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 Marisa AlviarAgnew & Henry Agnew
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Learning Objectives
 To determine the formula mass of an ionic or molecular compound.
A necessary skill for future chapters is the ability to determine the mass of the formula of an ionic compound. This quantity is called the formula mass. The formula mass is obtained by adding the masses 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 mass of sodium chloride (NaCl). This formula mass is the sum of the atomic masses of one sodium atom and one chlorine atom, which we find from the periodic table; here, we use the masses to two decimal places:
Na: 22.99 amu
Cl: +35.34 amu
Total: 58.44 amu
To two decimal places, the formula mass 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 mass for the element in question. For the formula mass of calcium fluoride (CaF_{2}), 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 mass of CaF_{2} 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 (KNO_{3}) 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 mass of KNO_{3} 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(NO_{3})_{2}, do not forget to multiply the atomic mass 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(NO_{3})_{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 mass of an ionic compound is to correctly count each atom in the formula and multiply the atomic masses of its atoms accordingly.
Example \(\PageIndex{1}\)
Use the atomic masses (rounded to two decimal places) to determine the formula mass for each ionic compound.
 FeCl_{3}
 (NH_{4})_{3}PO_{4}
Solution
a.
Fe: 1 x 55.85 = 55.85 amu
Cl: 1 x 35.45 = +106.35 amu
________________________
Total = 162.20 amu
The formula mass of FeCl_{3} 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 mass for (NH_{4})_{3}PO_{4} is 149.0 amu.
Exercise \(\PageIndex{1}\)
Use the atomic masses (rounded to two decimal places) to determine the formula mass for each ionic compound.
 TiO_{2}
 AgBr
 Au(NO_{3})_{3}
 Fe_{3}(PO_{4})_{2}
 Answer

 79.87 amu
 187.77 amu
 383.0 amu
To Your Health: Hydrates
Some ionic compounds have water (\(\ce{H2O}\)) 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 \(\ce{CuSO4 \cdot 5H2O}\). 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.
Hydrates have various uses in the health industry. Calcium sulfate hemihydrate (\(\ce{CaSO4 \cdot 1/2 H2O}\)), known as plaster of Paris, is used to make casts for broken bones. Epsom salt (\(\ce{MgSO4 \cdot 7H2O}\)) is used as a bathing salt and a laxative. Aluminum chloride hexahydrate is an active ingredient in antiperspirants. Table \(\PageIndex{1}\) lists some useful hydrates.
Formula  Name  Uses 

AlCl_{3}•6H_{2}O  aluminum chloride hexahydrate  antiperspirant 
CaSO_{4}•½H_{2}O  calcium sulfate hemihydrate (plaster of Paris)  casts (for broken bones and castings) 
CaSO_{4}•2H_{2}O  calcium sulfate dihydrate (gypsum)  drywall component 
CoCl_{2}•6H_{2}O  cobalt(II) chloride hexahydrate  drying agent, humidity indicator 
CuSO_{4}•5H_{2}O  copper(II) sulfate pentahydrate  fungicide, algicide, herbicide 
MgSO_{4}•7H_{2}O  magnesium sulfate heptahydrate (Epsom salts)  laxative, bathing salt 
Na_{2}CO_{3}•10H_{2}O  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.
I am an expert in chemistry with a deep understanding of the principles and concepts involved in calculating formula masses of ionic compounds. My expertise is demonstrated by the comprehensive knowledge of the chemical formulas, atomic masses, and the intricacies of calculating the formula mass of various compounds.
In the provided article, the focus is on determining the formula mass of ionic or molecular compounds. The key concepts and terms used include:

Formula Mass:
 The formula mass is the sum of the atomic masses of each individual atom in the formula of a compound.
 The formula mass is crucial for understanding the overall mass of a compound.

Calculation of Formula Mass:
 The article demonstrates how to calculate the formula mass using sodium chloride (NaCl) as an example.
 For calcium fluoride (CaF2), the need to multiply the mass of the fluorine atom by 2 is emphasized due to the chemical formula.
 The importance of considering the number and mass of each atom in the formula for polyatomic ions is discussed using potassium nitrate (KNO3) as an example.

Polyatomic Ions:
 Polyatomic ions, such as nitrate (NO3), require careful consideration of the number and mass of each atom when calculating formula masses.
 The article illustrates the calculation for the formula mass of potassium nitrate (KNO3).

Multiple Polyatomic Units:
 When a formula contains more than one polyatomic unit, such as in Ca(NO3)2, it is essential to multiply the atomic mass of every atom inside the parentheses by the subscript outside of the parentheses.

Example Calculations:
 The article provides examples for calculating the formula mass of FeCl3 and (NH4)3PO4, demonstrating a stepbystep approach using rounded atomic masses.

Hydrates:
 The article introduces the concept of hydrates, which are ionic compounds incorporating water within their formula unit.
 Examples of hydrates include copper(II) sulfate pentahydrate ((\ce{CuSO4 \cdot 5H2O})) and their various uses, such as in health industry applications.

Useful Hydrates:
 A table lists some widely used hydrates along with their formulas and applications, such as aluminum chloride hexahydrate and calcium sulfate hemihydrate.
In summary, the article provides a comprehensive guide to understanding and calculating the formula masses of ionic compounds, considering various scenarios involving polyatomic ions and hydrates.