Phosphorus (V) chloride dissolves in water to form phosphoric acid, H_3PO_4 and hydrochloric acid. What is the value of (x + y) in the balanced equation for this reaction?
`PCl_(5(s)) + xH_2O_((I)) to H_3PO_4(aq) + yHCl_(aq)`

Explanation

To solve the problem, we need to write and balance the chemical equation for the reaction of phosphorus (V) chloride (PCl₅) with water (H₂O) to produce phosphoric acid (H₃PO₄) and hydrochloric acid (HCl).

### Step-by-Step Solution:

1. **Write the unbalanced equation:**
\[ PCl_5(s) + H_2O(l) \rightarrow H_3PO_4(aq) + HCl(aq) \]

2. **Identify the number of atoms for each element in the reactants and products:**
- **Reactants:**
- Phosphorus (P): 1 (from PCl₅)
- Chlorine (Cl): 5 (from PCl₅)
- Hydrogen (H): 2 (from H₂O)
- Oxygen (O): 1 (from H₂O)
- **Products:**
- Phosphorus (P): 1 (from H₃PO₄)
- Chlorine (Cl): 1 (from HCl)
- Hydrogen (H): 3 (from H₃PO₄) + 1 (from HCl) = 4
- Oxygen (O): 4 (from H₃PO₄)

3. **Balance the phosphorus atoms:**
- Phosphorus is already balanced (1 on each side).

4. **Balance the chlorine atoms:**
- There are 5 chlorine atoms in the reactants (from PCl₅) and only 1 in the products (from HCl).
- To balance chlorine, we need to multiply HCl by 5:
\[ PCl_5 + H_2O \rightarrow H_3PO_4 + 5HCl \]

5. **Update the number of atoms after balancing chlorine:**
- **Reactants:**
- Cl: 5 (from PCl₅)
- **Products:**
- Cl: 5 (from 5HCl)

6. **Balance the hydrogen atoms:**
- Now, we have 4 hydrogen atoms from H₃PO₄ and 5 from 5HCl, totaling 9 hydrogen atoms in the products.
- To balance hydrogen, we need 9 hydrogen atoms from water. Since each water molecule contributes 2 hydrogen atoms, we need to have:
\[ \frac{9}{2} = 4.5 \text{ H}_2O \]
- To avoid fractions, we can multiply the entire equation by 2:
\[ 2PCl_5 + 9H_2O \rightarrow 2H_3PO_4 + 10HCl \]

7. **Final balanced equation:**
\[ 2PCl_5 + 9H_2O \rightarrow 2H_3PO_4 + 10HCl \]

8. **Identify the values of x and y:**
- From the balanced equation, we see:
- \( x = 9 \) (the coefficient of H₂O)
- \( y = 10 \) (the coefficient of HCl)

9. **Calculate \( x + y \):**
\[ x + y = 9 + 10 = 19 \]

### Final Answer:
The value of \( x + y \) is **19**.