 # Balancing Equations

## What are chemical equations?

A chemical equation is a symbolic representation of a chemical reaction in terms of chemical formulas. An example of a chemical equation would be:

2Na + Cl2 - 2NaCl

This chemical equation would stand for the burning of sodium in chlorine to produce sodium chloride. The formulas on the left side of the equation would stand for the reactant. A reactant is the starting substance in a compound. The arrow, -, means either "yields" or "reacts to form." The formulas to the right of the arrow stand for the product formed in the chemical reaction. A product is the substance that results from a chemical reaction. The coefficient in front of the Na, 2, give the number of molecules or formula units involved in the reaction. Coefficients of one are usually understood, so they are not written.

Sometimes it helps to indicate the states or phases of the substances in a chemical reaction. We can do this by placing certain labels, which stand for the various phases, following the formula of a substance in a chemical equation. Here are the labels:

 (g)=gases (l)=liquid (s)=solid (aq)=aqueous solution

When we use the labels which we have just learned our former equation becomes:

2Na(s) + Cl2(g) - 2NaCl(s)

In a chemical equation we can also indicate the conditions under which the reaction takes place. If the reactants in the chemical reaction are heated, we indicate this with the Greek symbol delta, , over the arrow. Below is the equation that indicates that solid sodium nitrate, NaNO3 decompposes when heated to give us solid solium nitrate, which is NaNO2, and good ole oxygen, which is O2. Oftentimes in chemical reactions there will be the addition of a catalyst. A catalyst speeds up a chemical reaction without being consumed in the overall reaction. Guess what, as you probably expected, there is a way to represent the addition of a catalyst to a chemical reaction. We do this by writing the catalyst involved in the reaction over the arrow. Here is an example, say that we have an aqueous solution of hydrogen peroxide, which is H2O2. When this solution of hydrogen peroxide is exposed to platinum metal (Pt), the hydrogen peroxide decomposes into water and oxygen gas. The platinum speeds up the reaction of the decomposition of H2O2 into H2O and O2 and acts as a catalyst in this reaction (you see, hydrogen peroxide gradually decomposes on its own over time). We would represent the equation below: ## Balancing Equations

When the coefficients in a chemical equation are balanced, there are equal numbers of atoms of each element on both sides of the equation. We say that the chemical equation is balanced. You might ask, well, why does the chemical equation have to be balanced? Well, the answer to this stems from the atomic theory. In a chemical reaction, there is only a recombination of the atoms, no atoms are destroyed or created. Take our first equation:

2Na + Cl2 - 2NaCl

In this reaction you have 2 atoms of sodium + 1 molecule of chlorine reacting to form 2 molecules of sodium chloride, which is salt.

In our next example we have:

H3PO3 - H3PO4 + PH3

Since the coefficients that give us the number of molecules have not yet been determined, this chemical equation is not balanced. To balance this equation, we select coefficients that will make the numbers of atoms of each element equal on both sides of the equations. It is best to write the coefficients so that they are the smallest whole numbers possible. To balance the previous equation we first want to look at the pieces which comprise the overall chemical equation. We find that oxygen occurs in only one of the products, so it would probably be the easiest to balance first. We get:

4H3PO3 - 3H3PO4 + PH3

Doing this also balanced the number of P and H atoms. So this means that in just one step we arrived at the balanced equation. You see, we now have 12 atoms of oxygen, 12 atoms of hydrogen, and 4 atoms of phosphorus on both sides of the equation. Before we balanced the equation, we had 3 atoms of oxygen, 3 atoms of hydrogen, and 1 atom of phosphorus on the reactants side, and 4 atoms of oxygen, 6 atoms of hydrogen, and 2 atom of phosphorus on the products side.

## Types of Reactions

When we delve deeper into the study of chemistry, we find that there are several different types of reactions. There are several different ways to classify these reactions, mainly based on the patterns of similarity among them. There are 5 basic types of reactions we will be studying, and the way they are classified is based on how atoms or groups of atoms are rearranged during a particular reaction. These reactions are:

 1. Combination reactions 2. Decomposition reactions 3. Displacement reactions 4. Metathesis reactions 5. Combustion reactions

Combination Reactions

A combination reaction is a reaction in which two substances combine to form a third substance. A simple example would be where two elements react to form a compound of the elements. A good example of this would be:

2Na(s) + Cl2(g) - 2NaCl(s)

Combination reactions can also have compounds as the reactants. An example of this would be where phosphorus trichloride reacts with chlorine to form phosphorus pentachloride:

PCl3(l) + Cl2(g) - PCl5(s)

Here is another combination reaction, the burning of copper and oxygen to produce copper(II) oxide:

2Cu + O2 - 2 CuO

Decomposition Reactions

A decomposition reaction is a reaction in which a single compound reacts to give two or more substances. In order to decompose a compound, it is often necessary to raise the temperature. An example of a decomposition reaction would be the decomposition of mercury (II) oxide into mercury and oxygen when the compound is heated. A compound can also decompose into a compound and an element, or two compounds.

Displacement Reactions

Displacement reactions (sometimes referred to as single replacement reactions) are reactions in which an element reacts with a compound displacing an element from it. An example of this would be when a copper metal strip is dipped into a solution of silver nitrate. When this happens, crystals of silver metal are produced.

Cu(s) + 2AgNO3 (aq) - 2Ag (s) + Cu(NO3)2 (aq)

In this reaction, copper replaces the silver in silver nitrate. In the process it produces copper(II) nitrate solution and silver metal.

A fun fun fun single replacement reaction is one that we call "burning magnesium".

2Mg + CO2 - 2MgO + C Metathesis Reactions

A metathesis reaction is a reaction that appears to involve the exchange of parts of the reactants. Metathesis reactions are also referred to as double-replacement reactions. When the reactants in the reaction are ionic compounds in solution, cations and anions of the compounds are the parts exchanged. An example of a metathesis reaction would be the reaction of potassium iodide solution and lead (II) nitrate solution. The reactants are colorless liquids, yet one of the products of this reaction is lead (II) iodide, which forms a yellow precipitate. A precipitate is a solid compound formed during a reaction in solution.

2KI(aq) + Pb(NO3)2(aq) - 2KNO3(aq) + PbI2(s)

What happens in this metathesis reaction is that iodide ions in potassium iodide switch with the nitrate ions in lead (II) nitrate. What happens is that we get potassium nitrate (2KNO3) and lead (II) iodide (PbI2) as the products.

Here is another example of a double replacement reaction in which iron(III) chloride and sodium hydroxide are combined to produce a precipitate:

FeCl3 + 3NaOH - 3NaCl + Fe(OH)3

Combustion Reactions

So far, all the reactions which we have studied have been classified by the type of atom rearrangement that happens in the reaction. Combustion reactions are different in that they are characterized by the fact that one of the reactants is always oxygen. A combustion reaction is a reaction of a substance with oxygen, usually with the rapid release of heat to produce a flame. Organic compounds burn in oxygen to produce carbon dioxide and water vapor. Here is the formula for the chemical reaction involving butane burning in air to produce carbon dioxide and water vapor.

2C4H10(g) + 13O2(g) - 8CO2(g) + 10H2O(g)

Here is an example of a combustion reaction. It involves burning methane. This results in carbon dioxide and water being formed from the reaction:

CH4 + 2O2 - CO2 + 2H2O

# Stoichiometry

## Standard

Stoichiometry consists of the calculations in chemistry that involve how much of each reactant is required to make the products of the reaction. The coefficients in the balanced equation are used to determine the number of moles of each element that are required in the reaction. Therefore, from the equation,

3H2 + N2 -- 2NH3

you can surmise that to make 2 moles of ammonia you need three moles of hydrogen gas and one mole of nitrogen gas. Yes, I know that almost everyone reading this page is saying that hey that sounds really cool, but what good is it to know how many moles you need to make something. I have the answer, if you know how many moles you need you can convert that to grams. On the periodic table there is an atomic weight. The atomic weight is equal to the number of grams in one mole of the element. If you have more than one element in a compound add the number of grams together according to the subscripts.

Examples:

1. How many moles of O2 are produced when 7.5 moles of KClO3 decompose according to the following equation?
2. KClO3 -- KCl + O2

Balance the Equation

2KClO3 -- 2KCl + 3O2 3. How many grams of Al will react with 2.3 moles of HCl according to this equation?
4. Al + HCl -- AlCl3 + H2

Balance the Equation

2Al + 6HCl -- 2AlCl3 + 3H2 5. How many grams of ammonia are produced when 32g of nitrogen react with excess hydrogen?
• N2 + H2 -- NH3

Balance the Equation

N2 + 3H2 -- 2NH3 • ## Limiting Reactant

Now you say that stoichiometry is great, but what if you don't have such pretty numbers that work out evenly? That is where limiting reactant comes into play. In most situations one reactant will run out before the other. The reactant that is totally consumed is called the limiting reactant because it stops the reaction. Any other reactant that does not run out is called the excess reactant. Therefore the amount of product that can be produced is directly related to the limiting reactant.

The first step in a limiting reactant question is to determine the limiting reactant. To do this, for all reactants calculate the amount of product that would be produced if all of the reactant was used and there was excess of all the other reactants. The reactant that has the least product is the limiting reactant.

The amount of products is due to the amount of the limiting reactant.

An example:

Using the following reaction

Zn(s) + 2HCl(aq) -- ZnCl2(aq) + H2(g)

Which is the limiting reactant and how much H2 is produced if there is 0.30 mol of Zn and 0.52 moles of HCl?

Step one:  Since HCl is the limiting reactant, the number of moles of H2 produced is .26 moles.