Stoichiometry is founded upon the law of the conservation of mass. A chemical reaction’s ( RXN ) reactants and products must be balanced in such a way that a rearrangement of atoms ( or molecules ) occurs, but the total mass of atoms involved in the RXN is conserved.
Let’s begin with an examination of an unbalanced RXN in which molecular hydrogen ( H2 ) and molecular oxygen ( O2 ) react to form a molecule of water ( H2O ):
H2 + O2 → H2O ( unbalanced )
The arrow indicates that this RXN is essentially irreversible ( exothermic ), and a great deal of heat energy is liberated as water is formed. In order to convert water into hydrogen and oxygen, an energy input is required to break the H2O bonds during a RXN that is endothermic in nature.
There are two hydrogen atoms present in the reactants and products of the RXN; however, there are two atoms of oxygen reacting with the H2 molecule, but only one atom of oxygen appears in the products. As a consequence, the water molecule must be preceded with a coefficient of 2:
H2 + O2 → 2H2O
We now have a circumstance in which the oxygen atoms are balanced, but there are now four atoms of hydrogen within the two molecules of water. Since there are only two atoms of hydrogen among the reactants, the hydrogen molecule on the reactant side must be balanced with a coefficient of 2:
2H2 + O2 → 2H2O ( balanced )
We now have a balanced RXN.
Notice that we did not change the subscripts of either reactants or products to balance the RXN! If a subscript of an atom or molecule is changed, the entire nature of the reaction is changed. We could have changed the subscript of the water molecule to balance the equation, but the product of the reaction would be hydrogen peroxide instead of water:
H2 + O2 → H2O2 ( balance, but the product has changed )
This is a mistake that must be avoided at all costs! Let’s now balance a RXN between propane and oxygen that yields carbon dioxide and water as products:
C3H8 + O2 → CO2 + H2O ( unbalanced )
We must now make a difficult choice regarding which atom should be balanced first. Notice, however, that the oxygen molecule on the left-hand side ( LHS ) of the RXN stands alone, but oxygen atoms exist within two molecules on the right-hand side ( RHS ) of the RXN. This is a clear indication that the oxygen atom should be balanced last; it will be relatively simple to place an appropriate coefficient in front of the lone oxygen molecule on the LHS of the RXN after balancing the carbon and hydrogen atoms in the RXN.
Let’s first balance the carbon atoms. There are three atoms of carbon on the LHS of the RXN, but there’s only one carbon atom on the RHS of the RXN. Placing a coefficient of 3 in front of the carbon dioxide molecule will balance the carbon atoms:
C3H8 + O2 → 3CO2 + H2O
There are eight hydrogen atoms on the LHS of the RXN, but there are only two hydrogen atoms on the RHS of the RXN. Let’s place a coefficient of 4 in front of the water molecule to balance the hydrogen atoms:
C3H8 + O2 → 3CO2 + 4H2O
The carbon and hydrogen atoms are now balanced. There are now ten oxygen atoms contained in the products of the RXN, but only two oxygen atoms on the LHS of the RXN. The RXN will be balanced if a coefficient of 5 is placed in front of the oxygen molecule on the LHS of the RXN:
C3H8 + 5O2 → 3CO2 + 4H2O ( balanced )
A similar approach can be used to balance fairly complicated RXNs as well. Let’s consider a RXN between potassium chlorate and sucrose that yields potassium chloride, carbon dioxide, and water as by-products:
KClO3 + C12H22O11 → KCl + CO2 + H2O ( unbalanced )
The potassium ( K ) atom is part of one molecule on both sides of the RXN. The chlorine atom ( Cl ) is also part of one molecule on both sides of the RXN. Similarly, the carbon ( C ) and hydrogen ( H ) atoms are each part of one molecule on both sides of the RXN. Note, however, that the oxygen atoms ( O ) are split across two molecules on both sides of the RXN. Let’s balance the potassium, chlorine, carbon, and hydrogen atoms before balancing the oxygen atoms.
Notice that one atom of potassium and one atom of chlorine appear on the LHS and RHS of the RXN. For this reason, the potassium and chlorine atoms are already balanced; however, there are twenty-two hydrogen atoms on the LHS of the RXN, but there are only two hydrogen atoms on the RHS of the RXN. By placing a coefficient of 11 in front of the water molecule, the hydrogen atoms will be balanced:
KClO3 + C12H22O11 → KCl + CO2 + 11H2O
We must now place a coefficient of 12 in front of the carbon dioxide molecule:
KClO3 + C12H22O11 → KCl + 12CO2 + 11H2O
The oxygen atom is the only unbalanced atom remaining. There are fourteen oxygen atoms on the LHS of the RXN, but there are thirty-five oxygen atoms on the RHS of the RXN. As a consequence, we must increase the number of oxygen atoms on one of the molecules on the LHS of the RXN in order to establish balance.
On the LHS of the RXN, notice that the sucrose molecule contains eleven oxygen atoms, and the potassium chlorate molecule contains three molecules. If we put a coefficient of 8 in front of the potassium chlorate molecule, it will contain twenty-four atoms of oxygen. Since we need thirty-five atoms of oxygen on the LHS to balance the RXN, the following RXN will contain a balance of oxygen atoms:
8KClO3 + C12H22O11 → KCl + 12CO2 + 11H2O
The oxygen atoms are now balanced, but by placing a coefficient of 8 in front of the potassium chlorate, we have increased the potassium and chloride atoms by eight on the LHS of the RXN. We can easily balance the potassium and chloride atoms on the RHS of the RXN by placing a coefficient of 8 in front of the potassium chloride molecule:
8KClO3 + C12H22O11 → 8KCl + 12CO2 + 11H2O ( balanced )
Now that a strategy has been introduced to establish balance between atoms contained within the reactants and products of RXNs, we are ready to use balanced RXNs to predict the quantity of products that will occur when varying quantities of reactants interact with one another.
RENAISSANCE PHYSICS 