Balancing Equations Continued

Another Example on Balancing Chemical Equations

Write a balanced equation for the reaction of molecular nitrogen (N₂) and oxygen (O₂) to form dinitrogen pentoxide.

Solution

First, write the unbalanced equation.

\(\mathrm{N_2} + \mathrm{O_2} \longrightarrow \mathrm{N_2O_5} \text{ (unbalanced)}\)

Next, count the number of each type of atom present in the unbalanced equation.

Element	Reactants	Products	Balanced?
N	1 × 2 = 2	1 × 2 = 2	2 = 2, yes
O	1 × 2 = 2	1 × 5 = 5	2 ≠ 5, no

Though nitrogen is balanced, changes in coefficients are needed to balance the number of oxygen atoms. To balance the number of oxygen atoms, a reasonable first attempt would be to change the coefficients for the O₂ and N₂O₅ to integers that will yield 10 O atoms (the least common multiple for the O atom subscripts in these two formulas).

\(\mathrm{N_2} + \mathbf{5}\mathrm{O_2} \longrightarrow \mathbf{2}\mathrm{N_2O_5} \text{ (unbalanced)}\)

Element	Reactants	Products	Balanced?
N	1 × 2 = 2	2 × 2 = 4	2 ≠ 4, no
O	5 × 2 = 10	2 × 5 = 10	10 = 10, yes

The N atom balance has been upset by this change; it is restored by changing the coefficient for the reactant N₂ to 2.

\(\mathrm{2N_2} + \mathrm{5O_2} \longrightarrow \mathrm{2N_2O_5}\)

Element	Reactants	Products	Balanced?
N	2 × 2 = 4	2 × 2 = 4	4 = 4, yes
O	5 × 2 = 10	2 × 5 = 10	10 = 10, yes

The numbers of N and O atoms on either side of the equation are now equal, and so the equation is balanced.

Yet Another Example

It is sometimes convenient to use fractions instead of integers as intermediate coefficients in the process of balancing a chemical equation. When balance is achieved, all the equation’s coefficients may then be multiplied by a whole number to convert the fractional coefficients to integers without upsetting the atom balance.

For example, consider the reaction of ethane (C₂H₆) with oxygen to yield H₂O and CO₂, represented by the unbalanced equation:

\(\mathrm{C_2H_6} + \mathrm{O_2} \longrightarrow \mathrm{H_2O} + \mathrm{CO_2} \text{ (unbalanced)}\)

Following the usual inspection approach, one might first balance C and H atoms by changing the coefficients for the two product species, as shown:

\(\mathrm{C_2H_6} + \mathrm{O_2} \longrightarrow \mathrm{3H_2O} + \mathrm{2CO_2} \text{ (unbalanced)}\)

This results in seven O atoms on the product side of the equation, an odd number—no integer coefficient can be used with the O₂ reactant to yield an odd number, so a fractional coefficient, \(\frac{7}{2},\) is used instead to yield a provisional balanced equation:

\(\mathrm{C_2H_6} + \frac{7}{2} \mathrm{O_2} \longrightarrow \mathrm{3H_2O} + \mathrm{2CO_2} \text{ (unbalanced)}\)

A conventional balanced equation with integer-only coefficients is derived by multiplying each coefficient by 2:

\(\mathrm{2C_2H_6} + \mathrm{7O_2} \longrightarrow \mathrm{6H_2O} + \mathrm{4CO_2} \text{ (unbalanced)}\)

Finally with regard to balanced equations, recall that convention dictates use of the smallest whole-number coefficients. Although the equation for the reaction between molecular nitrogen and molecular hydrogen to produce ammonia is, indeed, balanced,

\(\mathrm{3N_2} + \mathrm{9H_2} \longrightarrow \mathrm{6NH_3}\)

the coefficients are not the smallest possible integers representing the relative numbers of reactant and product molecules. Dividing each coefficient by the greatest common factor, 3, gives the preferred equation:

\(\mathrm{N_2} + \mathrm{3H_2} \longrightarrow \mathrm{2NH_3}\)

Additional Information in Chemical Equations

The physical states of reactants and products in chemical equations very often are indicated with a parenthetical abbreviation following the formulas. Common abbreviations include s for solids, l for liquids, g for gases, and aq for substances dissolved in water (aqueous solutions, as introduced in Chemistry 101). These notations are illustrated in the example equation here:

\(\mathrm{2Na}(s) + \mathrm{2H_2O}(l) \longrightarrow \mathrm{2NaOH}(aq) + \mathrm{H_2}(g)\)

This equation represents the reaction that takes place when sodium metal is placed in water. The solid sodium reacts with liquid water to produce molecular hydrogen gas and the ionic compound sodium hydroxide (a solid in pure form, but readily dissolved in water).

Special conditions necessary for a reaction are sometimes designated by writing a word or symbol above or below the equation’s arrow. For example, a reaction carried out by heating may be indicated by the uppercase Greek letter delta (Δ) over the arrow.

\(\mathrm{CaCO_3}(s) \overset{\Delta}{\longrightarrow} \mathrm{CaO}(s) + \mathrm{CO_2}(g)\)

Other examples of these special conditions will be encountered in more depth in other tutorials.