To balance the equation AlN + H2O = NH3 + Al(OH)3 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 AlN + b H2O = c NH3 + d Al(OH)3
Step 2: Create a System of Equations
Create an equation for each element (Al, N, H, O) where each term represents the number of atoms of the element in each reactant or product.
Al: 1a + 0b = 0c + 1d N: 1a + 0b = 1c + 0d H: 0a + 2b = 3c + 3d O: 0a + 1b = 0c + 3d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator to lớn solve for each variable.
- 1a - 1d = 0
- 1a - 1c = 0
- 2b - 3c - 3d = 0
- 1b - 3d = 0
Use your graphing calculator's rref() function (or an online rref calculator) to lớn convert the following matrix into reduced row-echelon-form:
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[ 1 0 0 -1 0] [ 1 0 -1 0 0] [ 0 2 -3 -3 0] [ 0 1 0 -3 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 (AlN)
- b = 3 (H2O)
- c = 1 (NH3)
- d = 1 (Al(OH)3)
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.
AlN + 3 H2O = NH3 + Al(OH)3
| Al | 1 | 1 | ✔️ |
|---|---|---|---|
| N | 1 | 1 | ✔️ |
| H | 6 | 6 | ✔️ |
| O | 3 | 3 | ✔️ |
Since there is an equal number of each element in the reactants and products of AlN + 3H2O = NH3 + Al(OH)3, the equation is balanced.
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