Let's balance the given chemical equation step-by-step:
Chemical Equation:
[tex]\[ \text{NaOH} + \text{Al}_2\text{O}_3 \rightarrow \text{NaAlO}_2 + \text{H}_2\text{O} \][/tex]
First, we need to count the number of each type of atom on both sides of the equation to determine the coefficients that will balance the equation.
Step 1: Write down the number of atoms of each element in the reactants and the products without any coefficients.
Reactants:
- Sodium (Na): 1 (from NaOH)
- Oxygen (O): 1 (from NaOH) + 3 (from Al₂O₃) = 4
- Hydrogen (H): 1 (from NaOH)
- Aluminum (Al): 2 (from Al₂O₃)
Products:
- Sodium (Na): 1 (from NaAlO₂)
- Aluminum (Al): 1 (from NaAlO₂)
- Oxygen (O): 2 (from NaAlO₂) + 1 (from H₂O) = 3
- Hydrogen (H): 2 (from H₂O)
Step 2: Assign coefficients to balance the equation.
Starting with another element that appears in a complex molecule often helps. In this case, let's balance the aluminum (Al) atoms first.
We have 2 aluminum atoms in \( \text{Al}_2\text{O}_3 \):
[tex]\[ \text{Al}_2\text{O}_3 \][/tex]
To balance the Al in the products:
[tex]\[ 2 \times \text{NaAlO}_2 \rightarrow \text{2 NaAlO}_2 \][/tex]
Now, we have 2 aluminum atoms on both sides.
Re-assess the numbers:
Products:
- Sodium (Na): 2 (from 2 × NaAlO₂)
- Aluminum (Al): 2 (from 2 × NaAlO₂)
- Oxygen (O): 4 (from 2 × NaAlO₂)
- Hydrogen (H): 2 (from H₂O)
Next, balance Sodium (Na) atoms by making coefficients of \( \text{NaOH} \) number 2 as we require 2 sodium atoms:
[tex]\[ 2 \times \text{NaOH} \rightarrow \text{2 NaOH} \][/tex]
Reactants:
- Sodium (Na): 2 (from 2 × NaOH)
- Oxygen (O): 2 (from 2 × NaOH) + 3 (from Al₂O₃) = 5
- Hydrogen (H): 2 (from 2 × NaOH)
- Aluminum (Al): 2 (from Al₂O₃)
Finally, we balance the hydrogen (H) by ensuring that the product side equals the reactant side. We currently have 2 hydrogens in the reactants from 2 NaOH, so coefficient of \( H_2O \):
[tex]\[ H_2O \rightarrow H_2O \][/tex]
Balanced Equation:
[tex]\[ 2 \text{NaOH} + \text{Al}_2\text{O}_3 \rightarrow 2 \text{NaAlO}_2 + \text{H}_2\text{O} \][/tex]
Reassess the entire equation again:
Reactants:
- Sodium (Na): 2 (from 2 × NaOH)
- Oxygen (O): 2 (from 2 × NaOH) + 3 (from Al₂O₃) = 5
- Hydrogen (H): 2 (from 2 × NaOH)
- Aluminum (Al): 2 (from Al₂O₃)
Products:
- Sodium (Na): 2 (from 2 × NaAlO₂)
- Aluminum (Al): 2 (from 2 × NaAlO₂)
- Oxygen (O): 4 (from 2 × NaAlO₂) + 1 (from H₂O) = 5
- Hydrogen (H): 2 (from H₂O)
Therefore, the coefficients for the balanced chemical equation are:
[tex]\[ 2 \text{NaOH} + \text{Al}_2\text{O}_3 \rightarrow 2 \text{NaAlO}_2 + \text{H}_2\text{O} \][/tex]
The coefficients of the balanced equation are:
[tex]\[ 2, 1, 2, 1 \][/tex]
