To balance the given chemical reaction, let's follow these steps systematically:
The given reaction is:
[tex]\[ \text{TiCl}_4 + \text{H}_2\text{O} \longrightarrow \text{TiO}_2 + \text{HCl} \][/tex]
1. Identify the elements in the reaction:
- Titanium (Ti)
- Chlorine (Cl)
- Hydrogen (H)
- Oxygen (O)
2. Write down the number of atoms of each element on both sides of the reaction:
- Reactants: TiCl₄ + H₂O
- Titanium (Ti): 1 in TiCl₄
- Chlorine (Cl): 4 in TiCl₄
- Hydrogen (H): 2 in H₂O
- Oxygen (O): 1 in H₂O
- Products: TiO₂ + HCl
- Titanium (Ti): 1 in TiO₂
- Chlorine (Cl): 1 in HCl
- Hydrogen (H): 1 in HCl
- Oxygen (O): 2 in TiO₂
3. Balance the elements one by one:
- Titanium: There is 1 Titanium atom on both sides. No need to change anything here.
- Oxygen: There are 2 Oxygen atoms in TiO₂ on the product side and only 1 Oxygen atom in H₂O on the reactant side. So, to balance the Oxygen atoms, we need 2 H₂O molecules:
[tex]\[ \text{TiCl}_4 + 2\text{H}_2\text{O} \longrightarrow \text{TiO}_2 + \text{HCl} \][/tex]
- Hydrogen: Now the reactant side has 4 Hydrogen atoms (since we have 2 H₂O molecules). The product side has 1 Hydrogen atom in HCl. Therefore, to balance Hydrogen, we need 4 molecules of HCl:
[tex]\[ \text{TiCl}_4 + 2\text{H}_2\text{O} \longrightarrow \text{TiO}_2 + 4\text{HCl} \][/tex]
- Chlorine: Now there are 4 Chlorine atoms on the product side in 4 HCl molecules, and 4 Chlorine atoms on the reactant side in TiCl₄. Chlorine is balanced.
4. Combine the balance equation:
The balanced equation is:
[tex]\[ \text{TiCl}_4 + 2\text{H}_2\text{O} \longrightarrow \text{TiO}_2 + 4\text{HCl} \][/tex]
5. Sum the coefficients:
- Coefficient of TiCl₄ is 1
- Coefficient of H₂O is 2
- Coefficient of TiO₂ is 1
- Coefficient of HCl is 4
The sum of the coefficients is:
[tex]\[ 1 + 2 + 1 + 4 = 8 \][/tex]
So, the answer is 8.
