To determine the balanced chemical equation for the reaction between phosphoric acid (H[tex]\(_3\)[/tex]PO[tex]\(_4\)[/tex]) and hydrochloric acid (HCl) to produce phosphorus pentachloride (PCl[tex]\(_5\)[/tex]) and water (H[tex]\(_2\)[/tex]O), follow these steps:
1. Write the unbalanced equation:
[tex]\( H_3PO_4 + HCl \rightarrow PCl_5 + H_2O \)[/tex]
2. Identify the number of atoms of each element in the reactants and products:
- Reactants:
- H (hydrogen): 3 (from H[tex]\(_3\)[/tex]PO[tex]\(_4\)[/tex]) + 1 (from HCl) = 4 atoms
- P (phosphorus): 1 (from H[tex]\(_3\)[/tex]PO[tex]\(_4\)[/tex])
- O (oxygen): 4 (from H[tex]\(_3\)[/tex]PO[tex]\(_4\)[/tex])
- Cl (chlorine): 1 (from HCl)
- Products:
- P (phosphorus): 1 (from PCl[tex]\(_5\)[/tex])
- Cl (chlorine): 5 (from PCl[tex]\(_5\)[/tex])
- H (hydrogen): 2 (from H[tex]\(_2\)[/tex]O)
- O (oxygen): 1 (from H[tex]\(_2\)[/tex]O)
3. Balance the atoms one element at a time:
- To balance the chlorine (Cl) atoms, we need 5 HCl molecules:
[tex]\( H_3PO_4 + 5 HCl \rightarrow PCl_5 + H_2O \)[/tex]
- Check the balancing of other elements:
- P (phosphorus): 1 on both sides
- Cl (chlorine): 5 on both sides
- H (hydrogen): 3 (from H[tex]\(_3\)[/tex]PO[tex]\(_4\)[/tex]) + 5 (from 5 HCl) = 8 on the reactants side, and 2 on the products side (H[tex]\(_2\)[/tex]O).
- O (oxygen): 4 on the reactants side, and 1 on the products side.
- The hydrogen and oxygen atoms are not balanced yet. To adjust this, one should explore the given answer options.
Upon reviewing the given answer options and confirming the element counts from each option:
- Option (a) has 2H[tex]\(_2\)[/tex]O which provides 2 hydrogen atoms, which is not enough.
- Option (b) has 4 H[tex]\(_2\)[/tex]O (provides 8 hydrogen atoms), but it conflicts with the initially simplest identified balancing through required steps.
- Option (d) miscalculates required balance verification.
- Option (c):
The correct balanced equation ensuring both conservations:
[tex]\[ H_3PO_4 + 5 HCl \rightarrow PCl_5 + 4 H_2O \][/tex]
So the balanced chemical equation is:
[tex]\[ H_3PO_4 + 5 HCl \rightarrow PCl_5 + 4 H_2O \][/tex]
