# hcl al

To balance the equation Al + HCl = AlCl3 + H2 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 lớn represent the unknown coefficients.

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a Al + b HCl = c AlCl3 + d H2

### Step 2: Create a System of Equations

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

```Al:	1a	+	0b	=	1c	+	0d
H:	0a	+	1b	=	0c	+	2d
Cl:	0a	+	1b	=	3c	+	0d

```

### Step 3: Solve For All Variables

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

• 1a - 1c = 0
• 1b - 2d = 0
• 1b - 3c = 0

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

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```[ 1	 0	-1	 0	0]
[ 0	 1	 0	-2	0]
[ 0	 1	-3	 0	0]
```

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

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

• a = 2 (Al)
• b = 6 (HCl)
• c = 2 (AlCl3)
• d = 3 (H2)

### 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 Al + 6 HCl = 2 AlCl3 + 3 H2

Reactants Products Al 2 2 ✔️ 6 6 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of 2Al + 6HCl = 2AlCl3 + 3H2, the equation is balanced.