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# 11.1: Chemical Equations

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

• Describe chemical reactions using word equations.
• Know the correct symbols to use in order to write skeleton equations for chemical reactions.
• Use coefficients to balance chemical equations so that the law of conservation of mass is followed.

## Lesson Vocabulary

• balanced equation
• chemical equation
• coefficient
• skeleton equation

### Recalling Prior Knowledge

• What kinds of observations indicate that a chemical reaction may be occurring?
• What are chemical reactions according to the principles detailed by John Dalton?
• What are reactants and products?
• What is the law of conservation of mass?

## Writing Chemical Equations

Chemical reactions are occurring all around you. Plants use sunlight to drive their photosynthetic process and produce energy. Cars and other vehicles burn gasoline in order to power their engines. Batteries use electrochemical reactions to produce energy and power many everyday devices. Many chemical reactions are going on inside you as well, especially during the digestion of food.

In math class, you have written and solved many mathematical equations. Chemists keep track of chemical reactions by writing equations as well. In any chemical reaction one or more substances, called reactants, are converted into one or more new substances, called products. The general form of the equation for such a process looks like this.

Reactants → Products

Unlike in a math equation, a chemical equation does not use an equal sign. Instead the arrow is called a yield sign and so the equation is described as “reactants yield products.”

### Word Equations

You can describe a chemical reaction by writing a word equation. When silver metal is exposed to sulfur it reacts to form silver sulfide. Silver sulfide is commonly known as tarnish and turns the surface of silver objects dark and streaky black (Figure below). The sulfur that contributes to tarnish can come from traces of sulfur in the air or from food such as eggs. The word equation for the process is:

Silver + sulfur → Silver sulfide

The silver and the sulfur are the reactants in the equation, while the silver sulfide is the product.

The coffee percolator on the left has been tarnished from exposure to sulfur. Tarnish is the chemical compound silver sulfide. The same percolator on the right has been polished with a tarnish removal product in order to restore its silver finish.

Another common chemical reaction is the burning of methane gas. Methane is the major component of natural gas and is commonly burned on a gas stove or in a Bunsen burner (Figure below). Burning is a chemical reaction in which some type of fuel is reacted with oxygen gas. The products of the reaction in the burning of methane as well as other fuels are carbon dioxide and water. The word equation for this reaction is:

Methane + oxygen → carbon dioxide + water

A Bunsen burner is commonly used to heat substances in a chemistry lab. Methane is reacted with oxygen to form carbon dioxide and water.

### Chemical Equations

Word equations are time-consuming to write and will not prove to be convenient for many of the things that chemists need to do with equations. A chemical equation is a representation of a chemical reaction that displays the reactants and products with chemical formulas. The chemical equation for the reaction of methane with oxygen is shown:

CH4 + O2 → CO2 + H2O

The equation above, called a skeleton equation, is an equation that shows only the formulas of the reactants and products with nothing to indicate the relative amounts. The first step in writing an accurate chemical equation is to write the skeleton equation, making sure that the formulas of all substances involved are written correctly. All reactants are written to the left of the yield arrow, separated from one another by a plus sign. Likewise, products are written to the right of the yield arrow, also separated with a plus sign.

It is often important to know the physical states of the reactants and products taking part in a reaction. To do this, put the appropriate symbol in parentheses after each formula: (s) for solid, (l) for liquid, (g) for gas, and (aq) for an aqueous (water-based) solution. At room temperature, the components of the previous reaction are in the following states:

CH4(g) + O2(g) → CO2(g) + H2O(l)

Table below shows a listing of symbols used in chemical equations. Some, such as the double arrow which represents equilibrium, and the use of a catalyst in a reaction, will be treated in detail in later chapters.

Symbols Used In Chemical Equations
Symbol Description
+ used to separate multiple reactants or products
yield sign; separates reactants from products
\begin{align*}\rightleftharpoons\end{align*} replaces the yield sign for reversible reactions that reach equilibrium
(s) reactant or product in the solid state
(l) reactant or product in the liquid state
(g) reactant or product in the gas state
(aq) reactant or product in an aqueous solution (dissolved in water)
\begin{align*}\mathrm{\overset{Pt}{\rightarrow}}\end{align*} formula written above the arrow is used as a catalyst in the reaction
\begin{align*}\overset{\Delta}{\rightarrow}\end{align*} triangle indicates that the reaction is being heated

## Balancing Chemical Equations

Suppose you were to write a word equation for building the ideal ham sandwich (Figure below). Perhaps you might come up with this:

Ham + cheese + tomato + pickles + bread → ham sandwich

The reactants are the “parts” or ingredients of the ham sandwich while the sandwich itself is the product. There is something missing from your equation, however. There is no indication how many of each “reactant” is required to make the “product.” For one thing, you would certainly need 2 slices of bread to make a conventional sandwich.

A ham sandwich can be thought of as the product of a reaction while all the individual ingredients are the reactants.

Let’s say that the perfect ham sandwich (HS) is composed of 2 slices of ham (H), a slice of cheese (C), a slice of tomato (T), 5 pickles (P), and 2 slices of bread (B). Accounting for the numbers of each reactant, as well as substituting symbols for words, your equation would become:

2H + C + T + 5P + 2B → HS

This now shows the correct quantities of the reactants. As one final improvement, we will change the “formula” of the product. Since the final sandwich contains all the reactants that went into it, its formula should reflect that.

2H + C + T + 5P + 2B → H2CTP5B2

The subscript after each symbol in the product stands for the number of that particular reactant found on the reactant side of the equation: 2 for H, 1 for C, etc.

Since the equation now shows equal numbers of each sandwich part on both sides of the equation, we say that the equation is balanced. Chemical equations must also be balanced in a similar way. A balanced equation is a chemical equation in which mass is conserved and there are equal numbers of atoms of each element on both sides of the equation. We can write a chemical equation for the reaction of carbon with hydrogen gas to form methane (CH4).

\begin{align*}\underset{1 \ \text{C atom}}{\text{C}(s)} + \underset{2 \ \text{H atoms}}{\text{H}_2(g)} \rightarrow \underset{1 \ \text{C atom}, \ 4 \ \text{H atoms}}{\text{CH}_4(g)} \end{align*}

In order to write a correct equation, you must first write the correct skeleton equation with the correct chemical formulas. Recall that hydrogen is a diatomic molecule and so is written as H2. When we count the number of atoms of both elements, shown under the equation, we see that the equation is not balanced. There are only 2 atoms of hydrogen on the reactant side of the equation, while there are 4 atoms of hydrogen on the product side. This violates the law of conservation of mass, which states that mass must be conserved in any chemical reaction or physical process. Another common way to express the law of conservation of mass is that matter cannot be created or destroyed.

As we saw in the chapter Atomic Structure, John Dalton’s atomic theory stated that chemical reactions are separations, combinations, or rearrangements of atoms. Atoms themselves cannot be created or destroyed. Dalton’s theory explains the law of conservation of mass and the process of balancing an equation ensures that the law is followed. We can balance the above equation by adding a coefficient of 2 in front of the formula for hydrogen.

C(s) + 2H2(g) → CH4(g)

A coefficient is a small whole number placed in front of a formula in an equation in order to balance it. The 2 in front of the H2 means that there are a total of 2 × 2 = 4 atoms of hydrogen as reactants. Visually, the reaction looks like:

In the balanced equation, there is one atom of carbon and four atoms of hydrogen on both sides of the arrow. Below are guidelines for writing and balancing chemical equations.

1. Determine the correct chemical formulas for each reactant and product.
2. Write the skeleton equation by placing the reactant(s) on the left side of the yield sign (→) and the product(s) on the right side. If there is more than one reactant or product, separate with plus signs.
3. Count the number of atoms of each element that appears as a reactant and as a product. If a polyatomic ion is unchanged on both sides of the equation, count it as a unit.
4. Balance each element one at a time by placing coefficients in front of the formulas. No coefficient is written for a 1. It is best to begin by balancing elements that only appear in one formula on each side of the equation. You can only balance equations by using coefficients; NEVER change the subscripts in a chemical formula that you already know is correct.
5. Check each atom or polyatomic ion to be sure that they are equal on both sides of the equation.
6. Make sure that all coefficients are in the lowest possible ratio. If necessary, reduce to the lowest ratio.

Sample Problem 11.1: Balancing Chemical Equations

Aqueous solutions of lead(II) nitrate and sodium chloride are mixed. The products of the reaction are an aqueous solution of sodium nitrate and a solid precipitate of lead(II) chloride.

Step 1: Plan the problem.

Follow the steps for writing and balancing a chemical equation.

Solve.

Write the skeleton equation with the correct formulas.

Pb(NO3)2(aq) + NaCl(aq) → NaNO3(aq) + PbCl2(s)

Count the number of each atom or polyatomic ion on both sides of the equation (Table below).

Unbalanced Reactants/Products
reactants products
1 Pb atom 1 Pb atom
2 NO3- 1 NO3-
1 Na atoms 1 Na atoms
1 Cl atom 2 Cl atoms

The nitrate ions and the chlorine atoms are unbalanced. Start by placing a 2 in front of the NaCl. This increases the reactant counts to 2 Na atoms and 2 Cl atoms. Then place a 2 in front of the NaNO3. The result is:

Pb(NO3)2(aq) + 2NaCl(aq) → 2NaNO3(aq) + PbCl2(s)

The new count for each atom and polyatomic ion becomes (Table below):

Balanced Reactants/Products
reactants products
1 Pb atom 1 Pb atom
2 NO3- 2 NO3-
2 Na atoms 2 Na atoms
2 Cl atom 2 Cl atoms

The equation is now balanced since there are equal numbers of atoms of each element on both sides of the equation.

Practice Problems
1. Balance the following equations.
1. Zn(s) + HCl(aq) → ZnCl2(aq) + H2(g)
2. Li(s) + N2(g) → Li3N(s)
2. Create a balanced chemical equation from the following word equations.
1. Potassium + water → potassium hydroxide + hydrogen gas
2. Sodium phosphate + calcium chloride → sodium chloride + calcium phosphate

Some equations provide a challenge to balancing when one or more of the elements can’t be balanced by simply using one coefficient. Aluminum reacts with oxygen gas to form aluminum oxide according to the equation:

Al(s) + O2(g) → Al2O3(s)

Since there are 2 oxygen atoms on the reactant side and 3 oxygen atoms on the product side, no single whole-number coefficient will balance the oxygen atoms. Find the least common multiple of 2 and 3, which is 6. Placing a 3 in front of the O2 and a 2 in front of the Al2O3 will result in 6 oxygen atoms on both sides. Finish by balancing the aluminum with a 4.

4Al(s) + 3O2(g) → 2Al2O3(s)

The equation is balanced with 4 Al atoms and 6 O atoms on each side.

Finally, we will return to the equation from earlier where methane was reacted with oxygen to form carbon dioxide and water.

CH4(g) + O2(g) → CO2(g) + H2O(l)

The element oxygen appears in two different places on the product side of the equation, so you should not start by trying to balance the oxygen. Instead, balance the carbon and the hydrogen first. The carbon is already balanced, but the hydrogen is balanced by placing a 2 in front of the water.

CH4(g) + O2(g) → CO2(g) + 2H2O(l)

Now count the total number of oxygen atoms on the product side: two from the CO2 and two from the 2H2O to give a total of four. Place a 2 in front of the O2.

CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

Balancing difficult equations can be a trial-and-error process and is a skill that requires practice. If you find that one particular strategy with a tough equation isn’t working, start over and balance a different element first. Persistence will lead you to the correct balanced equation.

You can watch a video lecture about balancing chemical equations at http://www.khanacademy.org/science/chemistry/chemical-reactions-stoichiometry/v/balancing-chemical-equations

You can also play a game called "Balancing Act" at http://education.jlab.org/elementbalancing/index.html

## Lesson Summary

• Chemical reactions can be described as the process of one or more reactants being transformed into one or more products. In a word equation, the names of the reactants are separated from the names of the products by a yield arrow.
• A skeleton equation shows the chemical formulas and physical states of the reactants and products, but it does not account for their relative amounts.
• Chemical reactions result solely from the rearrangement of atoms, so the law of conservation of mass must be observed. Coefficients are placed in front of chemical formulas to balance a chemical equation, meaning that the same quantities of each kind of atom are present on each side of the equation.

## Lesson Review Questions

### Reviewing Concepts

1. Identify the reactants and products in each chemical reaction.
1. In photosynthesis, carbon dioxide and water react to form glucose and oxygen.
2. Magnesium oxide forms when magnesium is exposed to oxygen gas.
2. What is the relationship between an equal sign and a yield sign?
3. Write sentences that completely describe the chemical reactions shown in the skeleton equations below.
1. \begin{align*}\text{H}_2\text{O}_2(l) \overset{\text{MnO}_2}{\rightarrow} \text{H}_2\text{O}(l) + \text{O}_2(g)\end{align*}
2. \begin{align*}\text{CuCO}_3(s) \overset{\Delta}{\rightarrow} \text{CuO}(s) + \text{CO}_2(g)\end{align*}
3. \begin{align*}\text{Cs}(s) + \text{H}_2\text{O}(l) \rightarrow \text{CsOH}(aq) + \text{H}_2(g)\end{align*}
4. How many atoms of each element are represented by the following combinations of coefficients and chemical formulas?
1. 5Br2
2. 2NH3
3. 4(NH4)2SO4
4. 2CH3COOH
5. 3Fe(NO3)3
6. 2K3PO4
5. The skeleton equation for the reaction of nitrogen gas with oxygen gas to form dinitrogen monoxide is shown below. Explain why the equation below is not a correctly balanced equation for this reaction.

### Problems

1. Balance each of the following equations.
1. KClO3 → KCl + O2
2. Ca(OH)2 + HBr → CaBr2 + H2O
3. C4H10 + O2 → CO2 + H2O
4. NH3 + CuO → Cu + N2 + H2O
2. Write and balance chemical equations for each of the following word equations.
1. sodium carbonate → sodium oxide + carbon dioxide
2. tetraphosphorus decoxide + water → phosphoric acid
4. ammonium carbonate → ammonia + water + carbon dioxide
3. Write and balance chemical equations from the following descriptions. Include symbols for the physical states of each reaction component.
1. Solid barium oxide is reacted with water and forms aqueous barium hydroxide.
2. Aqueous lithium phosphate reacts with aqueous iron(III) nitrate to form aqueous lithium nitrate and solid iron(III) phosphate.
3. Aluminum metal is reacted with an aqueous solution of zinc chloride to form aqueous aluminum chloride and solid zinc.
4. Iron(III) oxide solid reacts with carbon monoxide gas to produce iron and carbon dioxide gas.
4. The following equations are incorrect in some way. Identify and correct each error, and then balance the corrected equation.
1. K + O2 → KO2
2. Ag2O → Ag2 + O
3. NaCl + F2 → NaF2 + Cl

## Points to Consider

It is important for a chemist to be able to predict the products of chemical reactions. This task is made easier by placing known reactions into specific categories based on the ways in which the substances behave in those reactions.

• What are combination and decomposition reactions?
• What are single replacement and double replacement reactions?
• What is a combustion reaction?

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