Balancing Chemical Formula

Balancing chemical formula Cover

Core Concepts

In this article you’ll learn how to balance a chemical formula and how to determine an element’s charge from balancing. You’ll learn some key rules to remember and have access to a table with charges of polyatomic ions!

Topics Covered In Other Articles:

What is a Chemical Formula?

First, let’s define what a chemical formula is. Whenever you have different types of elements that mix together and create a new substance with designated ratios, you have what is called a compound. Each of these compounds can be written using a formula to tell you the ratio of element to element in one molecule. The relative ratios of each substance are indicated with subscript. For example, for the compound of carbon dioxide (CO2) there is a 1:2 ratio of carbon to oxygen.

Chemical Formula Units

Sometimes, molecules have certain “units”, or groups, of atoms that are useful to indicate in the chemical formula. In ionic compounds, these units are usually polyatomic ions. For instance, a molecule of calcium hydroxide contains 1 calcium atom, 2 oxygen atoms, and 2 hydrogen atoms. It is perfectly accurate to write the formula of calcium hydroxide as CaO2H2. However, most chemists express calcium hydroxide instead as Ca(OH)2. Placing parentheses around the OH suggests that the hydrogens and oxygens form an important unit, the hydroxide group. Thus, by writing the chemical formula as such, we know from looking at the formula that two hydroxide groups are attached to a central calcium atom.

showing chemical formula and units of calcium hydroxide
Chemical structure of calcium hydroxide with two hydroxide groups (red and white) connected to a central calcium ion (green).

Since calcium hydroxide is an ionic compound, he formula Ca(OH)2 also indicates the ionic species that the molecule dissociates into. Specifically, we know it dissociates into 1 Ca2+ cation and 2 OH anions.

Ionic Charge and Formal Charge

When chemists use the term “charge”, there exist two distinct phenomena that they could refer to. In an ionic compound, “charge” means ionic charge, indicating the surplus or deficiency of electrons once the ions dissociate. For instance, clorine has a -1 ionic charge in NaCl, because when dissociated, the Cl ions have 1 extra electron compared to neutral chlorine. Sodium has a +1 charge in NaCl, because the resultant Na+ ions have 1 less electron than neutral sodium.

When chemists talk about covalent compounds, “charge” instead refers to formal charge. Because covalent bonds share electrons, we can’t cleanly divide electrons between atoms to determine which has more or less electrons than their neutral state. However, since covalent bonds often involve unequal sharing of electrons, we can make a rough approximation of electron surplus or deficiency using formal charge. For instance, let’s look at chloroform, CHCl3. Highly electronegative chlorine tends to absorb 1 additional electron in covalent structures to complete its octet, giving it a formal charge of -1, just like its ionic charge in NaCl. Hydrogen, by contrast, often gives away its valence electron for a formal charge of +1. Since chloroform is neutral, we know all the formal charges equal 0 when added. Thus, we can solve for the formal charge of carbon to be +2.

     \begin{align*} {C+H+3(Cl) &= 0} \\ {C+1+3(-1)&=0} \\ {C&=-(1+3(-1))} \\ {C&=2} \end{align*}

Writing Formulas

Before we get into writing chemical formulas and balancing compounds it’s important to remember specific rules about elements’ charges.

Some Tips/Rules

  • Rule 1: When an element is in its elemental state (solid, liquid, gas), it’s charge is zero.
    • Ex. Li (s) has a charge of 0 and so does Fe (s)
  • Rule 2: There are 7 elements diatomic elements. This means that they show up in pairs in their natural states. These elements are Hydrogen (H2), Oxygen (O2), Nitrogen (N2), Fluorine (F2), Iodine (I2), Chlorine (Cl2), and Bromine (Br2).
    • To remember these you either pretend it’s a name HON FIClBr or use the mnemonic “Harry Owns Nine Frogs In California Bay.
  • Rule 3: Certain elements tend to have only one charge across the various molecules they are found in:
    • Aluminum: +3
    • Boron: +3
    • Alkaline Earth Metals: (Be, Ca, Mg, Sr, etc.) +2
    • Copper: +2
    • Zinc: +2
    • Alkali Metals: (Li, Na, K, Rb, etc.) +1
    • Hydrogen: +1, except in hydride compounds (ex. NaH) where charge is -1
    • Halogens: (F, Cl, Br, I, etc.) -1, except in polyatomic ions (ex. ClO4, IO3) where charge is variable
    • Oxygen: -2, except in peroxide compounds (ex. H2O2) where charge is -1
    • Nitrogen: -3, expect in polyatomic ions (ex. NO2) where charge is variable
  • Rule 4: When balancing a compound, the overall charge needs to be zero unless otherwise specified.
    • The only compounds that have an overall charge that isn’t zero are ionic compounds.
  • Rule 5: Polyatomic ions are ionic molecules that have a set overall charge. Below is a table that shows the most common polyatomic ions.
    • Note: The charge of these ions is the superscript to top right of the chemical formula!

Polyatomic Ion Chemical Formula List

H2PO4dihydrogen phosphate
HC2O4hydrogen oxalate
HPO42-hydrogen phosphate
HSO4hydrogen sulfate
C2O42- oxalate
ClO4 perchlorate
MnO4 permanganate

How To Balance Compounds

Balancing compounds can be a little tricky. It’s all one big puzzle though! If you know for instance in the compound NaCl (table salt), that Cl (chlorine) has a -1 charge then Na needs to have a +1 to get an overall charge of 0! Below, are some practice problems that you can try!

Balancing Chemical Formula Practice:

Practice 1

What is the charge on the Carbon (C) in the compound carbon monoxide, CO?

Practice 2

What is the charge on the magnesium (Mn) in manganate, MnO4?

Practice 3

What is the formula for iron (III) chloride?

Practice 4

What is cyanide?

Practice 5

What is the formal charge of phosphorus in HPO42-?

Chemical Formula Practice Problem Solutions

Solution 1

In the compound carbon monoxide, CO we know that the oxygen generally has a -2 charge from its placement on the periodic table. In order to get the overall compound to have a charge of zero, the carbon (C) has to have a charge of +2!

Solution 2

The ion manganate can be a little tricky to determine the charge of the magnesium because the overall compound has a -1 charged, indicated by the minus sign at the top right of the formula. We know that oxygen (O) has a -2 charge from the periodic table and there are four of them giving an overall -8 charge. So, we have the charge of manganese plus the -8 charge of the oxygens to equal an overall -1 charge on the molecule. Using algebra, we can deduce that the charge of manganese must be +7 because 7 + (-8) = -1!

Solution 3

The chemical formula for iron (III) chloride is FeCl3. From the written name we see a roman numeral for three in parentheses behind the iron. This means that iron needs to have a +3 charge. From chlorine’s placement on the periodic table, we know that chlorine generally has a -1 charge. So, in order to get an overall charge of 0, we have to have 3 chlorine atoms for every one iron giving a formula of FeCl3.

Solution 4

Cyanide is a polyatomic ion which can be found in the table to this article! It will be helpful to have the ions in the table memorized including their formulas, names and charges!

Solution 5

Since hydrogen has a +1 charge, oxygen has a -2 charge, and the ion has an overall charge of -2, we can set up the following equation to solve for the charge of phosphorus: P+1+4(-2)=-2. By solving for the charge of phosphorus, we find that it must be +5.