# Balance the following chemical equations using the algebraic method. Make sure you show all your work and explain each the step.?

C2H2 + O2 --> CO2 + H2O

H2SO4 + NaHCO3 ----> Na2SO4 + CO2 + H2O

H2S + H3AsO4 ----> As2S3 + S +H2O

Ca10F2(PO4)6 + H2SO4---->Ca(H2PO4)2 + CaSO4 + HF

C7H10N + O2 ----> CO2 + H2O + NO2

### 1 Answer

- Roger the MoleLv 75 months ago
Most of these reactions can be easily balanced without going to the trouble of the algebraic method. So I'm choosing the third one to show the details, since it is not quite so easy.

First, assign an algebraic variable to each compound in the formula:

a H2S + b H3AsO4 → c As2S3 + d S + e H2O

Now the essence of the problem is to find the lowest integer values for all five variables which cause the equation to be balanced chemically.

Write an algebraic equation showing the balance of each element separately. (The numbers in square brackets are just putting a name to each equation so we can talk about them. They aren't necessary when doing it yourself.)

hydrogen: 2 a + 3 b = 2 e [1]

sulfur: a = 3 c + d [2]

arsenic: b = 2 c [3]

oxygen: 4 b = e [4]

(It isn't necessary in any of the five given chemical equations in this question, but sometimes it is necessary to have an extra equation here showing the balance of charges or oxidation states.)

Use your favorite algebraic method to solve the four equations simultaneously. (The matrix method is too difficult to show in YA, so I will use the substitution method.)

Substitute equation [4] into equation [1]:

2 a + 3 b = 2 (4 b)

Expand and simplify:

2 a = 5 b

Let a be equal to 5. (The exact choice of the value for a isn't terribly important. It can be adjusted later if necessary. Mostly it should chosen to be relatively small, but still keep the next step in integers.)

Solve for b:

b = 2 x 5 / 5 = 2

Substitute this value for b into equation [3]:

2 = 2 c

Solve for c:

c = 1

Substitute these values for a and c into equation [2]:

5 = 3 (1) + d

Solve for d:

d = 2

Substitute the value for b into equation [4]:

4 (2) = e

Solve for e:

e = 8

Substitute the values of all the variables into the original chemical equation:

5 H2S + 2 H3AsO4 → 1 As2S3 + 2 S + 8 H2O

Check to see that the coefficients are the lowest possible integers. (They are in this case.) (This is the point at which the value of a might need adjusting, but not this time.)