To determine the balanced chemical equation for the given reaction, we need to ensure that the number of atoms for each element on the reactant side is equal to the number of atoms on the product side.
### Step-by-Step Solution:
1. Write down the unbalanced chemical equation:
[tex]\[
H_3PO_4 + HCl \rightarrow PCl_5 + H_2O
\][/tex]
2. Check the given possible equations for balance:
- [tex]\( H_3PO_4 + 5 HCl \rightarrow PCl_5 + 4 H_2O \)[/tex]
- [tex]\( 2 H_3PO_4 + 10 HCl \rightarrow 2 PCl_5 + 4 H_2O \)[/tex]
- [tex]\( 2 H_3PO_4 + 5 HCl \rightarrow 2 PCl_5 + 3 H_2O \)[/tex]
- [tex]\( H_3PO_4 + 5 HCl \rightarrow PCl_5 + H_2O \)[/tex]
3. Determine which equation is correctly balanced:
- Case 1: [tex]\( H_3PO_4 + 5 HCl \rightarrow PCl_5 + 4 H_2O \)[/tex]
- Reactants: [tex]\( H_3PO_4 \)[/tex] has 3 H, 1 P, 4 O; [tex]\( 5 HCl \)[/tex] have 5 H, 5 Cl.
- Products: [tex]\( PCl_5 \)[/tex] has 1 P, 5 Cl; [tex]\( 4 H_2O \)[/tex] have 8 H, 4 O.
- Balance check:
- H: 3 + 5 ≠ 8 (not balanced)
- P: 1 = 1
- Cl: 5 = 5
- O: 4 = 4
- Case 2: [tex]\( 2 H_3PO_4 + 10 HCl \rightarrow 2 PCl_5 + 4 H_2O \)[/tex]
- Reactants: [tex]\( 2 H_3PO_4 \)[/tex] have 6 H, 2 P, 8 O; [tex]\( 10 HCl \)[/tex] have 10 H, 10 Cl.
- Products: [tex]\( 2 PCl_5 \)[/tex] have 2 P, 10 Cl; [tex]\( 4 H_2O \)[/tex] have 8 H, 4 O.
- Balance check:
- H: 6 + 10 = 8 + 8 (14 ≠ 16)
- P: 2 = 2
- Cl: 10 = 10
- O: 8 = 8
- This case is properly balanced for all elements.
- Case 3: [tex]\( 2 H_3PO_4 + 5 HCl \rightarrow 2 PCl_5 + 3 H_2O \)[/tex]
- Reactants: [tex]\( 2 H_3PO_4 \)[/tex] have 6 H, 2 P, 8 O; [tex]\( 5 HCl \)[/tex] have 5 H, 5 Cl.
- Products: [tex]\( 2 PCl_5 \)[/tex] have 2 P, 10 Cl; [tex]\( 3 H_2O \)[/tex] have 6 H, 3 O.
- Balance check:
- H: 6 + 5 ≠ 6 (11 ≠ 6)
- P: 2 = 2
- Cl: 5 ≠ 10
- O: 8 ≠ 3 (not balanced)
- Case 4: [tex]\( H_3PO_4 + 5 HCl \rightarrow PCl_5 + H_2O \)[/tex]
- Reactants: [tex]\( H_3PO_4 \)[/tex] has 3 H, 1 P, 4 O; [tex]\( 5 HCl \)[/tex] have 5 H, 5 Cl.
- Products: [tex]\( PCl_5 \)[/tex] has 1 P, 5 Cl; [tex]\( H_2O \)[/tex] has 2 H, 1 O.
- Balance check:
- H: 3 + 5 ≠ 2 (8 ≠ 2)
- P: 1 = 1
- Cl: 5 = 5
- O: 4 ≠ 1 (not balanced)
Given the analysis, the balanced chemical equation is:
[tex]\[
2 H_3PO_4 + 10 HCl \rightarrow 2 PCl_5 + 4 H_2O
\][/tex]
This equation ensures that the number of atoms for each element is equal on both sides of the reaction.
