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3.9: Formula Weight

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    Learning Objectives
    • To determine the formula mass of an ionic compound.

    Formula Weight

    One skill needed in future chapters is the ability to determine the mass of the formula of an ionic compound. This quantity is called the formula weight (formula mass). The formula weight is obtained by adding the atomic weight of each individual atom in the formula of the compound. Because a proper formula is electrically neutral (with no net electrons gained or lost), the ions can be considered atoms for the purpose of calculating the formula mass.

    Let us start by calculating the formula weight of sodium chloride (NaCl). This formula weight is the sum of the atomic weights of one sodium atom and one chlorine atom, which we find from the periodic table; here, we use the atomic weights to two decimal places:

    Na: 22.99 amu

    Cl: +35.34 amu

    Total: 58.44 amu

    To two decimal places, the formula weight of NaCl is 58.44 amu.

    When an ionic compound has more than one anion or cation, you must remember to use the proper multiple of the atomic weights for the element in question. For the formula mass of calcium fluoride (CaF2), we must multiply the mass of the fluorine atom by 2 to account for the two fluorine atoms in the chemical formula:

    Ca: 1 x 40.08 = 40.08 amu

    F: 2 x 19.00 = +38.00 amu

    Total = 78.08 amu

    The formula weight of CaF2 is 78.08 amu.

    For ionic compounds with polyatomic ions, the sum must include the number and mass of each atom in the formula for the polyatomic ion. For example, potassium nitrate (KNO3) has one potassium atom, one nitrogen atom, and three oxygen atoms:

    K: 1 x 39.10 = 39.10 amu

    N: 1 x 14.00 = +14.00 amu

    O: 3 x 16.00 = +48.00 amu

    Total = 101.10 amu

    The formula weight of KNO3 is 101.10 amu.

    Potassium nitrate is a key ingredient in gunpowder and has been used clinically as a diuretic.

    When a formula contains more than one polyatomic unit in the chemical formula, as in Ca(NO3)2, do not forget to multiply the atomic weights of every atom inside of the parentheses by the subscript outside of the parentheses. This is necessary because the subscript refers to the entire polyatomic ion. Thus, for Ca(NO3)2, the subscript 2 implies two complete nitrate ions, so we must sum the masses of two (1 × 2) nitrogen atoms and six (3 × 2) oxygen atoms, along with the mass of a single calcium atom:

    Ca: 1 x 40.08 = 40.08 amu

    N: 2 x 14.00 = +28.00 amu

    O: 6 x 16.00 = +96.00 amu

    Total = 164.08 amu

    The key to calculating the formula weight of an ionic compound is to correctly count each atom in the formula and multiply the atomic weights of its atoms accordingly.

    Example \(\PageIndex{1}\)

    Use the atomic masses (rounded to two decimal places) to determine the formula weight for each ionic compound.

    1. FeCl3
    2. (NH4)3PO4

    Solution

    a.

    Fe: 1 x 55.85 = 55.85 amu

    Cl: 3 x 35.45 = +106.35 amu

    ________________________

    Total = 162.20 amu

    The formula weight of FeCl3 is 162.2 amu.

    b. When we distribute the subscript 3 through the parentheses containing the formula for the ammonium ion, we see that we have 3 nitrogen atoms and 12 hydrogen atoms. Thus, we set up the sum as follows:

    N: 3 x 14.00 = 42.00 amu

    H: 12 x 1.00 = +12.00 amu

    P: 1 x 30.97 = +30.97 amu

    O: 4 x 16.00 = +64.00 amu

    Total = 148.97 amu

    The formula weight for (NH4)3PO4 is 149.0 amu.

    Exercise \(\PageIndex{1}\)

    Use the atomic weights (rounded to two decimal places) to determine the formula weight for each ionic compound.

    1. TiO2
    2. AgBr
    3. Au(NO3)3
    4. Fe3(PO4)2

    Answer

    a. 79.87 amu

    b. 187.77 amu

    c. 383.0 amu

    To Your Health: Hydrates

    Some ionic compounds have water (H2O) incorporated within their formula unit. These compounds, called hydrates, have a characteristic number of water units associated with each formula unit of the compound. Hydrates are solids, not liquids or solutions, despite the water they contain.

    To write the chemical formula of a hydrate, write the number of water units per formula unit of compound after its chemical formula. The two chemical formulas are separated by a vertically centered dot. The hydrate of copper(II) sulfate has five water units associated with each formula unit, so it is written as CuSO4•5H2O. The name of this compound is copper(II) sulfate pentahydrate, with the penta- prefix indicating the presence of five water units per formula unit of copper(II) sulfate.

    220px-Short_Leg_Walking_Cast.JPG
    Figure used with permisson from Wikipedia.

    Hydrates have various uses in the health industry. Calcium sulfate hemihydrate (CaSO4•½H2O), known as plaster of Paris, is used to make casts for broken bones. Epsom salt (MgSO4•7H2O) is used as a bathing salt and a laxative. Aluminum chloride hexahydrate is an active ingredient in antiperspirants. The accompanying table lists some useful hydrates.

    Table \(\PageIndex{1}\): Names and Formulas of Some Widely Used Hydrates
    Formula Name Uses
    AlCl3•6H2O aluminum chloride hexahydrate antiperspirant
    CaSO4•½H2O calcium sulfate hemihydrate (plaster of Paris) casts (for broken bones and castings)
    CaSO4•2H2O calcium sulfate di hydrate (gypsum) drywall component
    CoCl2•6H2O cobalt(II) chloride hexahydrate drying agent, humidity indicator
    CuSO4•5H2O copper(II) sulfate pentahydrate fungicide, algicide, herbicide
    MgSO4•7H2O magnesium sulfate heptahydrate (Epsom salts) laxative, bathing salt
    Na2CO3•10H2O sodium carbonate decahydrate (washing soda) laundry additive/cleaner

    Key Takeaway

    • Formula masses of ionic compounds can be determined from the masses of the atoms in their formulas.

    Contributors and Attributions

    This page titled 3.9: Formula Weight is shared under a not declared license and was authored, remixed, and/or curated by Deboleena Roy (American River College).