# c 2 h 2 ra c 2 h 6

To balance the equation C2H2 + H2 = C2H6 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 lớn represent the unknown coefficients.

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a C2H2 + b H2 = c C2H6

### Step 2: Create a System of Equations

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

```C:	2a	+	0b	=	2c
H:	2a	+	2b	=	6c

```

### Step 3: Solve For All Variables

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

• 2a - 2c = 0
• 2a + 2b - 6c = 0

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

```[ 2	 0	-2	0]
[ 2	 2	-6	0]
```

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

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

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• a = 1 (C2H2)
• b = 2 (H2)
• c = 1 (C2H6)

### 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.

C2H2 + 2 H2 = C2H6

Reactants Products C 2 2 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of C2H2 + 2H2 = C2H6, the equation is balanced.