To balance the chemical equation:
[tex]\[ \text{Na}_2\text{HPO}_4 \rightarrow \text{Na}_4\text{P}_2\text{O}_7 + \text{H}_2\text{O} \][/tex]
we need to make sure that the number of atoms of each element on the reactant side (left side) is equal to the number of atoms on the product side (right side). Here's a step-by-step balancing process:
1. Count Sodium (Na) atoms:
- On the left: There are 2 sodium atoms from one molecule of [tex]\(\text{Na}_2\text{HPO}_4\)[/tex].
- On the right: We aim to have 4 sodium atoms in [tex]\(\text{Na}_4\text{P}_2\text{O}_7\)[/tex]. To achieve this, we need 2 molecules of [tex]\(\text{Na}_2\text{HPO}_4\)[/tex] to provide 4 sodium atoms.
2. Count Phosphorus (P) atoms:
- On the left: There is 1 phosphorus atom per molecule of [tex]\(\text{Na}_2\text{HPO}_4\)[/tex]. With 2 molecules, we have:
[tex]\[
2 \text{ molecules} \times 1 (\text{P}) = 2 \text{ phosphorus atoms}
\][/tex]
- On the right: There are 2 phosphorus atoms in one molecule of [tex]\(\text{Na}_4\text{P}_2\text{O}_7\)[/tex].
3. Count Oxygen (O) atoms:
- On the left: Each [tex]\(\text{Na}_2\text{HPO}_4\)[/tex] molecule has 4 oxygen atoms. Thus, with 2 molecules, we get:
[tex]\[
2 \text{ molecules} \times 4 (\text{O}) = 8 \text{ oxygen atoms}
\][/tex]
- On the right: [tex]\(\text{Na}_4\text{P}_2\text{O}_7\)[/tex] has 7 oxygen atoms. To balance the remaining oxygen atoms:
[tex]\[
8 (\text{left O atoms}) - 7 (\text{right O atoms in Na}_4\text{P}_2\text{O}_7) = 1 \text{ oxygen atom from } \text{H}_2\text{O}
\][/tex]
However, [tex]\(\text{H}_2\text{O}\)[/tex] molecules must be balanced as whole units, which means we need to combine correctly.
4. Count Hydrogen (H) atoms:
- On the left: There are 2 hydrogen atoms from both molecules of [tex]\(\text{Na}_2\text{HPO}_4\)[/tex].
- On the right: Each [tex]\(\text{H}_2\text{O}\)[/tex] molecule contributes 2 hydrogen atoms. Thus, to match:
[tex]\[
2 (\text{left H atoms}) \rightarrow 2 \text{ total molecules of } \text{H}_2\text{O}
\][/tex]
Considering we must have whole molecules in the product side and re-evaluating the balancing, it will be:
The coefficient for [tex]\(\text{Water} (\text{H}_2\text{O}) \)[/tex]: 7
So, the balanced chemical equation is:
[tex]\[ \boxed{2} \text{Na}_2\text{HPO}_4 \rightarrow \boxed{1} \text{Na}_4\text{P}_2\text{O}_7 + \boxed{7} \text{H}_2\text{O} \][/tex]
Final coefficients are:
[tex]\[ \text{Na}_2\text{HPO}_4: 2 \quad \text{Na}_4\text{P}_2\text{O}_7: 1 \quad \text{H}_2\text{O}: 7 \][/tex]
