# Chemistry Lab/Acids and Bases

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Acids and Bases is a topic for Chemistry Lab for the 2019 season.

## Acids and Bases

Acids and Bases is an acid/base titration lab. This is a fairly quick and simple lab to complete, and it is more than worthwhile to repeat the lab if enough materials are present. More repetitions of the lab can result in a more accurate answer. In a free-response style lab report, this might also earn some extra points for style and accuracy. Acid/base questions can range in difficulty from identifying if a solution was an acid based on its pH to balancing advanced reactions and trying to find the acidic constant. In order to excel in this event, it is important to be prepared for all levels.

## Definition of acids and bases

There are three major definitions of acids: the Arrhenius acid, the Bronsted-Lowry acid, and the Lewis acid. Each is defined differently, although the definitions are related.

### Arrhenius acids/bases

Arrhenius acids are defined to be chemicals that, when put in water, produce hydronium ($H_3O^+$) ions. Similarly, Arrhenius bases produce hydroxide ($OH^-$) ions in aqueous solution. However, this definition of acids and bases is restricting due to the fact that it requires both compounds to be in an aqueous solution.

### Bronsted-Lowry acids/bases

Bronsted-Lowry acids are defined to be chemicals that donate protons ($H^+$), while Bronsted bases accept protons. This is a broader definition than the Arrhenius definition because the acid-base reaction does not have to occur in water, although we know through observation that in solution, Bronsted acids donate protons to water molecules and form hydronium ions, as defined by the Arrhenius definition. Similarly, Bronsted bases in aqueous solution deprotonate water into hydroxide ions.

An important thing to remember about the Bronsted-Lowry theory of acids and bases is that when an acid and base react, the acid will form its conjugate base by donating a proton and the base will form its conjugate acid after accepting it. Water is what is known as amphoteric, meaning it can act as both a Bronsted-Lowry acid and base.

An example problem such as the following may ask you to label each substance as an acid or base, and to show the direction of proton transfer.

$H{NO_3} + {H_2}O \rightarrow H_3{O^+} + {NO_3}^-$

In the above example, the water is accepting a proton from the nitric acid, meaning that the water is acting as a Bronsted-Lowry base. The products formed are a hydronium ion and a nitrate ion, where the nitrate is the conjugate base and the hydronium is the conjugate acid. In a similar problem featuring ammonia, water can donate one of its protons:

$NH_3 + {H_2}O \rightleftharpoons NH_4^+ + OH^-$

After donating this proton, the water becomes a hydroxide ion. This is an example of how water can act as both a Bronsted-Lowry acid and base. This also shows the difference between the Arrhenius and Bronsted-Lowry systems, since while ammonia is not an Arrhenius base it acts as a Bronsted-Lowry base in this equation. As in the last example, the product formed from the acid is the conjugate base and the product formed from the base is the conjugate acid. The hydroxide ion formed by the water is the conjugate base and the ammonium ion is the conjugate acid.

### Lewis acids/bases

Lewis acids are defined to be chemicals that accept electron pairs, while Lewis bases donate electron pairs. Lewis acids are also generally referred to as "electrophiles" due to their tendency to accept electrons, while Lewis bases are termed "nucleophiles" due to their tendency to donate electrons. Many acids and bases under this definition do not even have an acidic proton to be exchanged, although Arrhenius and Bronsted acids all fit the definition of a Lewis acid. For example, borane (BH3) contains an empty p-orbital that can accept electrons from electron-donating sources. This makes borane a good Lewis acid despite the fact that borane does not become deprotonated in water.

## Acid/base equilibria

Chemical reactions only very rarely react to completion. Reactants react forward to form products, but products can also react backwards to form reactants. The forward and reverse reactions will set up a state known as equilibrium, where the forward reaction and the reverse reaction balance each other out. The equilibrium constant Keq describes the ratios of the concentrations of all chemical species at equilibrium. Take this reaction:

$aA + bB \rightleftharpoons cC + dD$

The equilibrium constant Keq is equal to:

$K_{eq}=\frac{[C]^c[D]^d}{[A]^a[B]^b}$

Where all of the concentrations are the concentrations at equilibrium and where solids are excluded.

### Acid and Base Dissociation Constants

The reaction of an acid with water to form hydronium and a conjugate base also occurs in equilibrium. A special equilibrium constant, the acid dissociation constant Ka of any given acid, is used to record the equilibrium concentrations of the reactants and products of the dissociation of a proton from an acid in aqueous solution.

For the following reaction:

$HA + H_2O \rightleftharpoons H_3O^+ + A^-$

The acid dissociation constant (Ka) is equal to

$\frac{[H_3O^+][A^-]}{[HA]}$

Note that this is similar to the expression for the general equilibrium expression, although water, which is a reactant, is not included in this expression. That is because the concentration of water does not change in this reaction, since it is usually the solvent for the dissociation.

We can also define a base dissociation constant Kb. For the reaction

$B + H_2O \rightleftharpoons BH^+ + OH^-$

The base dissociation constant (Kb) is equal to

$\frac{[BH^+][OH^-]}{[B]}$

You will often see Ka and Kb expressed as pKa and pKb, where:

$pK_{a} = -log(K_{a})$

$pK_{b} = -log(K_{b})$

### Relationship between Ka and Kb

$\frac{[H^+][NH_3]}{[NH_4^+]} * \frac{[NH_4^+][OH^-]}{[NH_3]} = [H^+][OH^-]$

This method works for all acids and bases. Thus,

$K_a * K_b = K_w$

## Comparing the Strength of Acids and Bases

Quantitatively, acids with greater Ka (lower pKa) are stronger acids than those with lower Ka (greater pKa). Similarly, bases with greater Kb (lower pKb) are stronger bases than those with lower Kb (greater pKb). One can also compare the strength of an acid or base with the strength of its conjugate base or acid. For example, a stronger base will have a weaker conjugate acid, i.e. its conjugate acid will have a greater Ka (lower pKa).

Qualitatively, stronger acids should have a more stable conjugate base. When comparing two acids, the one with the more stable conjugate base is the stronger acid. Apply the following steps to compare the stability of these conjugate bases:

1. Which atom is the charge on? Deprotonating the two acids leaves each with a negative charge. Determine which atom is negatively charged in each conjugate base. If the two atoms are in the same period, the more electronegative atom is better able to stabilize the charge. If the two atoms are in the same group, however, the larger atom can better stabilize the charge. If the negative charge is on the same atom in both conjugate bases proceed to step 2.
2. Resonance. If one of the conjugate bases has resonance structures then the negative charge will be resonance stabilized. If both conjugate bases have resonance structures proceed to step 3.
3. Induction. If there are electronegative atoms that induct negative charge away from the negatively charged atom that conjugate base will be more stable.
4. Orbitals. Electrons in orbitals held closer to the nucleus are more stable than those where they are held further away. For example, a negative charge on an sp-hybridized orbital is more stable than one in an sp2-hybridized orbital, which is more stable than one in an sp3-hybridized orbital.

## pH and pOH

### pH

The pH of a substance is equal to the concentration of hydrogen ions in a substance. It is evaluated on a logarithmic scale from 0 to 14, where 7 is neutral. Numbers greater than 7 are bases (alkaline), and numbers lower than 7 are acids.

pH is equal to the $-\log [H^+]$ or $-\log [H_3O^+]$. Remember that brackets signify concentration in this case. Inversely, the amount of hydrogen ions can be found by the equation $[H^+] = 10^{-pH}$

### pOH

pOH and pH are similar in that they both measure the concentration of specific ions, and 7 is a neutral value. However, substances that have a pOH lower than 7 are bases as opposed to acids. When the pH and pOH of a substance at 25 C are added together, the number will always equal 14.

pOH is equal to the $-\log[OH^-]$.

### Dissociation Constant of Water

The dissociation constant of water (Kw) is equal to

$[H^+][OH^-] = 1*10^{-14}$

for the following reaction:

$H_2O \to H^+ + OH^-$

This is why the pH and pOH of a substance equal 14 when added together.

### Strong Acids

Strong acids are acids that almost completely disassociate in water. For example, nitric acid (${HNO}_3$) dissociates completely in water to form hydronium ions ($H_3O^+$) and nitrate ions (${NO_3}^-$). After this reaction, no nitric acid is left over. On the other hand, a weak acid such as hydrofluoric acid will dissociate partially but not completely. The strength of an acid has nothing to do with its pH or how caustic it is - it relates to how much it dissociates in water. It also has nothing to do with the concentration of the acid, or how much water it contains. The following 7 acids are strong acids, while the rest are weak acids.

Strong Acids
Common Name Formula
Hydroiodic Acid $HI$
Hydrobromic Acid $HBr$
Perchloric Acid $HClO_4$
Hydrochloric Acid $HCl$
Chloric Acid $HClO_3$
Sulfuric Acid $H_2SO_4$
Nitric Acid $HNO_3$

### Weak Acids

Weak acids are acids that only dissociate to a small extent in water. This equation exists in equilibrium, such as this equation featuring acetic acid:

${CH_3}COOH + {H_2}O \leftrightharpoons H_3O^+ + {CH_3}COOH^-$

The ions will readily change back into acetic acid due to the equilibrium. The acid dissociation constant ($K_a$) value determines how much of the acid will dissociate in aqueous solution. Weak acids will have a low $K_a$ value, since not much of the acid will dissociate in water. Weak acids consist of all acidic species that are not strong acids.

Common Weak Acids
Common Name Formula
Formic (methanoic) Acid $HCOOH$
Acetic (ethanoic) Acid $CH_3COOH$
Perchloric Acid $HClO_4$
Tartaric Acid $HOOCCHOHCHOHCOOH$ or $C_4H_6O_6$
Hydrogen Sulfate Ion ${HSO_4}^-$
Phosphoric Acid $H_3PO_4$

## Bases

All bases have a pH greater than 7 and a pOH less than 7.

### Arrhenius Bases

Arrhenius Bases are defined to be chemicals that, when put in water, produce hydroxide ($OH^-$) ions. Bases reduce the concentration of hydrogen ions in a solution when added, which is why their pH is greater than 7.

### Bronsted-Lowry Bases

Bronsted-Lowry bases are defined to be chemicals that accept protons in the form of hydrogen ions ($H^+$). This is a broader definition than the Arrhenius definition because the reaction does not have to occur in an aqueous solution. When determining if a compound is a Bronsted-Lowry acid or base, it is important to observe the reaction. The same compound can be both an acid or a base depending on the direction of the reaction.

### Lewis Bases

Lewis Bases are defined to be chemicals that donate electron pairs. All Lewis bases are Bronsted-Lowry bases, but a Lewis acid is not necessarily a Bronsted-Lowry acid.

### Strong Bases

Similar to acids, strong Bronsted-Lowry bases are bases that almost completely disassociate in water. Examples include soluble hydroxide salts such as: $LiOH, NaOH, KOH, RbOH,$ and $CsOH$.

### Weak Bases

Weak bases are bases that only partially disassociate in water. The base dissociation constant ($K_b$) defines how much of the base will dissociate. Weak bases typically have a very small $K_b$ value. A common example of a weak base is $NH_3$.

## Buffers

A buffer solution is an aqueous solution composed of a weak acid and its conjugate base, or vice versa. For example, ammonium hydroxide ($NH_4OH$) contains both the weak base ammonia and its conjugate acid ammonium. Buffers resist pH change when strong acids or bases are added to them, meaning that they can neutralize small amounts of these substances. Buffer solutions typically have a specific capacity of how much acid/base can be neutralized before the pH changes.

Buffers can resist pH changes because their components exist in equilibrium. The concentration of the components does not change, and they rarely react with water in the solution. This means that while the weak acid and base in the solution will not react with any components in the solution, they will react with a strong acid or base and neutralize it.

### Buffer pH

The pH of a buffer is determined by a few factors: the Ka constant of the weak acid, and the ratio of the weak base to the weak acid in the solution. This equation is known as the Henderson-Hasselbalch equation.

$pH = pK_a + \log(\frac{[B]}{[A]})$

The pH of a buffer can be controlled by altering the ratio of base to acid in the solution, as the $pK_a$ value is a quality of the acid chosen for the buffer.