric acid that could dissolve the least reactive of all substances, gold.

If an acid and a base were dissolved together and solution, they neutralized one another, creating created a salt that could be recovered if the water of the solution was evaporated.

As early as the 14th century, chemists used a dye called litmus, made from lichen, to distinguish between acids and bases. Paper stained with this dye would turn red in the presence of acids, and blue in the presence of bases. Originally, chemists propose that oxygen, already known as a highly reactive substance, was responsible for the characteristic behavior of acids, but some acid-like substances did not contain oxygen. Eventually in the 19th century chemists established that hydrogen was the characteristic element found in all acids.

Arrhenius defined acids as substances that increase the hydrogen ion H+ in a solution; bases increase the hydroxide ion OH- in solution. This definition worked very well for many substances traditionally identified as acids. Most of these substances contain hydrogen, and increase the hydrogen ion count in solution by dissolving and separating from the their own H+ ion. For example, in water, HCl dissociated into hydrogen ions and chlorine ions, increasing the number of hydrogen ions in solution. Similarly, well-known bases such as lye (sodium hydroxide, NaOH) increased the number of hydroxide ions when dissolved in water by separating from the hydroxide ion they contained.

HCl → H+ + Cl-

NaOH → Na+ + OH-

We can now explain the neutralization of an acid and base is the rearrangement of the acid anion and the base cation together, making a salt, and the hydrogen ion and hydroxide ion forming a water molecule.

HCl(aq) + NaOH(aq) → H2O(l) + NaCl(aq)

##### There's a problem with Arrhenius' definitions.

Arrhenius' explanation didn't always correctly identify acids and bases in every situation. While most acids increase the hydrogen ion concentration by releasing an H+ ion they contain, and bases increase the hydroxide concentration by releasing the OH- ion they contain, it's also possible to increase a ion concentration by splitting a water molecule and then consuming one of the ions. This is how ammonia works:

NH3 + H2O → NH4+ + OH-

Ammonia reacts with the water molecule, splitting it into H+ and OH-, thin fuses with the hydrogen ion, leaving the hydroxide ion free, and increasing the hydroxide ion count. Because it increases the hydroxide ion concentration, it fits the definition of an Arrhenius base.

Now consider an acid-base reaction involving ammonia as the base. In the reaction between ammonia and hydrochloric acid, there is no component with a hydroxide ion. If however we consider the intermediate reaction of ammonia with water, we can explain the interaction of ammonia and hydrochloric acid in terms of Arrhenius acids and bases.

First, the hydrochloric acid dissociates:

HCl → H+ + Cl-

And of course, the ammonia dissociates as we discussed above.

NH3 + H2O → NH4+ + OH-

Now we add the two reactions together and eliminate species (molecules) that occur on both sides of the reaction arrows — the water molecule components. We wind up with the interaction of an acid and a base forming a new species.

HCl + NH3 + H2O → H+ + Cl- + NH4+ + OH-

HCl + NH3 + H2O → Cl- + NH4+ + H2O

HCl + NH3 → NH4Cl

So that works nicely. The problem is that we get exactly the same reaction if we combine ammonia gas with hydrogen chloride gas, where there is no "intermediate" step involving hydroxide ions. In the gas version of the reaction, the Arrhenius definition would not recognize ammonia as a base or hydrogen chloride as an acid — which makes the Arrhenius definition inconsistent. And if there's one thing a good scientist hates, it is inconsistency.

#### Hydronium

At this point, it is useful to recognize that in real water, H+ ions don't existing in isolation: they form complexes with water molecules. Modern chemists prefer to talk about hydronium, the complex formed by a water molecule with a hydrogen attached as a H-bond or H3O+, rather than H+ by itself. So you will often see [H3O+] rather than [H+], becuase it more accurately reflects what is actually going on in water. (It turns out that lots of complexes are possible with water molecules...but that's beyond the scope of this course).

#### Brønsted-Lowry to the rescue!

If we look, however, at an "acid" as a proton donor and a base as a proton acceptor, then we can account for both the solution and gas versions of the hydrogen chloride reaction with ammonia by identifying HCl as the acid (donating a proton) and NH3 as the base (accepting the proton). This tidies things up nicely by extending the identifying characteristic of "proton receptor" to some substances that don't contain and can't donate hydroxide ions, making them bases.

In proposing their solution to the ammonia-hydrogen chloride problem, however Brønsted and Lowry went a bit further and created some other useful concepts.

If an acid is a proton donor, and a base is a proton receptor, and if chemical reactions are reversible, then we can see a molecule A with its H as an acid, and a molecule A without its H as a base. We have either the dissociation of an acid to a hydrogen ion base anion (negative ion) if the reaction runs forward, or a synthesis of a base and a hydrogen ion to form an acid.

HA + H2O ⇔ A- + H3O+

In this case, the A- anion is a base made from, or conjugate to its acid partner.

Likewise, the dissociation of a base in water and its reverse reaction create a base - conjugate acid pair:

BOH ⇔ B+ + OH-

#### Amphoteric substances

As it may be apparent already, there are situations where some substances, like water, can act as both an acid and a base. These are amphoteri substances.

Water acting like an acid: H2O → H+ + OH-

Water acting like a base: H2O + H+ → H3O+

When we dissolve acids or bases in water, we need to also consider their interaction with the water molecules, as well as their interaction with each other. Water may act as a base with strong acids, or as an acid with strong bases.

### Acid-Base equilibrium constants

We now turn our attention to situations that involve acids, bases, or water acting like an acid or base, and apply the same analysis for systems that equilibrium that we used for non-acid-base reactions. The general rule for reaction quotient still applies, where K = Q at equlibrium:

$K={Q}_{\mathrm{equilibrium}}=\frac{{\mathrm{\left[C\right]}}^{c}{\mathrm{\left[D\right]}}^{d}}{{\mathrm{\left[A\right]}}^{a}{\mathrm{\left[B\right]}}^{b}}$

Consider the reaction that occurs in pure water, when some water molecules temporarily split into the hydrogen and hydroxide ion. We know this occurs, because even pure water is weekly conductive, indicating the presence of ions, which can only come from the water molecules themselves. We have the reaction (using the hydronium ion form)

2H2O(l) → H3O+(aq) + OH-(aq)

So the equilibrium constant will be

K = [H3O+(aq)][OH-(aq)]/[H2O(l)]2

But pure liquids and solids have a constant concentration of "1", so we can ignore any concentration factor that includes H2O(l). Our equation for the equilibrium constant of pure water becomes:

K = [H3O+(aq)][OH-(aq)]

From experiment, we can determine that this equilibrium constant, which we will designate with a subscript W, is equal to 10-14.

Kw = [H3O+(aq)][OH-(aq)] = 1 * 10-14

If we start with pure water, we will have an equal number of H3O+ ions and OH- ions. Neutral water therefore has concentrations [H3O+] = [OH-] = 10-7. This is actually a very small amount. Remember that these are molarity concentrations. If we have one mole = 6.022 * 1023 water molecules, then 10-7 * 6.022 * 1023 = 6.022 * 1016 molecules will be dissociated at any given moment. This is a ratio of 1016/1023. This means that 109 (one billion) molecules of water, one or two molecules will be dissociated into H+ and OH- at any time, and the H+ ion will form an H3O+ complex, affecting a second molecule. The rest remain water molecules.

### pH Notation

Because they work so much with acids and bases, chemists came up with a shorthand way of designating the concentrations of hydronium (or the hydrogen ion) and the hydroxide ion using "pH" notation:

pH = -log [H3O+]

pOH = -log [OH-]

##### Math refresher

A logarithm is a way of expressing an exponential relationship in terms of the exponent. If

In pH notation, if

Just to make things simpler, the pH ignores the negative sign:

Practice with pH

Consider an aqueous 0.0025M HCl solution. HCl is a strong acid; so all of the available HCL molecules would dissociate and we will wind up with a solution that has an excess 0.0025 M H3O+ concentration. We can alternately express this concentration as

pH = -log [H3O+] = -log (0.0025) = - (-2.60) = 2.60

Because Kw = [H3O+][OH-] = 10-14, pH + pOH = 14. So in this case, 14 - 2.6 = 11.4 = pOH.

### Salts

In chemistry, a salt is an ionic compound that is composed of the anion (negative ion) of an acid when the H+ and the cation (positive ion) of a base when the OH- is removed. The classic example is table salt:

Dissociation of hydrochloric acid: HCl → H+ + Cl- Dissociation of sodium hydroxide acid: NaOH → Na+ + OH-
Recombination of hydrogen and hydroxide ions: H+ + OH- → H2O
Recombination of acid anion and base cation: Cl- + Na+ → NaCl

Unless the anion or cation of a dissociating salt reacts with the water molecules in an aqueous solution, dissolving a salt does not result in an acid or basic solution. Anions that are the conjugate bases of strong acids don't interact with water and don't by themselves change the pH of a solution. These are neutral ions with respect to acidity. But many ions do react in solution — creating a acid or base by interacting with water. The breakup of K3PO4 results in K+ ions (no effect) and PH43-, which happen to be weakly basic, because PH43- is a base.

### Discussion Questions

• Why do definitions of a concept like "acid" change?