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3.6: Ionic Bonding: Writing Chemical Formulas of Ionic Compounds Containing Main Group Elements

  • Page ID
    213171
  • Learning Objectives
    • Write the chemical formulas of ionic compounds containing main group elements.

    Two types of particles, atoms and ions, have now been discussed in this text.  An atom, while net-neutral, generally does not possess an octet, which is energetically-unfavorable, and, therefore, will ionize to achieve a more stable configuration.  The ionization process, in which an atom gains or loses up to three valence electrons, does result in a particle that contains eight, fully-paired valence electrons.  While ionization improves the stability of a particle's electron configuration, relative to that of an atom, the resultant particle is charged.  As its charged state is inherently destabilizing, a single ion cannot exist alone in nature and instead must combine with an ion of the opposite charge to form an ionic compound.  If the correct cation-to-anion ratio is achieved, an ionic compound will be highly stable, as it will exist as a net-neutral species consisting of particles that have achieved octet configurations.  The process for determining these cation-to-anion ratios, which will ultimately be denoted with subscripts in chemical formulas, will be described in the following paragraphs and expanded upon in the next several sections of this chapter.

    Writing Chemical Formulas of Ionic Compounds Containing Main Group Elements

    A chemical formula is an abbreviation that indicates both the type and relative proportion of elements that are present in a compound.  Elemental symbols are used to identify which elements are contained in the compound, and a whole-number subscript indicates the quantity in which the previous element is present.  If no subscript is written, an unwritten "1" is understood.  The subscripts in the chemical formula of an ionic compound will vary, based on the identities of the cation and anion that are being combined.

    For example, consider nitrogen and potassium

    Based on the combinations listed in Section 3.2, these elements will combine to form an ionic compound.  Recall that an ionic bond is produced when a cation exists in close physical proximity to an anion, creating an electrostatic attractive force.  In the given combination, nitrogen, a non-metal, ionizes to form an anion, and potassium, a metal, ionizes to form a cation.  After establishing that a pair of chemicals will form an ionic bond, a five-step process can be employed to determine the chemical formula of the resultant ionic compound. 

    1. Write the ion symbol for the ion that results upon the ionization of each of the given elements.  Based on the information presented in the previous sections of this chapter, nitrogen ionizes to form N3, and potassium ionizes to form K+1
       
    2. In order to ensure consistent formatting in all ionic chemical formulas, the symbol for the cation is written first.  In this example, K+1 will be written before N3 in the final chemical formula. 
       
    3. The signs of the ions are only used to determine the relative order in which the ion symbols are written.  As this information was established in the previous step, the "+" and "" signs can be removed, so that only the base elemental symbols and numerical superscripts remain.  In this example, the "+" sign is removed from K+1 and the "" sign is removed from N–3.  The revised symbols are written as K1 and N3, respectively.
       
    4. Use subscripts to indicate how many of each of the given ions are present in the base chemical formula.  Two different processes, both of which are presented below, can be used to determine this information. 
       
      1. The first process, which is considered the more "scientifically-correct" method, is known as the "Ratio Method," as it establishes the correct cation-to-anion ratio by equating the total charges of the cations to the sum of the charges of the anions, in order to ensure that the final compound will be a net-neutral species.  To determine this ratio, a mini-equation, in which the larger superscript value is multiplied by 1, and the smaller superscript value is multiplied by a variable, such as x, is solved.  In the current example, the larger superscript value is "3," and the smaller superscript value is "1."  Therefore,

        3(1) = 1(x
        3 = x 

        This result indicates that for every 1 of the ions with the larger superscript value, in this case, N3, 3 of the other ions, K1, are required to achieve charge-balance between them. 

        To apply this information, remove the numerical superscripts from each symbol and instead utilize subscripts to indicate the ratio established above.  Therefore, the resultant chemical formula, which is called a base formula, is K3N1.
         
      2. The alternative process for establishing this chemical formula is a "shortcut" known as the "Criss-Cross Method."  In this system, the superscript on the first symbol becomes the subscript on the second symbol, and the superscript on the second symbol is repositioned as the subscript on the first symbol, as shown below.

        Potassium Nitride.png

        This "shortcut" is known as the "Criss-Cross Method" because the numerical values effectively "criss-cross" over one another when they are moved to their new positions.  The resultant base formula is identical to what was derived using the first method:  K3N1
         
    5. The final step in this process is to ensure that the subscripts in the base formula are mathematically-appropriate for inclusion in an ionic compound. 
       
      1. If possible, the subscripts must be reduced to the lowest-common ratio of whole numbers by dividing both of the subscripts by the same numerical value.  This division should only be performed if both of the resultant subscripts remain whole numbers.  In the current example, no such division is possible.  Therefore, the chemical formula remains unchanged:  K3N1.

      2. If a "1" has been explicitly-written as a subscript, it must be removed.  As indicated previously, values of "1" are usually implicitly-understood in chemistry and, therefore, should not be written in a chemical formula.  In this example, the formula shown above does include an explicitly-written "1" and, therefore, should be revised to K3N.

    The chemical formula that results upon the completion of this final step is a chemically-correct formula for an ionic compound.  Therefore, K3N is the chemical formula for the compound formed when nitrogen and potassium bond with one another.
     

    Example \(\PageIndex{1}\)

    Write the chemical formula for the compound that is formed when aluminum and sulfur bond with one another.

    Solution

    Based on the combinations listed in Section 3.2, these elements will combine to form an ionic compound, because aluminum, a metal, ionizes to form a cation (Al+3), and sulfur, a non-metal, ionizes to form an anion (S–2).  The ion symbol for the cation is currently written first, as is required in an ionic chemical formula, so the order in which the ions are written should not change.  Removing the "+" and "" signs yields Al3 and S2, respectively.

    The subscripts for the base formula can be determined using either of the methods described above.

    The "Ratio" Method 
    Recall that this process establishes the correct cation-to-anion ratio by equating the total charges of the cations to the sum of the charges of the anions, in order to ensure that the final compound will be a net-neutral species.  To determine this ratio, a mini-equation, in which the larger superscript value is multiplied by 1, and the smaller superscript value is multiplied by a variable, such as x, is solved.  In the current example, the larger superscript value is "3," and the smaller superscript value is "2."  Therefore,

    3(1) = 2(x)
    1.5 = x

    This result indicates that for every 1 of the ions with the larger superscript value, in this case, Al3, 1.5 of the other ions, S2, are required to achieve charge-balance between them.  However, subscripts must be written as whole-number values, as it is physically-impossible for a fraction of an ion to exist.  Therefore, the half-fraction is cleared by doubling both of the numbers in the ratio indicated above.  Therefore, for every 2 of the ions with the larger superscript value, in this case, Al3, 3 of the other ions, S2, are required to achieve charge-balance between them.

    To apply this information, the numerical superscripts are removed from each symbol, and subscripts are utilized to indicate the ratio established above.  The resultant base formula is Al2S3.

    The "Criss-Cross" Method 
    In this system, the superscript on the first symbol becomes the subscript on the second symbol, and the superscript on the second symbol is repositioned as the subscript on the first symbol, as shown below.

    Aluminum Sulfide.png

    The resultant base formula is identical to what was derived using the first method:  Al2S3.

    The final step in this process is to ensure that the subscripts in the base formula are mathematically-appropriate for inclusion in an ionic compound.  In the current example, the subscripts are already the lowest-common ratio of whole numbers, so should not be further divided.  Furthermore, no explicitly-written "1"s are present.  Therefore, in this example, the base formula, Al2S3, is the chemically-correct formula for the compound formed when aluminum and sulfur bond with one another.

    Exercise \(\PageIndex{1}\)

    Write the chemical formula for the compound that is formed when each of the following combinations of elements bond with one another.

    1. Calcium and oxygen
    2. Chlorine and magnesium
    Answer a
    Based on the combinations listed in Section 3.2, these elements will combine to form an ionic compound, because calcium, a metal, ionizes to form a cation (Ca+2), and oxygen, a non-metal, ionizes to form an anion (O–2).  The ion symbol for the cation is currently written first, as is required in an ionic chemical formula, so the order in which the ions are written should not change.  Removing the "+" and "" signs yields Ca2 and O2, respectively.

    The subscripts for the base formula for this chemical combination can be determined using either of the methods described above.

    The "Ratio" Method 
    Recall that this process establishes the correct cation-to-anion ratio by equating the total charges of the cations to the sum of the charges of the anions, in order to ensure that the final compound will be a net-neutral species.  To determine this ratio, a mini-equation, in which the larger superscript value is multiplied by 1, and the smaller superscript value is multiplied by a variable, such as x, is solved.  In the current example, the superscript values are equal.  Therefore,

    2(1) = 2(x)
    1 = x

    This result indicates that these ions must be combined in a 1 to ratio, in order to achieve charge-balance between them.  To apply this information, the numerical superscripts are removed from each symbol, and subscripts are utilized to indicate the ratio established above.  The resultant base formula is Ca1O1.

    The "Criss-Cross" Method 
    In this system, the superscript on the first symbol becomes the subscript on the second symbol, and the superscript on the second symbol is repositioned as the subscript on the first symbol, as shown below.

    Calcium Oxide.png

    The resultant base formula, Ca2O2, is not identical to what was derived using the first method.

    The final step in this process is to ensure that the subscripts in the base formula are mathematically-appropriate for inclusion in an ionic compound.  However, as the base formula derived from the "Ratio Method" is different from the result of the "Criss-Cross Method," both will be investigated further in this step.

    First, consider the base formula derived using the "Ratio Method", Ca1O1.  In this chemical formula, the subscripts are already the lowest-common ratio of whole numbers, so should not be further divided.  However, this formula does include two explicitly-written "1"s and, therefore, should be revised to CaO.

    Next, analyze the base formula that resulted from using the "Criss-Cross Method," Ca2O2.  In this chemical formula, both of the subscripts must be divided by 2, in order to reduce them to the lowest-common ratio of whole numbers.  This division results in a revised base formula of Ca1O1.  Note that this formula is identical to the base formula that was initially derived from the "Ratio Method."  This formula does include two explicitly-written "1"s and, therefore, should be revised to CaO.

    Therefore, while the base formulas were not immediately identical, both resulted in the conclusion that CaO is the chemically-correct formula for the compound formed when calcium and oxygen bond with one another.

    Answer b
    Based on the combinations listed in Section 3.2, these elements will combine to form an ionic compound, because chlorine, a non-metal, ionizes to form an anion (Cl–1), and magnesium, a metal, wll ionizes to form a cation (Mg+2).  The ion symbol for the cation is currently written second.  Ionic chemical formulas require that the symbol for the cation should be written first; therefore, the order in which the ions are written should be reversed.  As a result, Mg+2 will be written before Cl–1 in the final chemical formula.  Removing the "+" and "" signs yields Mg2 and Cl1, respectively.

    The subscripts for the base formula for this chemical combination can be determined using either of the methods described above.

    The "Ratio" Method 
    To determine the correct cation-to-anion ratio, a mini-equation, in which the larger superscript value is multiplied by 1, and the smaller superscript value is multiplied by a variable, such as x, is solved.  In the current example, the larger superscript value is "2," and the smaller superscript value is "1."  Therefore,

    2(1) = 1(x)
    2 = x

    This result indicates that for every 1 of the ions with the larger superscript value, in this case, Mg2, 2 of the other ions, Cl1, are required to achieve charge-balance between them.  To apply this information, the numerical superscripts are removed from each symbol, and subscripts are utilized to indicate the ratio established above.  The resultant base formula is Mg1Cl2.

    The "Criss-Cross" Method 
    In this system, the superscript on the first symbol becomes the subscript on the second symbol, and the superscript on the second symbol is repositioned as the subscript on the first symbol, as shown below.

    Magnesium Chloride.png

    The resultant base formula is identical to what was derived using the first method:  Mg1Cl2.

    The final step in this process is to ensure that the subscripts in the base formula are mathematically-appropriate for inclusion in an ionic compound.  In this example, the subscripts are already the lowest-common ratio of whole numbers, so should not be further divided.  However, this formula does include an explicitly-written "1" and, therefore, should be revised to MgCl2.

    Therefore, MgCl2 is the chemically-correct formula for the compound formed when chlorine and magnesium bond with one another.