Phosphorus(V) chloride dissolves in water to form phosphoric acid, `H_(3)PO_(4)` and hydrochloric acid. What are the values of x, y and z in the balanced equation for this reaction?
`PCl_(5(s)) + xH_(2)O_((l)) to y H_(3)PO_(4(aq)) +z HCl_((aq))`

Options

A. `{:(x,y,z),(2,1,4):}`
B. `{:(x,y,z),(2,2,5):}`
C. `{:(x,y,z),(4,2,4):}`
D. `{:(x,y,z),(4,1,5):}`

Explanation

To balance the equation for the reaction of phosphorus(V) chloride with water, we start with the unbalanced equation:

\[ PCl_5(s) + x H_2O(l) \rightarrow y H_3PO_4(aq) + z HCl(aq) \]

### Step 1: Identify the Reactants and Products
- Reactant: Phosphorus(V) chloride (PCl₅)
- Reactant: Water (H₂O)
- Products: Phosphoric acid (H₃PO₄) and Hydrochloric acid (HCl)

### Step 2: Write the Unbalanced Equation
The unbalanced equation can be written as:
\[ PCl_5 + H_2O \rightarrow H_3PO_4 + HCl \]

### Step 3: Count the Atoms on Both Sides
- On the left side:
- Phosphorus (P): 1
- Chlorine (Cl): 5
- Hydrogen (H): 2 (from H₂O)
- Oxygen (O): 1 (from H₂O)

- On the right side:
- Phosphorus (P): 1 (from H₃PO₄)
- Chlorine (Cl): 1 (from HCl)
- Hydrogen (H): 3 (from H₃PO₄) + 1 (from HCl) = 4
- Oxygen (O): 4 (from H₃PO₄)

### Step 4: Balance Phosphorus
Phosphorus is already balanced with 1 atom on each side.

### Step 5: Balance Chlorine
To balance chlorine, we need 5 chlorine atoms on the right side. Since each HCl provides 1 chlorine atom, we need 5 HCl:
\[ PCl_5 + H_2O \rightarrow H_3PO_4 + 5 HCl \]

### Step 6: Update the Count
Now we have:
- On the right side:
- Chlorine (Cl): 5 (from 5 HCl)
- Hydrogen (H): 3 (from H₃PO₄) + 5 (from 5 HCl) = 8
- Oxygen (O): 4 (from H₃PO₄)

### Step 7: Balance Hydrogen and Oxygen
Now we need to balance hydrogen and oxygen. We have 8 hydrogen atoms on the right side and 2 from one water molecule on the left. Therefore, we need 4 water molecules:
\[ PCl_5 + 4 H_2O \rightarrow H_3PO_4 + 5 HCl \]

### Step 8: Final Count
- Left side:
- P: 1
- Cl: 5
- H: 8 (from 4 H₂O)
- O: 4 (from 4 H₂O)

- Right side:
- P: 1 (from H₃PO₄)
- Cl: 5 (from 5 HCl)
- H: 8 (3 from H₃PO₄ + 5 from 5 HCl)
- O: 4 (from H₃PO₄)

### Conclusion
The balanced equation is:
\[ PCl_5 + 4 H_2O \rightarrow H_3PO_4 + 5 HCl \]

From this balanced equation, we can determine:
- \( x = 4 \)
- \( y = 1 \)
- \( z = 5 \)

### Final Answer
- \( x = 4 \)
- \( y = 1 \)
- \( z = 5 \)