# al2so43 hcl

To balance the equation Al2(SO4)3 + HCl = H2SO4 + AlCl3 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 tướng represent the unknown coefficients.

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a Al2(SO4)3 + b HCl = c H2SO4 + d AlCl3

### Step 2: Create a System of Equations

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

```Al:	2a	+	0b	=	0c	+	1d
S:	3a	+	0b	=	1c	+	0d
O:	12a	+	0b	=	4c	+	0d
H:	0a	+	1b	=	2c	+	0d
Cl:	0a	+	1b	=	0c	+	3d

```

### Step 3: Solve For All Variables

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

• 2a - 1d = 0
• 3a - 1c = 0
• 12a - 4c = 0
• 1b - 2c = 0
• 1b - 3d = 0

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

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```[ 2	 0	 0	-1	0]
[ 3	 0	-1	 0	0]
[ 12	 0	-4	 0	0]
[ 0	 1	-2	 0	0]
[ 0	 1	 0	-3	0]
```

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

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

Xem thêm: bài giải toán lớp 4

• a = 1 (Al2(SO4)3)
• b = 6 (HCl)
• c = 3 (H2SO4)
• d = 2 (AlCl3)

### 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.

Al2(SO4)3 + 6 HCl = 3 H2SO4 + 2 AlCl3

Reactants Products Al 2 2 ✔️ 3 3 ✔️ 12 12 ✔️ 6 6 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of Al2(SO4)3 + 6HCl = 3H2SO4 + 2AlCl3, the equation is balanced.