ARTICLE 7 
STOICHIOMETRY


Stoichiometry is a section of chemistry that involves using relationships between reactants and/or products in a chemical reaction to determine desired quantitative data. In Greek, stoikhein means element and metron means measure, so stoichiometry literally translated means the measure of elements. In order to use stoichiometry to run calculations about chemical reactions, it is important to first understand the relationships that exist between products and reactants and why they exist, which require understanding how to balanced reactions.

Balancing

In chemistry, chemical reactions are frequently written as an equation, using chemical symbols. The reactants are displayed on the left side of the equation and the products are shown on the right, with the separation of either a single or double arrow that signifies the direction of the reaction. The significance of single and double arrow is important when discussing solubility constants, but we will not go into detail about it in this module. To balance an equation, it is necessary that there are the same number of atoms on the left side of the equation as the right. One can do this by raising the coefficients.

Reactants to Products

A chemical equation is like a recipe for a reaction so it displays all the ingredients or terms of a chemical reaction. It includes the elements, molecules, or ions in the reactants and in the products as well as their states, and the proportion for how much of each particle is create relative to one another, through the stoichiometric coefficient. The following equation demonstrates the typical format of a chemical equation:

2Na(s)+2HCl(aq)→2NaCl(aq)+H2(g)(1)$$\begin{array}{}\text{(1)}& 2N{a}_{(s)}+2HC{l}_{(aq)}\to 2NaC{l}_{(aq)}+H_{2(g)}\end{array}$$

In the above equation, the elements present in the reaction are represented by their chemical symbols. Based on the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction, every chemical reaction has the same elements in its reactants and products, though the elements they are paired up with often change in a reaction. In this reaction, sodium (Na$Na$), hydrogen (H$H$), and chloride (Cl$Cl$) are the elements present in both reactants, so based on the law of conservation of mass, they are also present on the product side of the equations. Displaying each element is important when using the chemical equation to convert between elements.

Stoichiometric Coefficients

In a balanced reaction, both sides of the equation have the same number of elements. The stoichiometric coefficient is the number written in front of atoms, ion and molecules in a chemical reaction to balance the number of each element on both the reactant and product sides of the equation. Though the stoichiometric coefficients can be fractions, whole numbers are frequently used and often preferred. This stoichiometric coefficients are useful since they establish the mole ratio between reactants and products. In the balanced equation:

2Na(s)+2HCl(aq)→2NaCl(aq)+H2(g)(2)$$\begin{array}{}\text{(2)}& 2N{a}_{(s)}+2HC{l}_{(aq)}\to 2NaC{l}_{(aq)}+H_{2(g)}\end{array}$$

we can determine that 2 moles of HCl$HCl$ will react with 2 moles of Na(s)$N{a}_{(s)}$ to form 2 moles of NaCl(aq)$NaC{l}_{(aq)}$ and 1 mole of H2(g)$H_{2(g)}$. If we know how many moles of Na$Na$ we start out with, we can use the ratio of 2 moles of NaCl$NaCl$to 2 moles of Na to determine how many moles of NaCl$NaCl$ were produced or we can use the ration of 1 mole of H2$H_2$ to 2 moles of Na$Na$ to convert to NaCl$NaCl$. This is known as the coefficient factor. The balanced equation makes it possible to convert information about one reactant or product to quantitative data about another element. Understanding this is essential to solving stoichiometric problems.

Example 1

Lead (IV) hydroxide and sulfuric acid react as shown below. Balance the reaction.

Pb(OH)4+H2SO4→Pb(SO4)2+H2O$$Pb(OH{)}_4+H_{2}S{O}_4\to Pb(S{O}_4{)}_2+H_{2}O$$

SOLUTION

Start by counting the number of atoms of each element.

UNBALANCED  

Element	Reactant (# of atoms)	Product (# of atoms)
Pb	1	1
O	8	9
H	6	2
S	1	2

The reaction is not balanced; the reaction has 16 reactant atoms and only 14 product atoms and does not obey the conservation of mass principle. Stoichiometric coefficients must be added to make the equation balanced. In this example, there are only one sulfur atom present on the reactant side, so a coefficient of 2 should be added in front of H2SO4$H_{2}S{O}_4$ to have an equal number of sulfur on both sides of the equation. Since there are 12 oxygen on the reactant side and only 9 on the product side, a 4 coefficient should be added in front of H2O$H_{2}O$ where there is a deficiency of oxygen. Count the number of elements now present on either side of the equation. Since the numbers are the same, the equation is now balanced.  

Pb(OH)4+2H2SO4→Pb(SO4)2+4H2O$$Pb(OH{)}_4+2H_{2}S{O}_4\to Pb(S{O}_4{)}_2+4H_{2}O$$

BALANCED

Element	Reactant (# of atoms)	Product (# of atoms)
Pb	1	1
O	12	12
H	8	8
S	2	2

Balancing reactions involves finding least common multiples between numbers of elements present on both sides of the equation. In general, when applying coefficients, add coefficients to the molecules or unpaired elements last. 

A balanced equation ultimately has to satisfy two conditions.

1. The numbers of each element on the left and right side of the equation must be equal.
2. The charge on both sides of the equation must be equal. It is especially important to pay attention to charge when balancing redox reactions.

Stoichiometry and Balanced Equations

In stoichiometry, balanced equations make it possible to compare different elements through the stoichiometric factor discussed earlier. This is the mole ratio between two factors in a chemical reaction found through the ratio of stoichiometric coefficients. Here is a real world example to show how stoichiometric factors are useful.