## Introduction

Chemical equations are used to describe the reactants and products in a chemical reaction. However, the equation needs to be balanced to ensure that the number of atoms on each side of the equation is equal. In this article, we'll show you how to balance the equation for aluminum nitrate and water using algebraic equations.

## Word Equation

*Aluminum nitrate + water → nitric acid + aluminum hydroxide*

## Input Interpretation

*Al(NO3)3 + 3H2O → 3HNO3 + Al(OH)3*

**Step 1 **

Write the Balanced Equation Algebraically To balance the equation, we need to add stoichiometric coefficients to the reactants and products. Let's call these coefficients c1, c2, c3, and c4:

* c1Al(NO3)3 + c2H2O → c3 3HNO3 + c4Al(OH)3*

**Step 2 **

Equate the Number of Atoms Next, we need to set the number of atoms in the reactants equal to the number of atoms in the products for each element. For aluminum (Al), we have:

*c1 = c4*

For nitrogen (N), we have:

*3c1 = c3*

For oxygen (O), we have:

*9c1 + c2 = 3c3 + 3c4*

For hydrogen (H), we have:

*2c2 = c3 + 3c4*

**Step 3 **

Solve for the Coefficients Since there are four unknowns and only four equations, we can solve for the coefficients by choosing an arbitrary value for one of them. Let's set c1 = 1:

*c1 = 1 c2 = 3 c3 = 3 c4 = 1*

**Step 4 **

Substitute the Coefficients Now we can substitute the coefficients back into the balanced equation:

*Al(NO3)3 + 3H2O → 3HNO3 + Al(OH)3*