# Write complete balanced equations for the following acid-base reactions?

1. H2SO4(aq) + KOH(aq) →

2. H3PO4(aq) + Ca(OH)2(aq) →

3. HNO3(aq) + Mg(OH)2(aq) →

1. All are neutralization reactions, in which an acid and base react to form a salt and water.

1. H2SO4(aq) + 2KOH(aq) → K2SO4 + 2H2O

2. 2H3PO4(aq) + 3Ca(OH)2(aq) → Ca3(PO4)2 + 6H2O

3. 2HNO3(aq) + Mg(OH)2(aq) → Mg(NO3)2 + 2H2O

## Relevant information

The definition of an acid is often cited as: any compound that increases the amount of hydrogen ion (H+) in an aqueous solution. The chemical opposite of an acid is a base. The equivalent definition of a base is that a base is a compound that increases the amount of hydroxide ion (OH−) in an aqueous solution. These original definitions were proposed by Arrhenius (the same person who proposed ion dissociation) in 1884, so they are referred to as the Arrhenius definition of an acid and a base, respectively.

You may recognize that, based on the description of a hydrogen atom, an H+ ion is a hydrogen atom that has lost its lone electron; that is, H+ is simply a proton. Do we really have bare protons moving about in aqueous solution? No. What is more likely is that the H+ ion has attached itself to one (or more) water molecule(s). To represent this chemically, we define the hydronium ion H3O+(aq), a water molecule with an extra hydrogen ion attached to it. as H3O+, which represents an additional proton attached to a water molecule. We use the hydronium ion as the more logical way a hydrogen ion appears in an aqueous solution, although in many chemical reactions H+ and H3O+ are treated equivalently.

For purposes of this brief introduction, we will consider only the more common types of acid-base reactions that take place in aqueous solutions. In this context, an acid is a substance that will dissolve in water to yield hydronium ions, H3O+. As an example, consider the equation shown here:

$\text{HCl}(aq) + \text{H}_2 \text{O}(aq) \longrightarrow \text{Cl}^{-}(aq) + \text{H}_3 \text{O}^{+}(aq)$

The process represented by this equation confirms that hydrogen chloride is an acid. When dissolved in water, H3O+ ions are produced by a chemical reaction in which H+ ions are transferred from HCl molecules to H2O molecules (Figure 1).

Figure 1. When hydrogen chloride gas dissolves in water, (a) it reacts as an acid, transferring protons to water molecules to yield (b) hydronium ions (and solvated chloride ions).

The nature of HCl is such that its reaction with water as just described is essentially 100% efficient: Virtually every HCl molecule that dissolves in water will undergo this reaction. Acids that completely react in this fashion are called strong acids, and HCl is one among just a handful of common acid compounds that are classified as strong (Table 1).

Compound Formula Name in Aqueous Solution
HBr hydrobromic acid
HCl hydrochloric acid
HI hydroiodic acid
HNO3 nitric acid
HClO4 perchloric acid
HClO3 chloric acid
H2SO4 sulfuric acid
Table 1. Common Strong Acids

A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions.

Compound Formula Name in Aqueous Solution
HF hydrofluoric acid
HCN hydrocyanic acid
HC2H3O2 acetic acid
HNO2 nitrous acid
HClO hypochlorous acid
HClO2 chlorous acid
H2SO3 sulfurous acid
H2CO3 carbonic acid
H3PO4 phosphoric acid
Table 2. Common Weak Acids

Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a weak acid is acetic acid, the main ingredient in food vinegars:

$\text{CH}_3 \text{CO}_2 \text{H}(aq) + \text{H}_2 \text{O}(l) \leftrightharpoons \text{CH}_3 {\text{CO}_2}^{-}(aq) + \text{H}_3 \text{O}^{+}(aq)$

When dissolved in water under typical conditions, only about 1% of acetic acid molecules are present in the ionized form, $\text{CH}_3 {\text{CO}_2}^{-}$(Figure 2). The use of a double-arrow in the equation above denotes the partial reaction aspect of this process, a concept addressed fully in the chapters on chemical equilibrium.)

Figure 2. (a) Fruits such as oranges, lemons, and grapefruit contain the weak acid citric acid. (b) Vinegars contain the weak acid acetic acid. (credit a: modification of work by Scott Bauer; credit b: modification of work by Brücke-Osteuropa/Wikimedia Commons)

A base is a substance that will dissolve in water to yield hydroxide ions, OH−. The most common bases are ionic compounds composed of alkali or alkaline earth metal cations (groups 1 and 2) combined with the hydroxide ion—for example, NaOH and Ca(OH)2. When these compounds dissolve in water, hydroxide ions are released directly into the solution. For example, KOH and Ba(OH)2 dissolve in water and dissociate completely to produce cations (K+ and Ba2+, respectively) and hydroxide ions, OH−. These bases, along with other hydroxides that completely dissociate in water, are considered strong bases.

Consider as an example the dissolution of lye (sodium hydroxide) in water:

$\text{NaOH}(s) \longrightarrow \text{Na}^{+}(aq) + \text{OH}^{-}(aq)$

This equation confirms that sodium hydroxide is a base. When dissolved in water, NaOH dissociates to yield Na+ and OH− ions. This is also true for any other ionic compound containing hydroxide ions. Since the dissociation process is essentially complete when ionic compounds dissolve in water under typical conditions, NaOH and other ionic hydroxides are all classified as strong bases.

Unlike ionic hydroxides, some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other compounds, and an active ingredient in household cleaners (Figure 3). When dissolved in water, ammonia reacts partially to yield hydroxide ions, as shown here:

$\text{NH}_3(aq) + \text{H}_2 \text{O}(l) \rightleftharpoons {\text{NH}_4}^{+}(aq) + \text{OH}^{-}(aq)$

Under typical conditions, only about 1% of the dissolved ammonia is present as NH4+ ions.

Figure 3. Ammonia is a weak base used in a variety of applications. (a) Pure ammonia is commonly applied as an agricultural fertilizer. (b) Dilute solutions of ammonia are effective household cleansers. (credit a: modification of work by National Resources Conservation Service; credit b: modification of work by pat00139)

## Acid-Base Reactions

An acid-base reaction is one in which a hydrogen ion, H+, is transferred from one chemical species to another. Such reactions are of central importance to numerous natural and technological processes, ranging from the chemical transformations that take place within cells and the lakes and oceans, to the industrial-scale production of fertilizers, pharmaceuticals, and other substances essential to society. The subject of acid-base chemistry, therefore, is worthy of thorough discussion.

The reaction between an acid and a base is called an acid-base reaction or a neutralization reaction. Although acids and bases have their own unique chemistries, the acid and base cancel each other’s chemistry to produce a rather innocuous substance—water. In fact, the general acid-base reaction is

acid + base $\longrightarrow$ water + salt

where the term salt is used to define any ionic compound (soluble or insoluble) that is formed from a reaction between an acid and a base. In chemistry, the word salt refers to more than just table salt. For example, the balanced chemical equation for the reaction between HCl(aq) and KOH(aq) is

HCl(aq) + KOH(aq) $\longrightarrow$ H2O(ℓ) + KCl(aq)

where the salt is KCl. By counting the number of atoms of each element, we find that only one water molecule is formed as a product. However, in the reaction between HCl(aq) and Mg(OH)2(aq), additional molecules of HCl and H2O are required to balance the chemical equation:

2 HCl(aq) + Mg(OH)2(aq) $\longrightarrow$ 2 H2O(ℓ) + MgCl2(aq)

Here, the salt is MgCl2. This is one of several reactions that take place when a type of antacid—a base—is used to treat stomach acid.

There are acid-base reactions that do not follow the “general acid-base” equation given above.  For example, , the balanced chemical equation for the reaction between HCl(aq) and NH3(aq) is

HCl(aq) + NH3(aq) $\longrightarrow$ NH4Cl(aq)

### Example 1

Write the neutralization reactions between each acid and base.

a) HNO3(aq) and Ba(OH)2(aq)             b)H3PO4(aq) and Ca(OH)2(aq)

Solution

First, we will write the chemical equation with the formulas of the reactants and the expected products; then we will balance the equation.

a) The expected products are water and barium nitrate, so the initial chemical reaction is

HNO3(aq) + Ba(OH)2(aq) $\longrightarrow$ H2O(ℓ) + Ba(NO3)2(aq)

To balance the equation, we need to realize that there will be two H2O molecules, so two HNO3 molecules are required:

2HNO3(aq) + Ba(OH)2(aq) $\longrightarrow$ 2H2O(ℓ) + Ba(NO3)2(aq)

This chemical equation is now balanced.

b) The expected products are water and calcium phosphate, so the initial chemical equation is

H3PO4(aq) + Ca(OH)2(aq) $\longrightarrow$ H2O(ℓ) + Ca3(PO4)2(s)

According to the solubility rules, Ca3(PO4)2 is insoluble, so it has an (s) phase label. To balance this equation, we need two phosphate ions and three calcium ions; we end up with six water molecules to balance the equation:

2 H3PO4(aq) + 3 Ca(OH)2(aq) $\longrightarrow$ 6 H2O(ℓ) + Ca3(PO4)2(s)

This chemical equation is now balanced.

Test Yourself

Write the neutralization reaction between H2SO4(aq) and Sr(OH)2(aq).

H2SO4(aq) + Sr(OH)2(aq) $\longrightarrow$ 2 H2O(ℓ) + SrSO4(aq)

Neutralization reactions are one type of chemical reaction that proceeds even if one reactant is not in the aqueous phase. For example, the chemical reaction between HCl(aq) and Fe(OH)3(s) still proceeds according to the equation

3 HCl(aq) + Fe(OH)3(s) $\longrightarrow$ 3 H2O(ℓ) + FeCl3(aq)

even though Fe(OH)3 is not soluble. When one realizes that Fe(OH)3(s) is a component of rust, this explains why some cleaning solutions for rust stains contain acids—the neutralization reaction produces products that are soluble and wash away. Washing with acids like HCl is one way to remove rust and rust stains, but HCl must be used with caution!

Complete and net ionic reactions for neutralization reactions will depend on whether the reactants and products are soluble, even if the acid and base react. For example, in the reaction of HCl(aq) and NaOH(aq),

HCl(aq) + NaOH(aq) $\longrightarrow$ H2O(ℓ) + NaCl(aq)

the complete ionic reaction is

H+(aq) + Cl−(aq) + Na+(aq) + OH−(aq) $\longrightarrow$ H2O(ℓ) + Na+(aq) + Cl−(aq)

The Na+(aq) and Cl−(aq) ions are spectator ions, so we can remove them to have

H+(aq) + OH−(aq) $\longrightarrow$ H2O(ℓ)

as the net ionic equation. If we wanted to write this in terms of the hydronium ion, H3O+(aq), we would write it as

H3O+(aq) + OH−(aq) $\longrightarrow$ 2H2O(ℓ)

With the exception of the introduction of an extra water molecule, these two net ionic equations are equivalent.

However, for the reaction between HCl(aq) and Cr(OH)2(s), because chromium(II) hydroxide is insoluble, we cannot separate it into ions for the complete ionic equation:

2 H+(aq) + 2 Cl−(aq) + Cr(OH)2(s) $\longrightarrow$ 2 H2O(ℓ) + Cr2+(aq) + 2 Cl−(aq)

The chloride ions are the only spectator ions here, so the net ionic equation is

2 H+(aq) + Cr(OH)2(s) $\longrightarrow$ 2 H2O(ℓ) + Cr2+(aq)

### Example 2

Write balanced chemical equations for the acid-base reactions described here:

a) the weak acid hydrogen hypochlorite reacts with water

b) a solution of barium hydroxide is neutralized with a solution of nitric acid

Solution
a) The two reactants are provided, HOCl and H2O. Since the substance is reported to be an acid, its reaction with water will involve the transfer of H+ from HOCl to H2O to generate hydronium ions, H3O+ and hypochlorite ions, OCl−.

$\text{HOCl}(aq) + \text{H}_2 \text{O}(l) \rightleftharpoons \text{OCl}^{-}(aq) + \text{H}_3 \text{O}^{+}(aq)$

A double-arrow is appropriate in this equation because it indicates the HOCl is a weak acid that has not reacted completely.

b) The two reactants are provided, Ba(OH)2 and HNO3. Since this is a neutralization reaction, the two products will be water and a salt composed of the cation of the ionic hydroxide (Ba2+) and the anion generated when the acid transfers its hydrogen ion (NO3−).

$\text{Ba(OH)}_2(aq) + 2\text{HNO}_3(aq) \longrightarrow \text{Ba(NO}_3)_2(aq) + 2\text{H}_2 \text{O}(l)$

Test Yourself
Write the net ionic equation representing the neutralization of any strong acid with an ionic hydroxide. Hint: Consider the ions produced when a strong acid is dissolved in water.

$\text{H}_3 \text{O}^{+}(aq) + \text{OH}^{-}(aq) \longrightarrow 2\text{H}_2 \text{O}(l)$

### Example 3

Oxalic acid, H2C2O4(s), and Ca(OH)2(s) react very slowly. What is the net ionic equation between these two substances if the salt formed is insoluble? The anion in oxalic acid is the oxalate ion, C2O42−.

Solution

The products of the neutralization reaction will be water and calcium oxalate:

H2C2O4(s) + Ca(OH)2(s) $\longrightarrow$ 2 H2O(ℓ) + CaC2O4(s)

Because nothing is dissolved, there are no substances to separate into ions, so the net ionic equation is the equation of the three solids and one liquid.

Test Yourself

What is the net ionic equation between HNO3(aq) and Ti(OH)4(s)?

4 H+(aq) + Ti(OH)4(s) $\longrightarrow$ 4 H2O(ℓ) + Ti4+(aq)

Explore the microscopic view of strong and weak acids and bases.

## Gas-forming Acid-Base reactions

A driving force for certain acid-base reactions is the formation of a gas. Common gases formed are  H2, O2, and CO2.

For example:

2HCl(aq) + Na2CO3(aq) $\longrightarrow$ H2CO3(aq) + 2NaCl(aq) $\longrightarrow$ CO2(g) + H2O(l) + 2NaCl(aq)

The above example can be viewed as an acid-base reaction followed by a decomposition. The driving force in this case is the gas formation.  The decomposition of H2CO3 into CO2 and H2O is a very common reaction. Both Na2CO3 and NaHCO3 mixed with acid result in a gas-forming acid-base reaction.

HCl(aq) + NaHCO3(aq) $\longrightarrow$ H2CO3(aq) + NaCl(aq) $\longrightarrow$ CO2(g) + H2O(l) + NaCl(aq)

### Food and Drink App: Acids in Foods

Many foods and beverages contain acids. Acids impart a sour note to the taste of foods, which may add some pleasantness to the food. For example, orange juice contains citric acid, H3C6H5O7. Note how this formula shows hydrogen atoms in two places; the first hydrogen atoms written are the hydrogen atoms that can form H+ ions, while the second hydrogen atoms written are part of the citrate ion, C6H5O73−. Lemons and limes contain much more citric acid—about 60 times as much—which accounts for these citrus fruits being more sour than most oranges. Vinegar is essentially a ~5% solution of acetic acid (HC2H3O2) in water. Apples contain malic acid (H2C4H4O5; the name malic acid comes from the apple’s botanical genus name, malus), while lactic acid (HC3H5O3) is found in wine and sour milk products, such as yogurt and some cottage cheeses.

Table 3 “Various Acids Found in Food and Beverages” lists some acids found in foods, either naturally or as an additive. Frequently, the salts of acid anions are used as additives, such as monosodium glutamate (MSG), which is the sodium salt derived from glutamic acid. As you read the list, you should come to the inescapable conclusion that it is impossible to avoid acids in food and beverages.

Acid Name Acid Formula Use and Appearance
acetic acid HC2H3O2 flavouring; found in vinegar
adipic acid H2C6H8O4 flavouring; found in processed foods and some antacids
alginic acid various thickener; found in drinks, ice cream, and weight loss products
ascorbic acid HC6H7O6 antioxidant, also known as vitamin C; found in fruits and vegetables
benzoic acid HC6H5CO2 preservative; found in processed foods
citric acid H3C6H5O7 flavouring; found in citrus fruits
dehydroacetic acid HC8H7O4 preservative, especially for strawberries and squash
erythrobic acid HC6H7O6 antioxidant; found in processed foods
fatty acids various thickener and emulsifier; found in processed foods
fumaric acid H2C4H2O4 flavouring; acid reactant in some baking powders
glutamic acid H2C5H7NO4 flavouring; found in processed foods and in tomatoes, some cheeses, and soy products
lactic acid HC3H5O3 flavouring; found in wine, yogurt, cottage cheese, and other sour milk products
malic acid H2C4H4O5 flavouring; found in apples and unripe fruit
phosphoric acid H3PO4 flavouring; found in some colas
propionic acid HC3H5O2 preservative; found in baked goods
sorbic acid HC6H7O2 preservative; found in processed foods
stearic acid HC18H35O2 anticaking agent; found in hard candies
succinic acid H2C4H4O4 flavouring; found in wine and beer
tartaric acid H2C4H4O6 flavouring; found in grapes, bananas, and tamarinds

Table 3. Various Acids Found in Food and Beverages

## Key Concepts and Summary

Chemical reactions are classified according to similar patterns of behaviour. Acid-base reactions involve the transfer of hydrogen ions between reactants.

General acid-base reactions, also called neutralization reactions can be summarized with the following reaction equation:

ACID(aq) + BASE(aq) $\longrightarrow$ H2O(l) + SALT(aq) or (s)

The DRIVING FORCE for a general acid-base reaction is the formation of water.

Gas-forming acid-base reactions can be summarized with the following reaction equation:

ACID(aq) + NaHCO3 or Na2CO3(aq) $\longrightarrow$ H2O(l) + CO2(g) + SALT(aq) or (s)

The DRIVING FORCE for a gas-forming acid-base reaction is the formation of gas. There are three ways of

There are three ways of representing a neutralization reaction, using a molecular equation, complete ionic equation or net ionic equation, as described in section 6.1.

### Exercises

1. What is the Arrhenius definition of an acid?

2. What is the Arrhenius definition of a base?

3. Predict the products of each acid-base combination listed. Assume that a neutralization reaction occurs.

a)  HCl and KOH

b)  H2SO4 and KOH

c)  H3PO4 and Ni(OH)2

4.  Write a balanced chemical equation for each neutralization reaction in Exercise 3.

5.  Write a balanced chemical equation for the neutralization reaction between each given acid and base. Include the proper phase labels.

a)  HI(aq) + KOH(aq) $\longrightarrow$ ?

b)  H2SO4(aq) + Ba(OH)2(aq) $\longrightarrow$ ?

6.  Write the net ionic equation for each neutralization reaction in Exercise 7.

7.  Write the complete and net ionic equations for the neutralization reaction between HClO3(aq) and Zn(OH)2(s). Assume the salt is soluble.

8.  Explain why the net ionic equation for the neutralization reaction between HCl(aq) and KOH(aq) is the same as the net ionic equation for the neutralization reaction between HNO3(aq) and RbOH.

9.  Write the complete and net ionic equations for the neutralization reaction between HCl(aq) and KOH(aq) using the hydronium ion in place of H+. What difference does it make when using the hydronium ion?

10. Complete and balance the following acid-base equations:

a) HCl gas reacts with solid Ca(OH)2(s).

b) A solution of Sr(OH)2 is added to a solution of HNO3.

11. Complete and balance the equations for the following acid-base neutralization reactions. If water is used as a solvent, write the reactants and products as aqueous ions. In some cases, there may be more than one correct answer, depending on the amounts of reactants used.

a) $\text{Mg(OH)}_2(s) + \text{HClO}_4(aq) \longrightarrow$

b) $\text{SrO}(s) + \text{H}_2 \text{SO}_4(l) \longrightarrow$

12. Complete and balance the equations of the following reactions, each of which could be used to remove hydrogen sulfide from natural gas:

a) $\text{Ca(OH)}_2(s) + \text{H}_2 \text{S}(g) \longrightarrow$

b) $\text{Na}_2 \text{CO}_3(aq) + \text{H}_2 \text{S}(g) \longrightarrow$

1. An Arrhenius acid increases the amount of H+ ions in an aqueous solution.

2. An Arrhenius base increases the amount of OH– ions in an aqueous solution.

3. a)  KCl and H2O

b)  K2SO4 and H2O

c)  Ni3(PO4)2 and H2O

4. a)    HCl + KOH $\longrightarrow$ KCl + H2O

b)  H2SO4 + 2 KOH $\longrightarrow$ K2SO4 + 2 H2O

c)  2 H3PO4 + 3 Ni(OH)2 $\longrightarrow$ Ni3(PO4)2 + 6 H2O

5. a)  HI(aq) + KOH(aq) $\longrightarrow$ KCl(aq) + H2O(ℓ)

b)  H2SO4(aq) + Ba(OH)2(aq) $\longrightarrow$ BaSO4(s) + 2 H2O(ℓ)

6. a)  H+(aq) + OH−(aq) $\longrightarrow$ H2O(ℓ)

b)  2 H+(aq) + SO42−(aq) + Ba2+(aq) + 2 OH−(aq) $\longrightarrow$ BaSO4(s) + 2 H2O(ℓ)

7.  Complete ionic equation:

2 H+(aq) + 2 ClO3−(aq) + Zn2+(aq) + 2 OH−(aq) $\longrightarrow$ Zn2+(aq) + 2 ClO3−(aq) + 2 H2O(ℓ)

Net ionic equation:

2 H+(aq) + 2 OH−(aq) $\longrightarrow$ 2 H2O(ℓ)

8.  Because the salts are soluble in both cases, the net ionic reaction is just H+(aq) + OH−(aq) $\longrightarrow$ H2O(ℓ).

9.  Complete ionic equation:

H3O+(aq) + Cl−(aq) + K+(aq) + OH−(aq) $\longrightarrow$ 2 H2O(ℓ) + K+(aq) + Cl−(aq)

Net ionic equation:

H3O+(aq) + OH−(aq) $\longrightarrow$ 2 H2O(ℓ)

The difference is simply the presence of an extra water molecule as a product.

10. a) $2\text{HCl}(g) + \text{Ca(OH)}_2(s) \longrightarrow \text{CaCl}_2(s) + 2\text{H}_2 \text{O}(l)$;

b) $\text{Sr(OH)}_2(aq) + 2\text{HNO}_3(aq) \longrightarrow \text{Sr(NO}_3)_2(aq) + 2\text{H}_2 \text{O}(l)$;

11. a) $\text{Mg(OH)}_2(s) + 2\text{HClO}_4(aq) \longrightarrow \text{Mg}^{2+}(aq) + 2{\text{ClO}_4}^{-}(aq) + 2\text{H}_2 \text{O}(l);$
b) $\text{SrO}(s) + \text{H}_2 \text{SO}_4(l) \longrightarrow \text{SrSO}_4(s) + \text{H}_2 \text{O}$

12. a) $\text{Ca(OH)}_2(s) + \text{H}_2 \text{S}(g) \longrightarrow \text{CaS}(s) + 2\text{H}_2\text{O}(l);$
b) $\text{Na}_2 \text{CO}_3(aq) + \text{H}_2 \text{S}(g) \longrightarrow \text{Na}_2 \text{S}(aq) + \text{CO}_2(g) + \text{H}_2 \text{O}(l)$

## Glossary

acid: substance that produces H3O+ when dissolved in water

acid-base reaction: reaction involving the transfer of a hydrogen ion between reactant species

base: substance that produces OH− when dissolved in water

neutralization reaction: reaction between an acid and a base to produce salt and water

salt: ionic compound that can be formed by the reaction of an acid with a base that contains a cation and an anion other than hydroxide or oxide

strong acid: acid that reacts completely when dissolved in water to yield hydronium ions

strong base: base that reacts completely when dissolved in water to yield hydroxide ions

weak acid: acid that reacts only to a slight extent when dissolved in water to yield hydronium ions

weak base: base that reacts only to a slight extent when dissolved in water to yield hydroxide ions

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