Video Transcript
When heated, phosphorous acid,
H3PO3, decomposes into phosphoric acid, H3PO4, and the pungent toxic gas phosphine,
PH3. Write a balanced chemical equation
for this reaction using the smallest possible whole number coefficients for the
reactants and products.
Let’s begin by identifying the
reactants and products. Phosphorous acid decomposes. The keyword decomposes indicates
that we are talking about a decomposition reaction. In a decomposition reaction, one
single reactant breaks apart into two or more products. This means that phosphorous acid
will be the only reactant. The phosphorous acid decomposes
into phosphoric acid and phosphine. These are the products.
Now that we have identified the
reactant and products, we are ready to begin balancing this chemical equation. We will start by identifying the
elements involved in the reaction. Every element has a chemical symbol
and every chemical symbol is either a capital letter or a capital letter followed by
a lowercase letter. What we need to do is look at the
chemical equation and break it down into the individual letter groups.
At the start of the equation, we
see a capital H. This is a chemical symbol. This chemical symbol appears in two
additional molecules in the equation. We also see a capital P, which
appears in three molecules in the equation, and a capital O, which appears in two
molecules in the equation. Notice that we are ignoring the
subscript values for now. We can make a list of these
elements using a periodic table to match the chemical symbol to the element
name. Capital H represents hydrogen,
capital P represents phosphorus, and capital O represents oxygen. Next, we will count the number of
atoms of each element on both sides of the reaction.
We can make a chart to help us
organize this information. The chart consists of the elements
listed down the left-hand side and the unbalanced chemical equation written across
the top. We can divide the chart at the
arrow, separating the reactants from the products. Now, we can begin counting the
hydrogen atoms. On the reactant side, we see three
hydrogen atoms in each molecule of phosphorous acid. We can record this in our
chart. On the product side, there are
three atoms of hydrogen in each phosphoric acid molecule and three atoms of hydrogen
in each phosphine molecule.
Now, we can count the phosphorus
atoms. On the reactant side, we can see
one atom of phosphorus. And on the product side, we can see
one atom of phosphorus in each phosphoric acid molecule and one atom of phosphorus
in each phosphine molecule. Lastly, we will count the oxygen
atoms. On the reactant side, we see three
atoms of oxygen. And on the product side, we see
four atoms of oxygen. Now that we have counted the number
of atoms of each element, we can add coefficients to balance the chemical
equation. A chemical equation is balanced
when the number of atoms of each element is the same on both sides of the
reaction. There are three atoms of hydrogen
on the reactant side and three plus three, or six, atoms of hydrogen on the product
side. These values are not equal. This means that the hydrogen atoms
are unbalanced.
There is one atom of phosphorus on
the reactant side and one plus one, or two, total atoms of phosphorus on the product
side. These values are unequal, meaning
that the phosphorus atoms are unbalanced. There are three atoms of oxygen on
the reactant side and four atoms of oxygen on the product side. These values are not equal, meaning
that the oxygen atoms are also unbalanced. It can be difficult to decide which
element to begin balancing. One helpful hint is to begin
balancing with the element which appears in the least number of reactants and
products. Therefore, we will start by
balancing the oxygen atoms.
We need a coefficient such that
when placed in front of the phosphorous acid molecule, it gives us a total of four
oxygen atoms on the reactant side. We can label this coefficient
coefficient 𝑥. If one molecule of phosphorous acid
contains three atoms of oxygen, 𝑥 molecules of phosphorous acid will contain three
𝑥 atoms of oxygen. We can set the number of atoms of
oxygen on the reactant side equal to the number of atoms of oxygen on the product
side. We rearrange to solve for 𝑥 and
determine that 𝑥 equals four-thirds. This is the coefficient.
Placing a coefficient of
four-thirds in front of the phosphorous acid will change the number of hydrogen,
phosphorus, and oxygen atoms on the reactant side. This means that there are now four
atoms of hydrogen, four-thirds atoms of phosphorus, and four atoms of oxygen on the
reactant side. With four atoms of oxygen on the
reactant side and four atoms of oxygen on the product side, the oxygen atoms are
balanced.
Next, we can balance the hydrogen
atoms. In order to balance the hydrogen
atoms, we could place a coefficient in front of phosphoric acid or phosphine
gas. Placing a coefficient in front of
the phosphoric acid molecule would change the number of hydrogen, phosphorus, and
oxygen atoms on the product side. This would cause the oxygen atoms
to become unbalanced. But placing a coefficient in front
of the phosphine gas molecule would only affect the number of phosphorus and
hydrogen atoms. The oxygen atoms would be
unaffected and would remain balanced. Therefore, we should determine what
coefficient represented by the variable 𝑦 would balance the hydrogen atoms.
Coefficient 𝑦 represents the
number of phosphine gas molecules. If each phosphine gas molecule
contains three atoms of hydrogen, 𝑦 phosphine gas molecules will contain three 𝑦
atoms of hydrogen. We can set the number of hydrogen
atoms on the reactant side equal to the number of hydrogen atoms on the product side
and rearrange to solve for 𝑦. We determine that 𝑦 equals
one-third. Placing a coefficient of one-third
in front of the phosphine gas molecule will affect the number of phosphorus and
hydrogen atoms on the product side. One-third phosphine gas molecules
will contain one atom of hydrogen and one-third atoms of phosphorus. This gives us a total of four atoms
of hydrogen and four-thirds atoms of phosphorus on the product side.
The number of hydrogen and
phosphorus atoms are the same on both sides of the reaction. This means that the hydrogen and
phosphorus atoms are balanced. The reaction is balanced; however,
the question asked us to balance the reaction using whole-number coefficients. We can get rid of the fractions and
maintain a balanced chemical equation by multiplying all of the coefficients by
three. This gives us a final balanced
chemical equation of four H3PO3 yields three H3PO4 plus PH3.
