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Given the abundance of water on earth, it stands to reason that a great many chemical reactions take place in aqueous media. When ions are involved in these reactions, the chemical equations may be written with various levels of detail appropriate to their intended use. To illustrate this, consider a reaction between ionic compounds taking place in an aqueous solution. When aqueous solutions of CaCl 2 and AgNO 3 are mixed, a reaction takes place producing aqueous Ca(NO 3) 2 and solid AgCl: 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 O 2 and N 2O 5 to integers that will yield 10 O atoms (the least common multiple for the O atom subscripts in these two formulas). The numbers of H atoms on the reactant and product sides of the equation are equal, but the numbers of O atoms are not. To achieve balance, the coefficients of the equation may be changed as needed. Keep in mind, of course, that the formula subscripts define, in part, the identity of the substance, and so these cannot be changed without altering the qualitative meaning of the equation. For example, changing the reactant formula from H 2O to H 2O 2 would yield balance in the number of atoms, but doing so also changes the reactant’s identity (it’s now hydrogen peroxide and not water). The O atom balance may be achieved by changing the coefficient for H 2O to 2. Comparing the number of \(\ce{H}\) and \(\ce{O}\) atoms on either side of this equation confirms its imbalance: Element A conventional balanced equation with integer-only coefficients is derived by multiplying each coefficient by 2:
This balanced equation, derived in the usual fashion, is called a molecular equation because it doesn’t explicitly represent the ionic species that are present in solution. When ionic compounds dissolve in water, they may dissociate into their constituent ions, which are subsequently dispersed homogenously throughout the resulting solution (a thorough discussion of this important process is provided in the chapter on solutions). Ionic compounds dissolved in water are, therefore, more realistically represented as dissociated ions, in this case: Explicitly representing all dissolved ions results in a complete ionic equation. In this particular case, the formulas for the dissolved ionic compounds are replaced by formulas for their dissociated ions: 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 (\(\ce{Δ}\)) over the arrow. One dozen methane molecules and two dozen oxygen molecules react to yield one dozen carbon dioxide molecules and two dozen water molecules.left(1 CO_2 \text { molecule } \times \frac{2 O \text { atoms }}{ CO_2 \text { molecule }}\right)+\left(2 H_2 O \text { molecules } \times \frac{1 O \text { atom }}{ H_2 O \text { molecule }}\right)=4 O \text { atoms } \nonumber \] One mole of methane molecules and 2 moles of oxygen molecules react to yield 1 mole of carbon dioxide molecules and 2 moles of water molecules. Unlike these three ionic compounds, \(\ce{AgCl}\) does not dissolve in water to a significant extent, as signified by its physical state notation, s. 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 (C 2H 6) with oxygen to yield H 2O and CO 2, represented by the unbalanced equation: Write a balanced equation for the decomposition of ammonium nitrate to form molecular nitrogen, molecular oxygen, and water. (Hint: Balance oxygen last, since it is present in more than one molecule on the right side of the equation.) Answer
One methane molecule and two oxygen molecules react to yield one carbon dioxide molecule and two water molecules. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. A balanced chemical equation often may be derived from a qualitative description of some chemical reaction by a fairly simple approach known as balancing by inspection. Consider as an example the decomposition of water to yield molecular hydrogen and oxygen. This process is represented qualitatively by an unbalanced chemical equation: These coefficients yield equal numbers of both H and O atoms on the reactant and product sides, and the balanced equation is, therefore:The N atom balance has been upset by this change; it is restored by changing the coefficient for the reactant N 2 to 2. Following the usual inspection approach, one might first balance C and H atoms by changing the coefficients for the two product species, as shown: 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 the preceding chapter). These notations are illustrated in the example equation here: The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation.
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