4.1: Chemical reaction equations (2023)

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    Skills to develop

    • Derive chemical equations from narrative descriptions of chemical reactions.
    • Write and balance chemical equations in molecular, total ion, and net ion format.

    In the previous chapter, the use of chemical formulas to represent ionic and covalent compounds was presented. To extend this symbolism to represent both the identities and relative amounts of substances undergoing chemical (or physical) change, one must write and balancechemical equation. As an example, consider the reaction between a molecule of methane (CH4) and two diatomic oxygen molecules (O2) to produce a carbon dioxide (CO) molecule2) and two water molecules (H2ISLAND). The chemical equation representing this process is shown in the upper half of the figure \(\PageIndex{1}\), while space-filling molecular models are shown in the lower half of the figure.

    4.1: Chemical reaction equations (1)

    Figure \(\PageIndex{1}\): The reaction between methane and oxygen to form carbon dioxide and water (shown below) can be represented by a chemical equation using formulas (above).

    This example illustrates the fundamental aspects of any chemical equation:

    1. The reacting substances are namedreactant, and their formulas are placed on the left side of the equation.
    2. The substances that arise from the reaction are called upProducts, and their formulas are placed on the right side of the equation.
    3. Plus signs (+) separate individual reactant and product formulas and an arrow(⟶)separates the reactant and product sides (left and right) of the equation.
    4. The relative number of reactant and product species is represented bycoefficients (Numbers are immediately to the left of each formula). A coefficient of 1 is usually omitted.

    It is common practice to use the smallest possible integer coefficients in a chemical equation, as in this example. However, note that these coefficients represent thatrelativeNumber of reactants and products and can therefore be correctly interpreted as ratios. Methane and oxygen react to form carbon dioxide and water in the ratio 1:2:1:2. This relationship is satisfied when the number of these molecules is 1-2-1-2 or 2-4-2-4 or 3-6-3-6 etc. (Figure \(\PageIndex{ 2}\)). Likewise, these coefficients can be interpreted in terms of any unit of magnitude (number), allowing this equation to be read correctly in many ways, including:

    • Likemethane molecule andtoOxygen molecules react to shapelikecarbon dioxide molecule andtowater molecules.
    • A dozenmethane molecules andtwo dozenOxygen molecules react to shapea dozencarbon dioxide molecules andtwo dozenwater molecules.
    • A moleof methane molecules and2 molOxygen molecules react with yield1 molof carbon dioxide molecules and2 molof water molecules.

    4.1: Chemical reaction equations (2)

    Figure \(\PageIndex{2}\): Regardless of the absolute number of molecules involved, the ratio of the number of molecules of each species reacting (the reactants) to the molecules of each species forming (the products) is equal and given in the chemical equation.

    Because of this relative relationship, chemical equations give us a tool to translate between eventsmicroscopicallyin a reaction in terms of atoms and molecules and what happensmacroscopicallyin moles, which refers to measurable quantities such as mass and volume that we can work with in the laboratory.

    A chemical equation always represents both partsmicroscopicallyReaction (individual atoms and molecules) andmacroscopicallyreaction (mol).

    balancing equations

    If is a chemical equationbalanced it meansthat for each element involved in the reaction, the same number of atoms are represented on the reactant and product sides. This is a requirement that the equation must meet in order to be consistent with the law of conservation of matter. This can be confirmed by simply summing the number of atoms on each side of the arrow and comparing these sums to ensure they are equal. Note that the number of atoms for a given element is calculated by multiplying the coefficient of any formula containing that element by the index of the element in the formula. When an element appears in more than one formula on a given side of the equation, the number of atoms represented in each formula must be calculated and then added together. For example, both product species in the example reaction, \(\ce{CO2}\) and \(\ce{H2O}\), contain the element oxygen and thus the number of oxygen atoms on the product side of the equation is Actual

    \[\left(1\: \cancel{\ce{CO_2} \: \text{Molekül}} \times \dfrac{2\: \ce{O} \: \text{Atome}}{ \cancel{\ ce{CO_2} \: \text{Molekül}}}\right) + \left( \cancel{ \ce{2H_2O} \: \text{Molekül} }\times \dfrac{1\: \ce{O}\ : \text{Atom}}{\cancel{ \ce{H_2O} \: \text{Molekül}}}\right)=4\: \ce{O} \: \text{Atome}\]

    The equation for the reaction between methane and oxygen to form carbon dioxide and water is confirmed to be balanced using this approach, as shown here:

    \[\ce{CH4 +2O2\højrepil CO2 +2H2O}\]

    Element reactant Products Balanced?
    C 1×1 = 1 1×1 = 1 1 = 1, and
    H 4×1 = 4 2×2 = 4 4 = 4, and
    Ö 2×2 = 4 (1×2) + (2×1) = 4 4 = 4, and

    A balanced chemical equation can often be derived from a qualitative description of a chemical reaction by a relatively simple approach called balancing by inspection. As an example, consider the breakdown of water to form molecular hydrogen and oxygen. This process is represented qualitatively by aunbalancedchemical equation:

    \[\ce{H2O \rightarrow H2 + O2} \tag{unbalanced}\]

    A comparison of the number of H and O atoms on each side of this equation confirms their imbalance:

    Element reactant Products Balanced?
    H 1×2 = 2 1×2 = 2 2 = 2, and
    Ö 1×1 = 1 1×2 = 2 1 ≠ 2, no

    The number of H atoms on the reactant and product sides of the equation is the same, but the number of O atoms is not. To achieve equilibrium mustcoefficientsthe equation can be modified as needed. Remember, of course, thatFormula indexerpartially define the substance's identity and therefore cannot be changed without changing the qualitative meaning of the equation. For example, changing the reactant formula for H2O to H2Ö2would lead to an equilibrium in the number of atoms, but this also changes the identity of the reactant (it is now hydrogen peroxide and not water). The O atom balance can be achieved by changing the coefficient of H2O to 2

    \[\ce{2H2O \rightarrow H2 + O2} \tag{unbalanced}\]

    Element reactant Products Balanced?
    H 2 ×2 = 4 1×2 = 2 4 ≠ 2, no
    Ö 2×1 = 2 1×2 = 2 2 = 2, and

    The H atomic balance was disturbed by this change, but can be easily restored by changing the coefficient of H2product for 2.

    \[\ce{2H_2O \rightarrow 2H2 + O2} \tag{balanceret}\]

    Element reactant Products Balanced?
    H 2×2 = 4 2 ×2 = 2 4 = 4, and
    Ö 2×1 = 2 1×2 = 2 2 = 2, and

    These coefficients give the same number of H and O atoms on the reactant and product sides, and the balanced equation is therefore:

    \[\ce{2H_2O \rightarrow 2H_2 + O_2}\]

    Example \(\PageIndex{1}\):Balancing chemical equations

    Write a balanced equation for the reaction of molecular nitrogen (N2) and oxygen (O2) to nitrous oxide.


    First write the unbalanced equation.

    \[\ce{N_2 + O_2 \rightarrow N_2O_5} \tag{unbalanced}\]

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

    Element reactant Products Balanced?
    N 1×2 = 2 1×2 = 2 2 = 2, and
    Ö 1×2 = 2 1×5 = 5 2 ≠ 5, no

    Although nitrogen is in equilibrium, changes in coefficients are required 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 O2and N2Ö5to integers yielding 10 O atoms (the least common multiple of the O atom indices in these two formulas).

    \[\ce{N_2 + 5 O2 \rightarrow 2 N2O5} \tag{unbalanced}\]

    Element reactant Products Balanced?
    N 1×2 = 2 2 ×2 = 4 2 ≠ 4, no
    Ö 5 ×2 = 10 2 ×5 = 10 10 = 10, and

    The N atom balance is disturbed by this change; it is restored by changing the coefficient of the reactant N2to 2.

    \[\ce{2N_2 + 5O_2\højrepil 2N_2O_5}\]

    Element reactant Products Balanced?
    N 2 ×2 = 4 2×2 = 4 4 = 4, and
    Ö 5×2 = 10 2×5 = 10 10 = 10, and

    The number of N and O atoms on each side of the equation is now equal, so the equation is balanced.

    Exercise \(\PageIndex{1}\)

    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.)


    \[\ce{2NH4NO3 \rightarrow 2N2 + O2 + 4H2O} \nonumber\]

    Sometimes it is convenient to use fractions instead of whole numbers as intermediate coefficients when balancing a chemical equation. Once equilibrium is reached, all the coefficients of the equation can be multiplied by an integer to convert the fractional coefficients to integers without disturbing the atomic balance. Consider, for example, the reaction of ethane (C2H6) with oxygen to H2O og CO2, represented by the unbalanced equation:

    \[\ce{C_2H_6 + O_2 \rightarrow H_2O + CO_2} \tag{unbalanced}\]

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

    \[\ce{C_2H_6 + O_2 \rightarrow 3H_2O + 2CO_2} \tag{unausgeglichen}\]

    This results in seven O atoms on the product side of the equation, an odd number - an integer coefficient cannot be used for O2reactant to give an odd number, ie. a fractional coefficient,\(\ce{7/2}\),is used instead to obtain a tentative balanced equation:

    \[\ce{C2H6 + 7/2 O2\højrepil 3H2O + 2CO2} \nonummer \]

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

    \[\ce{2C2H6 +7O2\højrepil 6H2O + 4CO2}\]

    Regarding balanced equations, remember that convention dictates the use ofsmallest integer coefficients. Although the following equation for the reaction between molecular nitrogen and molecular hydrogen to form ammonia is actually balanced,

    \[\ce{3N2 +9H2\højrepil 6NH3}\]

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

    \[\ce{N2 + 3H2\højrepil 2NH3}\]

    Phet simulation

    Use this interactivelytutorialfor additional practice in balancing equations.

    Additional information in chemical equations

    The physical states of reactants and products in chemical equations are very often indicated by an abbreviation in parentheses after the formulas. Common abbreviations include:Sfor solids,lfor liquids,Gfor gases andaqfor substances dissolved in water (aqueous solutions). These notations are illustrated in the example equation here:

    \[\ce{2Na(s) + 2H2O(l) \rightarrow 2NaOH(aq) + H2(g)}\]

    This equation represents the reaction that takes place when sodium metal is added to water. The solid sodium reacts with liquid water to form molecular hydrogen gas and the ionic compound sodium hydroxide (a solid in its pure form but easily soluble in water).

    Special conditions required for a reaction are sometimes indicated by writing a word or symbol above or below the equation's arrow. For example, a reaction carried out by heating can be indicated by the capital Greek letter delta (Δ) above the arrow.

    \[\ce{CaCO3}(s)\xrightarrow{\:\Delta\:} \ce{CaO}(s)+\ce{CO2}(g)\]

    Other examples of these special conditions are treated in more detail in later chapters.

    In view of the abundance of water on earth, it is obvious that numerous chemical reactions take place in aqueous media. In the remainder of this chapter, we will examine the use of chemical equations to describe various classes of aqueous reactions, especially those involving ionic compounds. While understanding the qualitative characteristics of different types of reactions helps us predict when a chemical reaction will occur, writing balanced chemical equations for these reactions is an essential skill for predicting quantitative aspects of how they will occur .


    Chemical equations are symbolic representations of chemical and physical changes. Formulas for the substances undergoing changes (reactants) and the substances produced by the change (products) are separated by an arrow and preceded by integer coefficients indicating their relative numbers. Balanced equations are those whose coefficients result in an equal number of atoms for each element in the reactants and products.



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