To balance the chemical equation [tex]\( \square \, SiO_2 + \square \, CaC_2 \rightarrow \square \, Si + \square \, CaO + \square \, CO_2 \)[/tex], we need to ensure that the number of atoms of each element on the reactant side equals the number of atoms of each element on the product side. Let's break it down step-by-step:
1. Identify the elements involved:
- Silicon (Si)
- Oxygen (O)
- Calcium (Ca)
- Carbon (C)
2. Write the initial, unbalanced equation:
[tex]\[ SiO_2 + CaC_2 \rightarrow Si + CaO + CO_2 \][/tex]
3. Count the number of atoms of each element on both sides of the equation:
- Reactants: [tex]\( 1 \, Si \)[/tex], [tex]\( 2 \, O \)[/tex], [tex]\( 1 \, Ca \)[/tex], [tex]\( 2 \, C \)[/tex]
- Products: [tex]\( 1 \, Si \)[/tex], [tex]\( 2 \, O \)[/tex], [tex]\( 1 \, Ca \)[/tex], [tex]\( 1 \, C \)[/tex]
4. Balance the carbon atoms first.
To balance the carbon atoms, we need to have the same number of carbon atoms on both sides of the equation. Since there are 2 carbon atoms on the reactant side (from [tex]\( CaC_2 \)[/tex]) and only 1 carbon atom on the product side (from [tex]\( CO_2 \)[/tex]), we need to multiply [tex]\( CO_2 \)[/tex] by 2.
New equation:
[tex]\[ SiO_2 + CaC_2 \rightarrow Si + CaO + 2 \, CO_2 \][/tex]
5. Recount the atoms:
- Reactants: [tex]\( 1 \, Si \)[/tex], [tex]\( 2 \( O \)[/tex], [tex]\( 1 \, Ca \)[/tex], [tex]\( 2 \, C \)[/tex]
- Products: [tex]\( 1 \, Si \)[/tex], [tex]\( 4 \, O \)[/tex], [tex]\( 1 \, Ca \)[/tex], [tex]\( 2 \, C \)[/tex]
6. Balance the calcium and silicon atoms next.
Since we have 1 calcium atom on both sides already balanced and 1 silicon atom on both sides, these elements are balanced.
7. Now balance the oxygen atoms.
On the left side, we have 2 oxygen atoms from [tex]\( SiO_2 \)[/tex] but on the right side, we currently have a total of 3 oxygen atoms (1 in [tex]\( CaO \)[/tex] and 2x2 in [tex]\( CO_2 \)[/tex]). Therefore, by multiplying [tex]\( SiO_2 \)[/tex] by 2, [tex]\( CaO\)[/tex] by 2, and [tex]\( \( CaC_2 \)[/tex] by 2, we can ensure the balance of all atoms.
Final balanced equation:
[tex]\[1 SiO_2 + 2 CaC_2 \rightarrow 1 Si + 2 CaO + 1 CO_2 \][/tex]
So, filling in the boxes:
[tex]\[ 1 \, SiO_2 + 2 \, CaC_2 \rightarrow 1 \, Si + 2 \, CaO + 1 \, CO_2 \][/tex]
