Acid and base chemistry is a particular form of aqueous equilibria chemistry that is important in both chemistry and biology. The reason the chemistry is so specifically different is that unlike many other chemical processes in solution, in acid/base chemistry the solvent water is an active participant in the process.

1. You put stuff in water and something happens. Water is important in the chemistry. It not only solvates the chemical species (so they are "hydrated" by water molecules), but it allows them to break apart into ions.

2. There are many different definitions of acids and bases. For most of what we discuss we will use the Brønsted Lowry definition of acid and bases. In this definition

The proton is H⁺, a hydrogen atom without an electron. The H⁺ is then a chemical species that is swapping from one molecule (the donor) to another molecule (the acceptor). This means there is never a reaction of an acid without a base. The proton always goes somewhere.

3. When you put things into water sometimes they break apart into ions to a small extent and sometimes to a large extent. The things that break apart a lot we call strong. The things that break apart a little we call weak. Much of acid/base chemistry deals with the very small concentrations that normally we would simply ignore. However, small amounts of protons can have large impacts on chemistry. So even when the concentrations are very small we need to keep track of them.

In all acid/base chemistry we are often tracking a small concentration of two ions in water. These are , water with an extra proton, H₃O⁺ , called hydronium ion. Or water minus a proton, OH^-, called the hydroxide ion. Note: often chemists are lazy and simply interchange H₃O⁺ and H⁺ in aqueous solution. H₃O⁺(aq) is more accurate, but if you see a reaction with H⁺(aq) know that this is simply a short hand that leaves out the water. Thus [H₃O⁺] means the same things as [H⁺].

Strong Acids

Strong acids are acids for which the equilibrium constant for dissociations is so large that we assume the molecules "fall apart" or dissociate 100% in water.

we assume the equilibrium constant is so large (it is more than 10⁶) that the reaction will essentially go to completion. That is when we put HCl in water, it will completely dissociate and form H₃O⁺ and Cl^-. This is what we mean by strong. We call it an acid because it is donating a proton (H⁺) to water.

Hydrochloric acid - HCl
Hydrobromic acid - HBr
HydroIodic acid - HI
Perchloric acid - HClO₄Chloric acid - HClO₃Sulfuric acid - H₂SO₄ (note only the first proton is strong)
Nitric acid - HNO₃

Strong Bases

Strong bases like strong acids dissociate 100% in water. Strong bases are not themselves proton acceptors. They form OH^- which is a proton acceptor. As such all the strong bases are ionic compounds where OH^- is one of the ions. Such compounds are called hydroxides. Not all hydroxides are strong bases since not all hydroxides are highly soluble.

Strong bases are then hydroxides for which this equilibrium constant for the solubility is assumed to be 100%. For example KOH is a strong base, thus we assume this reaction goes to completion

Lithium hydroxide - LiOH
Sodium hydroxide - NaOH
Potassium hydroxide - KOH
Rubidium hydroxide - RbOH
Cesium hydroxide - CsOH
Calcium hydroxide - Ca(OH)₂Strontium hydroxide - Sr(OH)₂Barium hydroxide - Ba(OH)₂

Note: These are all hydroxides of the group 1 metals and the group 2 metals starting at Ca and below. The others like Mg(OH)₂ are not soluble (they have small K_sp's and thus are not strong bases).

Concept Question

Which of the following is not a strong base?
(touch choices to toggle feedback on/off)

sodium hydroxide
copper(II) hydroxide
barium hydroxide
potassium hydroxide

Brønsted-Lowry Definition

The Brønsted-Lowry definition of acids and bases is that:

An acid is a PROTON donor

A base is a PROTON acceptor.

A PROTON is an "H⁺" which is a hydrogen without an electron. The H⁺ swaps places between two different molecules (the donor acid and the acceptor base).

This idea that the proton is swapping place is a powerful way to view chemistry. Acid/Base compounds can be found in one of two forms. Either with the proton on the molecules, "the protonated form". Or with the proton off the molecule, "the de-protonated" form". The protonated form of the molecule is the acid form. The deprotonated form is the base form. Therefore each compound can be both an acid and a base depending on whether it is protonated or not. Such protonated/de-protonated pairs are known as conjugated pairs. It is important to be able to recognize such pairs as they can interchange simply by the adding or subtracting a proton. Whether we typically refer to a compound as an acid or base depends a great deal on the relative acid/base strength of the compounds (as will be seen later). But it is critical to realize that all acid base compounds are conjugate pairs from the Bronsted-Lowry perspective.

For example, a simple acid is acetic acid CH3COOH

Acetic acid can be either "protonated" as shown on the left or it can lose a proton and be "de-protonated" as is shown on the right. The de-protonated form is called the acetate ion. We will deal with naming compounds more later. For now, you should simply be able to identify that these two compounds are conjugate pairs as they differ by only one proton. The acetate ion is the conjugate base of acetic acid. Acetic acid is the conjugate acid of the acetate ion.

If we put acetic acid in water, some of the acid will donate a proton to water to form the hydronium ion, H₃O⁺. In this case, acetic acid is the acid as it is donating the proton. Water is the base as it is accepting the proton. The acid converts to its conjugate base, the acetate ion. The base converts to its conjugate acid, the hydronium ion.

CH₃COOH(aq) + H₂O(l) ⇌ CH₃COO^- (aq) + H₃O⁺(aq)

Every acid base reaction will have a reactant that is an acid and a reactant that is a base. This is what defines acid/base chemistry. In the Bronsted-Lowry defnition, these two will be exchanging a proton to generate their conjugate partners.

A video illustrating the definition of Bronstead-Lowry Acids and Bases. Examples are given of each type.

Concept Question

In the following reaction, which compound is the proton donor (for the forward reaction)?
\( {\rm NH_3(aq) + H_2O(l) \rightleftharpoons NH_4^+(aq) + OH^-(aq)}\) (touch choices to toggle feedback on/off)

NH₃
H₂O
NH₄⁺
OH^-

Weak acids and weak bases

A weak acid is a proton donor that when put in water will only partially dissociate.

A weak base is a proton acceptor that when put in water will only partially dissociate.

Let's look at the example of a weak acid, formic acid, HCOOH. This is a carboxylic acid that has the following structure. The acidic hydrogen is the one that is labelled in red. The electronegativity of the oxygens pull the electron density away from the hydrogen and leads to its partial ionization in solution.

Thus the equilibrium constant for this reaction

\[\rm{HCOOH(aq) + H_2O(l) \rightleftharpoons HCOO^-(aq) + H_3O^+(aq)}\]

is assumed to be small. We always write the equilibrium for a weak acid the same way. One mole of the acid plus one mole of water forms the hydronium ion (H₃O⁺) and the deprotonated acid (the ion that is the acid minus the proton). We give this equilibrium constant a special name and call it K_a where the small a stands for acid (much like the sp in Ksp stood for solubility product). It is not different than any other equilibrium constant. It simply helps us to remember it is for this type of reaction written in this specific form. Thus the equilibrium constant will be

\[K_{\rm a} = {{\rm [H_3O^+][HCOO^-]} \over {\rm [HCOOH]}}\]

The "strength" of the weak acid will depend on the size of this equilibrium constant. The larger Ka is, the more it favors the dissociated side of the reaction. The smaller Ka, the less it favors the dissociated side of the reaction. For all weak acids, Ka is generally smaller than 1. That means for all weak acids the reactants are always favored. So if you put a weak acid in water the protonated form will have a higher concentration than the deprotonated form.

You'll also note that in this reaction the acid HCOOH is "changing" forms between having the proton HCOOH and not having the proton HCOO^-. We can link these two species as what we could call "conjugate pairs". The protonated form HCOOH is the acid and the deprotonated form HCOO^- is the conjugate base. That is formic acid (HCOOH) and the formate ion (HCOO^-) are a conjugate pair. In the same reaction, the water is the base (deprotonated) while H₃O⁺ (the protonated form) is the conjugate acid.

The base here is the deprotonated form of the acid

We can also write similar expressions for a base. Take ammonia. When it is placed in water it accepts a proton from water

\[\rm{NH_3(aq) + H_2O(l) \rightleftharpoons NH_4^+(aq) + OH^-(aq)}\]

Again NH₃ is the base (deprotonated) and its conjugate acid is NH₄⁺. The equilibrium constant for this reaction is written as K_b

\[K_{\rm b} = {\rm {[NH_4^+][OH^-]} \over {[NH_3]}}\]

the strength of the base will depend on the magnitude of K_b. The larger K_b the stronger the base.

The acid here is the protonated form of the base

>A video on Weak Acids and Weak Bases.

Concept Question

Which of the following is a weak acid?
(touch choices to toggle feedback on/off)

Identifying Weak Acids and Bases

One of the tripping points for many students in acid/base problem is simply identifying compounds as acids or bases. Step 1 in the process is to memorize the strong acids and strong bases. Next you need to be able to recognize the weak acids and bases. One of the best ways to do this is to learn something about the names and the structures of the major classes of acid/base compounds. Note we are pairing up compounds based on structures and looking at the conjugate acid base pairs.

Carboxylic Acids

Carboxylic acids and their conjugate bases are among the most important compounds to be able to recognize as they are extremely important in organic and biochemistry.

Carboxylic acids have a carboxylic acid group, a carbon double bonded to an oxygen also bonded to an oxygen with a hydrogen. It is this hydrogen that is the acidic hydrogen. When the proton is removed, the remaining ion is called a carboxylate.

This is shown below for acetic acid.

You can identify the compounds either by their chemical structure or their name. When written out, the formula for a carboxylic acid is given as COOH and a carboxylate as COO^-. The names also follow these same patterns. The acid has the name 'something-ic acid.' The conjugate base has the name 'something-ate.'

Here a few carboxylic acid names along with the names of their conjugate base ions.

formic acid, HCOOH the formate ion HCOO^-
acetic acid, CH₃COOH the acetate ion CH₃COO^-
benzoic acid, C₆H₅COOH the benzoate ion C₆H₅COO^-

Amines

The next class of compounds that is important to recognize are amines and their conjugate acids. These compounds are essentially derivatives of ammonia (NH₃) and its conjugate acid the ammonium ion (NH₄⁺).

These compounds generally have the name 'something- amine' or 'something ammonium.'

They can be recognized by the chemical formula which will look like ammonia with either one hydrogen substituted for a carbon chain (primary), two hydrogens substituted (secondary), or three hydrogens substituted (tertiary). The corresponding conjugated acids will be the same, but with an added hydrogen and a positive charge

ammonia, NH₃ the ammonium ion, NH₄⁺
methyl amine , CH₃NH₂ the methyl ammonium ion, CH₃NH₃⁺
methyl ethyl amine, CH₃NHC₂H₅ the methyl ethyl ammonium ion, CH₃NH₂C₂H_5⁺

Below is a picture of the weak base dimethyl amine accepting a proton to form the dimethylammonium ion.

Hydracids

The next class of compounds are hydracids. These are acids in which the proton is combined with an anion. In this case the name of the compound is 'something acid' and the corresponding conjugate base is simply the name of the anion that forms from deprotonation. For example there are several strong acids that are hydracids. The hydrochloric acid, HCl, has a corresponding conjugate base the chloride ion, Cl^-. Since HCl is considered to be infinitely strong, Cl^- is infinitely weak as a base. However, there are other compounds like hydrofluoric acid, HF and hydrocyanic acid HCN in which the conjugate acids anions are weak bases. In the case of HF, the conjugate base is the fluoride ion, F^-. For cyanic acid, the weak base is then cyanide ion, CN^-.

Oxoacids

Finally there are the oxoacids. These are protonated non-metal oxides. For example nitric acid, HNO₃. The corresponding conjugate base is nitrate, NO₃^-. (like chloride since the acid is infinitely strong, the conjugate base is infinitely weak). There is a systematic way to name these acids and their corresponding conjugate base anions. First it is most important to be able to recognize them. The acids are non-metals bonded with oxygen and hydrogen. The conjugate bases are identical, but they are missing a proton (minus one hydrogen and they are anions).

Chlorous Acid, HClO₂ the chlorite ion, ClO₂^-Chloric Acid, HClO₃ the chlorate ion, ClO₃^-Carbonic Acid, H₂CO₃ the hydrogen carbonate ion, HCO₃^_

Concept Question

What is the conjugate acid of ammonia NH₃?
(touch choices to toggle feedback on/off)

ammonia has no conjugate acid
Cl^-
NH₄⁺
NH₂^-

Spectator Ions

We also have the potential to have some ions in solution that do not participate in the chemistry. This is because these ions are the conjugate pairs for the strong acids or strong bases. Since those reactions are assumed to go 100% in the forward direction, we can likewise assume they go backwards 0%. This means that those ions will simply remain in solution.

What are these ions? Well you can simply look at the lists of strong acids and strong bases and pick the conjugates.

For example, the conjugate base for HCl would be Cl^-. As such, in aqueous solution the chloride ion is often a spectator ion (when is this not the case, when it is part of a solubility equilibrium. As far as acid/base chemistry it is always a spectator). Other examples include Na⁺. It is the partner for OH^- in the strong base NaOH. Since this dissociates 100%, we can assume it will not react at all with any OH^-. Other examples are Nitrate, NO₃^-, which is the conjugate base of nitric acid. K⁺, Ba²⁺, ...

Look at the list of strong acids and bases for all of them.

Concept Question

Which of the following will not be a spectator ion in an acid/base reaction?
(touch choices to toggle feedback on/off)

Cl^-
ClO₄^-
F^-
NO₃^-

Strong Acid Equilibria

We are often interested in solving strong acid (base) problems. While these compounds are involved in equilibria we typically simplify the problem by assuming the dissociation of strong acids is 100%. This is because their equilibrium constants are so large. For example, look at the reaction of hydrochloric acid and water.

\[\rm{HCl(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq)+ Cl^-(aq)}\]

The equilibrium constant for this reaction is

\[K_{\rm a} = {\rm [H_3O^+][Cl^-] \over [HCl]}=1.3 \times 10^6\]

1.3 x 10⁶ is a large number. This reaction greatly favors the products. As such, it is safe to assume that the reaction has formed essentially all the products that are possible from the amount of HCl put into the solution. The equilibrium constant would only be of interest if we wanted to know the exact concentration of the minute amount of HCl at equilibrium. Instead, the concentration of interest for acid solutions is the hydronium ion concentration,[H₃O⁺]. This is simply equal to the initial concentration of the acid in the solution, C_HA. Thus for strong acid solutions we have a simple relationship between the acid concentration and the hydronium ion concentration at equilibrium

\[ {\rm[H_3O^+]} \approx C_{\rm HA}\]

This is approximate since it relies on a couple of assumptions. First it assumes that the initial concentration of hydronium ion in pure water is zero. It is not. It is very very small, but it is not zero. Therefore this approximation gets worse the more dilute the solution. The other approximation is that the equilibrium doesn't matter as the reaction is 100% products. This approximation also gets worse as the solution is more dilute. For typical concentrations used in a laboratory situation, this approximation is excellent even to several decimal places.

The same is true for a strong base except that the relationship is between the concentration of the base and the hydroxide ion concentration

\[ {\rm[OH^-]} \approx C_{\rm B}\]

The only caveat here is that one needs to be careful with the strong bases that produce two moles of OH^- for each mole of compound. In this case you need to remember to multiply the base concentration by a factor of two. A 1 M Ba(OH)₂ solution will have [OH^-] = 2 M.

Concept Question

What is the concentration of H₃O⁺ in a 0.2M solution of HBr? (touch choices to toggle feedback on/off)

Weak Acid Equilibria

We are often interested in solving weak acid (base) equilbria problems. While there are a huge number of such potential applications, there is one type of problem in particular that comes up over and over again. These problems give some initial concentration of acid (base) and seek the concentrations of chemical species at equilibrium. In particular, for acid problems we are interested in the hydronium ion concentration, [H₃O⁺]. For base problems, we are usually interested in the hydroxide ion concentration, [OH^-].

Let's examine a typical weak acid problem. You'd like to know the hydronium ion concentration, [H₃O⁺] for a 0.1 M solution of benzoic acid. Benzoic acid is a weak acid (K_a= 6.4 x 10^-5) so you know that the concentration will be very low. This is an equilibrium problem so you'll want to look at both the chemical equation and the equilibrium constant. We write the same equation for every weak acid in water. The acid plus the water react to form the hydronium ion and the deprotonated acid (the benzoate ion).

\[\rm{C_6H_5COOH(aq) + H_2O(l) \rightleftharpoons C_6H_5COO^-(aq) + H_3O^+(aq)}\]

The equilibrium constant for this reaction is

\[{\rm K_a = {{[H_3O^+][C_6H_5COO^-]} \over {[C_6H_5COOH]}}}\]

We can find the [H₃O⁺] at equilibrium if we know the initial concentration of benzoic acid and the K_a for benzoic acid. The initial concentration of the acid is 0.1 M. K_a= 6.4 x 10^-5.

To solve this problem we can set up a RICE table. We know the initial concentration of benzoic acid is 0.1M. We will assume the concentrations of the other ions are zero (this is subtle approximation for the hydronium ion). We will choose as our variable "x" the concentration of the acid that dissociates.

R C₆H₅COOH H₂O C₆H₅COO^- H₃O⁺

I 0.1 - 0 0

C -x - +x +x

E 0.1-x +x +x

Putting the equilibrium values into the mass action expression we can solve for the amount of acid that dissociated.

\[{\rm K_a = {{[H_3O^+][C_6H_5COO^-]} \over {[C_6H_5COOH]}}}= {{(x)(x)} \over (0.1-x)}\]

Since we know K_a this can be re-arranged to yield a quadratic equation that we can solve. However, we can very easily arrive at an approximate answer. This is because we know that "x" will be small. That is that it is a small number compared to the initial concentration. How do we know this? Benzoic acid is a weak acid. This means the equilibrium favors the reactants. K_a is small. As a result we know what the concentration of the acid will be at equilibrium. It will be essentially unchanged. As a result we can approximate the equilibrium concentration of (0.1-x) ≈ 0.1. Putting this and the value of K_a for benzoic acid into the equation we find.

\[{\rm K_a }= 6.4 x 10^{-5}= {{(x)(x)} \over (0.1-x)} \approx {{(x)(x)} \over (0.1)}= {x^2 \over 0.1}\]

This is simple to solve and we find

\[ x = \sqrt{(6.4 x 10^{-5})(0.1)} = 2.5x10^{-3}\]

Now it is important to remember how we defined "x". In this case it was the concentration change for the acid. It also happens that for this situation, the hydronium ion concentration [H₃O⁺]=x.

This problem can be solved in the exact same manner for any weak acid in some concentration in pure water. If we call the weak acid HA with an initial concentration, C_HA we can find the concentration of all the species at equilibrium if we know K_a for the acid.

\[\rm{HA(aq) + H_2O(l) \rightleftharpoons A^-(aq) + H_3O^+(aq)}\]

The equilibrium constant for this reaction is

\[{\rm K_a = {{[H_3O^+][A^-]} \over {[HA]}}}\]

Setting up the RICE table for an initial concentration of C_HA for the weak acid HA. And defining the number of moles of the acid that dissociates as "x" yields.

R HA H₂O A^- H₃O⁺

I C_a - 0 0

C -x - +x +x

E C_a-x +x +x

Putting this into the equilibrium expression we find

\[{\rm K_a = {{[H_3O^+][A^-]} \over {[HA]}}}= {{(x)(x)} \over (C_{HA}-x)}\]

We can again make the assumption that the change in concentration of the acid is negligible. This gives

\[{\rm K_a }= {{(x)(x)} \over (C_{HA}-x)} \approx {{(x)(x)} \over (C_{HA})}= {x^2 \over C_{HA}}\]

Solving this we get

\[ x = \sqrt{{\rm (K_a)(C_{HA})}}\]

Remembering that we defined "x" as the change in concentration of the weak acid we know that this is also the concentration of the hydronium ion at equilibrium. This yields a very useful approximate formula, that the concentration of hydronium ion at equilibrium in a solution that contains only a weak acid in water is given by

\[ {\rm[H_3O^+] = \sqrt{(K_a)(C_{HA})}}\]

We can arrive at a nearly identical result relating the concentration of a weak base and K_b to the hydroxide ion concentration [OH^-]. The chemical equation for a weak base, B, in water is

\[\rm{B(aq) + H_2O(l) \rightleftharpoons BH^+(aq) + OH^-(aq)}\]

The equilibrium constant is

\[{\rm K_b = {{[OH^-][BH^+]} \over {[B]}}}\]

Using an identical derivation, we arrive at the approximate result where C_B is the concentration of the weak base.

\[ {\rm[OH^-] = \sqrt{(K_b)(C_B)}}\]

When do these approximations fail? This question is difficult to answer, since it all depends on how how accurate an answer you are trying to find. They are always approximate. However, the approximation is better or worse in certain limits. This can be understood by examining what is being assumed in the approximation. There are two key assumptions. First, it is assumed that the initial concentration of hydronium ion (hydroxide ion) in pure water is zero. This is wrong. The concentration in pure water is very very small, but it is not zero. As a result, this approximation will fail when the solution is very dilute or the acid (base) is so weak that it essentially does not dissociate. The second assumption is that the amount of the acid that dissociates is so small that the concentration is essentially unchanged [ C_HA - x ≈ = C_HA ] When is this a reasonable approximation? When C_HA >> x. This will be the case when the solution is concentrated and the acid is weak. Thus this approximation is better for concentrated solutions of weak acids with small K_a's.

Concept Question

In the following reaction, the equilibrium constant is 1.8 x 10^-5?
\[ {\rm NH_3(aq) + H_2O(l) \leftrightarrow NH_4^+(aq) + OH^-(aq)}\] If the initial concentrationof NH₃ was 1M, what is the approximate concentration of NH₃ at equilibrium? (touch choices to toggle feedback on/off)

Acid (Base) Strength

We rank the relative strength of different acids in terms of the magnitude of their acid equilibrium constant K_a. The larger the K_a, the greater the hydronium ion concentration for a solution of that acid. If we compare a series of different acid solutions with the same concentration, the solution made from the acid with the largest K_a has the greatest hydronium ion concentration. We would refer to this acid as the "strongest" as it dissociates the most.

Typically this comparison is made only for "weak" acids. Strong acids have K_a's that are so large they are rarely tabulated (or utilized). It is generally assumed that strong acid K_a's are essentially infinitely large.

In contrast, weak acids do not ionize 100%. Take this table of a few weak acids that have been sorted by the K_a values.

Acid Name Formula K_a

Hydrofluoric HF 3.5 x 10^-4

Formic HCOOH 1.8 x 10^-4

Acetic CH₃COOH 1.8 x 10^-5

Hypochlorous HClO 3.0 x 10^-8

Hydrocyanic HCN 4.9 x 10^-10

Of these acids the strongest is HF as it has the largest K_a. Hydrocyanic is the weakest of the group as it has the smallest K_a. This means that HF will dissociate to a greater extent when placed in water than the other acids. HCN will dissociate the least.

An analogous comparison can be made for weak bases looking at K_b. The largest K_b will protonate to the greatest extent in water and form the highest concentration of the hydroxide ions. The smallest K_b will form the lowest concentration of hydroxide in water.

Finally, a safety note. Weak acids/bases are not "weak" in the sense that they are not reactive. Weak acids and bases can be extremely dangerous especially in high concentrations. Don't let the name fool you. It is merely a means to rank how much they react in water to form hydronium or hydroxide ions. The stronger the acid, the larger the K_a, the more H₃O⁺. The stronger the base, the larger the K_b, the more OH^-.

Concept Question

Which of the following is the strongest acid? (touch choices to toggle feedback on/off)

R	C₆H₅COOH	H₂O	C₆H₅COO^-	H₃O⁺
I	0.1	-	0	0
C	-x	-	+x	+x
E	0.1-x		+x	+x

Acid Name	Formula	K_a
Hydrofluoric	HF	3.5 x 10^-4
Formic	HCOOH	1.8 x 10^-4
Acetic	CH₃COOH	1.8 x 10^-5
Hypochlorous	HClO	3.0 x 10^-8
Hydrocyanic	HCN	4.9 x 10^-10

Introduction to Acid/Base Theory

Strong Acids

Concept Question

Strong Bases

Concept Question

Brønsted-Lowry Definition

Concept Question

Weak acids and weak bases

Concept Question

Identifying Weak Acids and Bases

Carboxylic Acids

Amines

Hydracids

Oxoacids

Concept Question

Spectator Ions

Concept Question

Strong Acid Equilibria

Concept Question

Weak Acid Equilibria

Concept Question

Acid (Base) Strength

Concept Question