Balancing Chemical EquationsKey Terms:

Balanced Chemical EquationsCoefficientSubscript

Lesson ObjectivesThe student will:

explain the roles of subscripts and coefficients in chemical equations.

write a balanced chemical equation when given the unbalanced equation for any chemical reaction.

explain the role of the law of conservation of mass in a chemical reaction.

Vocabularybalanced chemical equation

a chemical equation in which the number of each type of atom is equal on the two sides of the equation

Coefficient a whole number that appears in front of a

formula in a balanced chemical equationsubscript

part of the chemical formula that indicates the number of atoms of the preceding element

IntroductionEven though chemical compounds are broken up to

form new compounds during a chemical reaction, atoms in the reactants do not disappear, nor do new atoms appear to form the products. In chemical reactions, atoms are never created or destroyed. The same atoms that were present in the reactants are present in the products. The atoms are merely re-organized into different arrangements. In a complete chemical equation, the two sides of the equation must be balanced. That is, in a balanced chemical equation, the same number of each atom must be present on the reactant and product sides of the equation.

Balancing EquationsThe process of writing a balanced chemical

equation involves three steps. Step 1: Know what the reactants and products

are, and write a word equation for the reaction.Step 2: Write the formulas for all the reactants

and products.Step 3: Adjust the coefficients to balance the

equation.

Friendly ReminderThere are a number of elements shown in the

table that exist as diatomic molecules under normal conditions. When any of these elements appear in word equations, you must remember that the name refers to the diatomic molecule and insert the diatomic formula into the symbolic equation.

Coefficients and SubscriptsThere are two types of numbers that appear

in chemical equations. There are subscripts, which are part of the chemical formulas of the reactants and products, and there are coefficients that are placed in front of the formulas to indicate how many molecules of that substance are used or produced.

Example 1Write a balanced equation for the reaction that occurs

between chlorine gas and aqueous sodium bromide to produce liquid bromine and aqueous sodium chloride.

Step 1: Write the word equation (keeping in mind that chlorine and bromine refer to the diatomic molecules).chlorine + sodium bromide yields bromine + sodium

chlorideStep 2: Substitute the correct formulas into the equation.

Cl2+NaBr Br2+NaCl

Step 3: Insert coefficients where necessary to balance the equation.Cl2+2 NaBr Br2+ 2 NaCl

Example 2Write a balanced equation for the reaction between aluminum

sulfate and calcium bromide to produce aluminum bromide and calcium sulfate.

Step 1: Write the word equation. aluminum sulfate + calcium bromide yields aluminum bromide +

calcium sulfateStep 2: Replace the names of the substances in the word equation

with formulas. Al2(SO4)3+CaBr2 AlBr3+CaSO4

Step 3: Insert coefficients to balance the equation.products.

Al2(SO4)3 + CaBr2 2 AlBr3+CaSO4 Al2(SO4)3 + CaBr2 2 AlBr3+3 CaSO4 Al2(SO4)3 + 3 CaBr2 2 AlBr3+3 CaSO4 2 Al2(SO4)3 + 6 CaBr2 4 AlBr3 + 6 CaSO4

Practice Problem 1Given the following skeletal (un-balanced)

equations, balance them.CaCO3(s) CaO(s)+CO2(g)

CaCO3(s) CaO(s) + CO2(g)

H2SO4(aq) + Al(OH)3(aq) Al2(SO4)3(aq) + H2O(l)

3 H2SO4(aq) + 2 Al(OH)3(aq) Al2(SO4)3(aq) + 6 H2O(l)

Ba(NO3)2(aq) +Na2CO3(aq) BaCO3(aq)

+NaNO3(aq)

Ba(NO3)2(aq) + Na2CO3(aq) BaCO3(aq) +2 NaNO3(aq)

Conversion of Mass in Chemical ReactionsWe already know from the law of

conservation of mass that mass is conserved in chemical reactions. But what does this really mean? Consider the following reaction.Fe(NO3)3 + 3 NaOH Fe(OH)3 + 3 NaNO3

Verify to yourself that this equation is balanced by counting the number of each type of atom on each side of the equation. We can demonstrate that mass is conserved by determining the total mass on both sides of the equation.

Mass of Reactant SideFe(NO3)3 + 3 NaOH Fe(OH)3 + 3 NaNO3

Mass of the Reactant Side:1 molecule of Fe(NO3)3 molecular weight =

(1)*(241.9 daltons) = 241.9 daltons3 molecules of NaOHmolecular weight =

(3)*(40.0 daltons) = 120. daltonsTotal mass of reactants = 241.9 daltons + 120.

daltons = 361.9 daltons

Product Side MassFe(NO3)3 + 3 NaOH Fe(OH)3 + 3 NaNO3

1 molecule of Fe(OH)3molecular weight = (1)*(106.9 daltons) = 106.9 daltons

3 molecules of NaNO3molecular weight = (3)*(85.0 daltons) = 255 daltons

Total mass of products = 106.9 daltons + 255 daltons = 361.9 daltons

Lesson SummaryChemical equations must always be balanced.Balanced chemical equations have the same

number and type of each atom on both sides of the equation.

The coefficients in a balanced equation must be the simplest whole number ratio.

Mass is always conserved in chemical reactions.

Practice Problem 2Explain in your own words why coefficients

can change but subscripts must remain constant.

Which set of coefficients will properly balance the following equation: C2H6 + O2 CO2 + H2O

a) 1, 1, 1, 1b) 1, 3, 2, 2c) 1, 3.5, 2, 3d) 2, 7, 4, 6

Practice Problem 3When properly balanced, what is the sum of

all the coefficients in the following chemical equation: SF4 +

H2O H2SO3 + HF a) 4b) 7c) 9d) None of the above

Practice Problem 4When the following equation is balanced,

what is the coefficient found in front of the O2:

P4+O2+H2O H3PO4 a) 1b) 3c) 5d) 7