Certainly! Let's balance the chemical equation step-by-step:
[tex]\[ P_4(s) + NaOH(aq) + H_2O(l) \rightarrow PH_3(g) + Na_2HPO_3(aq) \][/tex]
### Step 1: Balance the Phosphorus (P) atoms
In [tex]\(P_4\)[/tex], there are 4 phosphorus atoms on the left side. To balance the phosphorus atoms on both sides, we need 4 molecules of [tex]\(PH_3\)[/tex], each containing 1 phosphorus atom:
[tex]\[ P_4(s) \rightarrow 4PH_3(g) \][/tex]
### Step 2: Balance the Sodium (Na) atoms
Next, we need to balance the sodium atoms. We see that [tex]\(Na_2HPO_3\)[/tex] has 2 sodium atoms per molecule. Since we need to produce 4 molecules of [tex]\(Na_2HPO_3\)[/tex] to balance the phosphorus, we will need:
[tex]\[ 4 \times 2 = 8 \][/tex]
So, we need 8 molecules of [tex]\(NaOH\)[/tex]:
[tex]\[ NaOH(aq) \rightarrow 4Na_2HPO_3(aq) \][/tex]
### Step 3: Balance the Hydrogen (H) atoms
We now need to balance the hydrogen atoms. On the product side, we have [tex]\(4PH_3\)[/tex], each containing 3 hydrogen atoms:
[tex]\[ 4 \times 3 = 12 \text{ hydrogen atoms} \][/tex]
Adding to that, we have 8 hydrogen atoms from [tex]\(8NaOH\)[/tex]:
[tex]\[ 12 + 8 = 20 \text{ hydrogen atoms required} \][/tex]
Since each water molecule ([tex]\(H_2O\)[/tex]) contains 2 hydrogen atoms, we need:
[tex]\[ \frac{20}{2} = 10 \][/tex]
### Step 4: Balance the Oxygen (O) atoms
Finally, we balance the oxygen atoms. We have 10 molecules of [tex]\(H_2O\)[/tex], each containing one oxygen atom:
[tex]\[ 10 \text{ oxygen atoms from } H_2O \][/tex]
And 8 molecules of [tex]\(NaOH\)[/tex], each containing one oxygen atom:
[tex]\[ 8 \text{ oxygen atoms from } NaOH \][/tex]
Therefore:
[tex]\[ 10 + 8 = 18 \text{ oxygen atoms on the reactant side} \][/tex]
On the product side, each [tex]\(Na_2HPO_3\)[/tex] has 3 oxygen atoms and we have 4 of them:
[tex]\[ 4 \times 3 = 12 \text{ oxygen atoms} \][/tex]
We need to distribute the rest between [tex]\(H_2O\)[/tex] molecules and fit with hydrogen atoms:
[tex]\[ 18 \text{ atoms result to 6 water molecules to fit both oxygen and hydrogen atoms required on both sides of the equation} \][/tex]
### Final Balanced Equation
Combining all these steps, the balanced equation is:
[tex]\[
P_4(s) + 8NaOH(aq) + 6H_2O(l) \rightarrow 4PH_3(g) + 4Na_2HPO_3(aq)
\][/tex]
This balanced equation ensures that the number of each type of atom is the same on both sides of the equation.
