To balance the given chemical equation: [tex]\(5_0 Na + H_2O \rightarrow NaOH + H_2\)[/tex], we need to follow these steps:
1. List the number of atoms of each element on both sides of the equation:
- On the reactants side (left side):
- Sodium (Na): [tex]\(5_0\)[/tex]
- Hydrogen (H): [tex]\(2\)[/tex] (from H[tex]\(_2\)[/tex]O)
- Oxygen (O): [tex]\(1\)[/tex] (from H[tex]\(_2\)[/tex]O)
- On the products side (right side):
- Sodium (Na): [tex]\(1\)[/tex] (from NaOH)
- Hydrogen (H): [tex]\(1\)[/tex] (from NaOH) + [tex]\(2\)[/tex] (from H[tex]\(_2\)[/tex]) = [tex]\(3\)[/tex]
- Oxygen (O): [tex]\(1\)[/tex] (from NaOH)
2. Balance the elements one at a time by adjusting the coefficients:
- Balancing Sodium (Na):
- Since there are 50 sodium atoms on the reactants side and only 1 on the products side, adjust the coefficient of NaOH on the products side to match:
[tex]\[
50 Na + H_2O \rightarrow 50 NaOH + H_2
\][/tex]
- Balancing Hydrogen (H):
- On the products side, we now have 50 NaOH, which contributes 50 hydrogen atoms.
- We also need to balance the H[tex]\(_2\)[/tex] gas on the products side. The simplest way to balance hydrogen is to adjust the coefficient of water (H[tex]\(_2\)[/tex]O) on the reactants side to ensure equal numbers of hydrogen atoms:
[tex]\[
50 Na + 50 H_2O \rightarrow 50 NaOH + 25 H_2
\][/tex]
- Here, each H[tex]\(_2\)[/tex]O provides 2 hydrogen atoms, so 50 H[tex]\(_2\)[/tex]O contributes 100 hydrogen atoms on the reactants side. Since 50 NaOH also contributes 50 hydrogen atoms on the products side, we need 25 H[tex]\(_2\)[/tex] molecules to provide the remaining 50 hydrogen atoms (2 per molecule).
- Balancing Oxygen (O):
- On both sides, each H[tex]\(_2\)[/tex]O and NaOH already have their oxygens balanced (50 atoms in total).
3. Final balanced equation:
[tex]\[
50 Na + 50 H_2O \rightarrow 50 NaOH + 25 H_2
\][/tex]
However, simplifying this equation in terms of the smallest whole number coefficients:
[tex]\[
2 Na + 2 H_2O \rightarrow 2 NaOH + H_2
\][/tex]
These coefficients are:
- [tex]\( Na \)[/tex] coefficient: [tex]\(2\)[/tex]
- [tex]\( H_2O \)[/tex] coefficient: [tex]\(2\)[/tex]
- [tex]\( NaOH \)[/tex] coefficient: [tex]\(2\)[/tex]
- [tex]\( H_2 \)[/tex] coefficient: [tex]\(1\)[/tex]
So the balanced chemical equation is:
[tex]\[
2Na + 2H_2O \rightarrow 2NaOH + H_2
\][/tex]
Which means we balanced the chemical equation correctly.
