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A second inventory shows
Reactants: 3 C
8 H
2 O
Products: 3 C
8 H (4 × 2 = 8)
10 O [(3 × 2) + (4 × 1) = 10]
The O atoms are still unbalanced. Place a 5 in front of O 2 , and the equa-
tion is balanced (5 × 2 = 10). Remember that you cannot change the
subscripts and that oxygen occurs as a diatomic molecule of O 2 .
C 3 H 8 ( g) + 5 O 2 ( g) → 3 CO 2 ( g) + 4 H 2 O( g)
(balanced)
Step 4: Another inventory shows (a) the number of atoms on both
sides are now equal and (b) the coefficients are 1:5 → 3:4, the
lowest possible whole number ratio. The equation is balanced.

EXAMPLE 10.6
One type of water hardness is caused by the presence of calcium
bicarbonate in solution, Ca(HCO 3 ) 2 . One way to remove the troublesome
calcium ions from wash water is to add washing soda, which is sodium
FIGURE 10.7 One of two burners is operating at the moment
carbonate, Na 2 CO 3 . The reaction yields sodium bicarbonate (NaHCO 3 )
as this hot air balloon ascends. The burners are fueled by propane and calcium carbonate (CaCO 3 ), which is insoluble. Since CaCO 3 is in-
(C 3 H 8 ), a liquefied petroleum gas (LPG). Like other forms of petro-
soluble, the reaction removes the calcium ions from solution. Write a
leum, propane releases large amounts of heat during the chemical balanced equation for the reaction.
reaction of burning.

SOLUTION
EXAMPLE 10.5
Propane is a liquefied petroleum gas (LPG) that is often used as a bot- Step 1: Write the unbalanced equation.
tled substitute for natural gas (Figure 10.7). Propane (C 3 H 8 ) reacts with Ca(HCO 3 ) 2 (aq) + Na 2 CO 3 (aq) → NaHCO 3 (aq) + CaCO 3 ↓
oxygen (O 2 ) to yield carbon dioxide (CO 2 ) and water vapor (H 2 O).
What is the balanced equation for this reaction? (not balanced)

Step 2: Inventory the numbers of each kind of atom. This reac-
SOLUTION tion has polyatomic ions that appear on both sides, so
they should be treated as independent units with a charge
Step 1: Write the correct formulas of the reactants and products in (generalization 2). The inventory is
an unbalanced equation.
Reactants: 1 Ca Products: 1 Ca
C 3 H 8 ( g) + O 2 ( g) → CO 2 ( g) + H 2 O( g) 2 (HCO 3 ) 1– 1(HCO 3 ) 1–
(unbalanced) 2 Na 1 Na
2– 2–
1 (CO 3 ) 1 (CO 3 )
Step 2: Inventory the numbers of each kind of atom.
Step 3: Placing a coefficient of 2 in front of NaHCO 3 will balance
Reactants: 3 C Products: 1 C
the equation,
8 H 2 H
Ca(HCO 3 ) 2 (aq) + Na 2 CO 3 (aq) → 2 NaHCO 3 (aq) + CaCO 3 ↓
2 O 3 O
(balanced)
Step 3: Determine where to place coefficients to balance the
equation. Looking at the compound with the most atoms Step 4: An inventory shows
(generalization 1), you can see that a propane molecule
has 3 C and 8 H. Placing a coefficient of 3 in front of CO 2 Reactants: 1 Ca Products: 1 Ca
1– 1–
and a 4 in front of H 2 O will balance these atoms (3 of C 2 (HCO 3 ) 2 (HCO 3 )
and 4 × 2 = 8 H atoms on the right are the same number 2 Na 2 Na
of atoms as C 3 H 8 has on the left), 2– 2–
1 (CO 3 ) 1 (CO 3 )
C 3 H 8 (g) + O 2 (g) → 3 CO 2 (g) + 4 H 2 O(g)
The coefficient ratio of 1:1 → 2:1 is the lowest whole number ratio. The
(not balanced) equation is balanced.

258 CHAPTER 10 Chemical Reactions 10-8