al(oh)3 + hcl

To balance the equation Al(OH)3 + HCl = AlCl3 + 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.

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(OH)3 + b HCl = c AlCl3 + d H2O

Step 2: Create a System of Equations

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

Al:	1a	+	0b	=	1c	+	0d
O:	3a	+	0b	=	0c	+	1d
H:	3a	+	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
  • 3a - 1d = 0
  • 3a + 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]
[ 3	 0	 0	-1	0]
[ 3	 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.

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  • a = 1 (Al(OH)3)
  • b = 3 (HCl)
  • c = 1 (AlCl3)
  • d = 3 (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.

Al(OH)3 + 3 HCl = AlCl3 + 3 H2O

Reactants Products
Al11✔️
O33✔️
H66✔️
Cl33✔️

Since there is an equal number of each element in the reactants and products of Al(OH)3 + 3HCl = AlCl3 + 3H2O, the equation is balanced.