# co o2 co2

To balance the equation CO + O2 = CO2 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.

### 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.

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a CO + b O2 = c CO2

### Step 2: Create a System of Equations

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

```C:	1a	+	0b	=	1c
O:	1a	+	2b	=	2c

```

### Step 3: Solve For All Variables

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

• 1a - 1c = 0
• 1a + 2b - 2c = 0

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

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```[ 1	 0	-1	0]
[ 1	 2	-2	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.

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• a = 2 (CO)
• b = 1 (O2)
• c = 2 (CO2)

### 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 CO + O2 = 2 CO2

Reactants Products C 2 2 ✔️ 4 4 ✔️

Since there is an equal number of each element in the reactants and products of 2CO + O2 = 2CO2, the equation is balanced.