To balance the chemical equation
[tex]\[ \text{Na} + \text{H}_2\text{O} \rightarrow \text{NaOH} + \text{H}_2 \][/tex]
we need to ensure that the number of atoms for each element is equal on both sides of the equation. Let’s proceed step-by-step to balance this equation.
1. Identify the elements involved: Sodium (Na), Hydrogen (H), and Oxygen (O).
2. Write down the count of each element on both sides of the equation initially:
[tex]\[
\begin{align*}
\text{Reactants:} & \quad \text{Na: } 1, \quad \text{H: } 2, \quad \text{O: } 1 \\
\text{Products:} & \quad \text{Na: } 1, \quad \text{H: } 3, \quad \text{O: } 1 \\
\end{align*}
\][/tex]
Initially, the equation looks like:
[tex]\[ \text{Na} + \text{H}_2\text{O} \rightarrow \text{NaOH} + \text{H}_2 \][/tex]
3. Balance the sodium atoms (Na):
Currently, there is 1 sodium atom on both sides of the equation. To balance sodium atoms, we need to have the same number of sodium atoms on both sides. If we have 2 sodium atoms on the reactants side, we should correspondingly have 2 sodium atoms on the products side.
Update the equation:
[tex]\[ 2\text{Na} + \text{H}_2\text{O} \rightarrow 2\text{NaOH} + \text{H}_2 \][/tex]
4. Balance the hydrogen atoms (H):
On the reactants side, we currently have 2 hydrogen atoms from [tex]\( \text{H}_2\text{O} \)[/tex]. On the products side, we have [tex]\( 2 \times \text{NaOH} \)[/tex] contributing 2 hydrogen atoms and [tex]\( \text{H}_2 \)[/tex] contributing another 2 hydrogen atoms. We need to balance these counts. One way to do this is to adjust the number of water molecules on the reactants side to match the total hydrogen count.
Update the equation:
[tex]\[ 2\text{Na} + 2\text{H}_2\text{O} \rightarrow 2\text{NaOH} + \text{H}_2 \][/tex]
5. Balance the oxygen atoms (O):
On the reactants side, there are 2 oxygen atoms from [tex]\( 2\text{H}_2\text{O} \)[/tex]. On the products side, there are 2 oxygen atoms from [tex]\( 2\text{NaOH} \)[/tex]. The counts are balanced.
6. Verify the balance:
[tex]\[
\begin{align*}
\text{Reactants:} & \quad \text{Na: } 2, \quad \text{H: } 4, \quad \text{O: } 2 \\
\text{Products:} & \quad \text{Na: } 2, \quad \text{H: } 4, \quad \text{O: } 2 \\
\end{align*}
\][/tex]
Both sides have 2 sodium atoms, 4 hydrogen atoms, and 2 oxygen atoms.
Therefore, the balanced chemical equation is:
[tex]\[ 2\text{Na} + 2\text{H}_2\text{O} \rightarrow 2\text{NaOH} + \text{H}_2 \][/tex]
