# h2s + o2

To balance the equation H2S + O2 = SO2 + H2O using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.

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### Step 1: Label Each Compound With a Variable

Label each compound (reactant or product) in the equation with a variable to tát represent the unknown coefficients.

a H2S + b O2 = c SO2 + d H2O

### Step 2: Create a System of Equations

Create an equation for each element (H, S, O) where each term represents the number of atoms of the element in each reactant or product.

H: 2a + 0b = 0c + 2d S: 1a + 0b = 1c + 0d O: 0a + 2b = 2c + 1d

### Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator to tát solve for each variable.

• 2a - 2d = 0
• 1a - 1c = 0
• 2b - 2c - 1d = 0

Use your graphing calculator's rref() function (or an online rref calculator) to tát convert the following matrix into reduced row-echelon-form:

[ 2 0 0 -2 0] [ 1 0 -1 0 0] [ 0 2 -2 -1 0]

The resulting matrix can be used to tát determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result to tát get the lowest, whole integer values.

• a = 2 (H2S)
• b = 3 (O2)
• c = 2 (SO2)
• d = 2 (H2O)

### Step 4: Substitute Coefficients and Verify Result

Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.

2 H2S + 3 O2 = 2 SO2 + 2 H2O

Reactants Products H 4 4 ✔️ 2 2 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of 2H2S + 3O2 = 2SO2 + 2H2O, the equation is balanced.

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