Balancing Equations
Chemical equations relate the amounts of chemicals that react together and the amounts of the products of their reaction. Knowledge of the relationships in amounts is important because businesses can efficiently spent their money on the materials for the “Products” they produce thereby maximizing their profit! Put simply, we can eliminate waste by applying our knowledge of chemistry. OK, enough of why. Let’s say we have some sodium and some chlorine and we want to make salt. Either substance is very harmful to us by itself, but the product is essential to life. (Disclaimer…don’t do this at home, besides being dangerous, it’s just cheaper to go by a box with the little girl with an umbrella in the rain from the grocery store.)
If you’ve paid attention to this point you know that the formula for salt is…
NaCl
That means one mole each of sodium and chlorine. We’ll leave the grams out of this for now since you know how the convert mols to grams. We will have to do this later since we can measure grams readily, but mols can’t be measured directly in our labs.
Ok, so where did the salt come from? Reacting sodium and chlorine together, of course. IF we have more mols of one than the other, we’ll have some of that left over…not good. We want just the right amounts of each. We have a language called the chemical equation to express these amounts.
Na + Cl ® NaCl
On the left we list the reactants, the right side lists the products, in this case just one, salt.
The arrow separates the reactants from the products. We can read this expression “ Sodium and Chlorine yields Sodium Chloride”
In this case it is obvious that we need just one mol of each to make one mol of salt. The subscipts of Na and Cl, both one, in the product tell us that one mol of each is needed. The reaction is balanced, there is an equal number of mols of each element on both sides of the equation. Equal mols means equal masses on each side, this is called conservation of mass.
How about the reaction in your previous lab? Magnesium and hydrochloric acid?
Mg + HCl ® MgCl2 + H2
If we look at this equation we notice that there is twice the number of mols of H and Cl in the products, than there are in the reactants. We need to balance the equation by multiplying selected reactants and products by coefficients that we must determine. So how do we select the right coefficients?...
First, set up a table of elements for each side, reactants and products.
Mg + HCl ® MgCl2 + H2
Reactants Products
Mg Mg
H H
Cl Cl
Second, write in the number of each element as the equation is written. The numbers will be the sum of the subscripts for each element on each side.
Mg + HCl ® MgCl2 + H2
Reactants Products
Mg 1 Mg 1
H 1 H 2
Cl 1 Cl 2
Now, we can see the equation is not balanced; there are more mols of H and Cl on the product side than there are on the reactant side. The magnesium is balanced.
A little intuition will tell you that we need to double the amount of H and Cl on the reactant side to balance this equation. Here’s how we show doing that. Both H and Cl are in one reactant, this simplifies matters. We double the amount by writing a coefficient of two in front of that reactant.
Mg + 2HCl ® MgCl2 + H2
Now we must rewrite the table of elements multiplying each subscript by the coefficient of the reactant, or product it appears in.
Reactants Products
Mg 1 Mg 1
H 1 2 H 2
Cl 1 2 Cl 2
Now this equation is balanced. There are equal numbers of mols of every element on both sides of the arrow. They won’t always be so simple, but you will get the hang of it with practice.
A few more things about equations and reactions.
When we reacted the magnesium and hydrochloric acid they were in different forms or phases. The magnesium was in solid form, the acid in solution. We can denote this in the equation as follows.
Mg (s) + 2HCl (aq) ® MgCl2 (aq) + H2 (g)
the subscripts in parenthesis are used to indicate
Solid (s)
Liquid (l)
Gas (g)
Aqueous solution (aq) [aqueous means the solvent is water]
Reactions can also produce, or require another thing… Heat. Remember the first lab we did with Calcium Chloride, baking soda and water? Calcium Chloride and water produced heat, it got hot, and we call this an exothermic reaction. The baking soda got cool, it required energy to proceed, and we call this an endothermic reaction.
This heat energy will be indicated by another term of calories, or kcal, on the appropriate side, reactant side for endothermic, and product side for exothermic. This change in energy can be shown by the greek letter delta, as shown below.
2H2 (g) + O2 (g) ® 2H2O(g) + Δ
Helpful hints:
#1 List elements in same order for each side so you can see at a glance that the equation is balanced or not.
Al + H2SO4 → Al2(SO4)3 + H2
R P
Al 1 2
H 2 2
SO4 1 3
#2 Keep polyatomic ions together if they appear in the same form on each side. Notice above, sulfate appears on both sides and is not split up at all during the reaction.
#3 If an element appears by itself, balance it last.
R P
CxHy + O2 → CO2 + H2O
C
H
O
Oxygen appears as an element on the reactant side. Balance Carbon and hydrogen first then do oxygen last.
#4 Combustion See above example.
Coefficient of Carbon dioxide = subscript of carbon on reactant side = x.
Coefficient of water = ½ subscript of hydrogen on reactant side = y/2.
Coefficeient of Oxygen = (x + ½ y)
# 5 When stuck, multiply all coefficients by 2. In the above example if y is an odd number, you will end up with a fractional coefficient for O2. Multiplying by 2 will make all coefficients integers.