To balance the chemical equation [tex]\( \square \: \text{SiO}_2 + \square \: \text{CaC}_2 \rightarrow \square \: \text{Si} + \square \: \text{CaO} + \square \: \text{CO}_2 \)[/tex], we need to ensure that the number of atoms of each element on the reactants side is equal to the number of atoms of the same element on the products side.
1. Balance Silicon (Si):
- There is 1 Si atom in [tex]\( \text{SiO}_2 \)[/tex].
- There is 1 Si atom on the product side.
- Si is already balanced.
2. Balance Oxygen (O):
- There are 2 O atoms in [tex]\( \text{SiO}_2 \)[/tex].
- There is 1 O atom in [tex]\( \text{CaO} \)[/tex] and 2 O atoms in [tex]\( \text{CO}_2 \)[/tex] on the product side.
- To have 2 O atoms on both sides, we need an additional O from [tex]\( \text{CaO} \)[/tex].
3. Balance Calcium (Ca):
- There is 1 Ca atom in [tex]\( \text{CaC}_2 \)[/tex].
- There is 1 Ca atom in [tex]\( \text{CaO} \)[/tex] on the product side.
- Ca is already balanced.
4. Balance Carbon (C):
- There are 2 C atoms in [tex]\( \text{CaC}_2 \)[/tex].
- There is 1 C atom in [tex]\( \text{CO}_2 \)[/tex] on the product side.
- We need 2 molecules of [tex]\( \text{CO}_2 \)[/tex] to balance Carbon.
After adjusting the coefficients, we check the balancing.
The balanced equation is:
[tex]\[ \text{SiO}_2 + \text{CaC}_2 \rightarrow \text{Si} + \text{CaO} + \text{CO}_2 \][/tex]
Now we ensure all elements are correctly balanced:
- Si: 1 Si atom on both sides.
- O: 2 O atoms from [tex]\( \text{SiO}_2 \)[/tex] on reactants side, and 1 O atom from [tex]\( \text{CaO} \)[/tex] and 2 O atoms from [tex]\( \text{CO}_2 \)[/tex] on products side (3 O total).
- Ca: 1 Ca atom on both sides.
- C: 2 C atoms on both sides.
The coefficients in the balanced equation are:
[tex]\[ 1 \: \text{SiO}_2 + 1 \: \text{CaC}_2 \rightarrow 1 \: \text{Si} + 1 \: \text{CaO} + 2 \: \text{CO}_2 \][/tex]
Thus, the balanced chemical equation is:
[tex]\[ 1 \: \text{SiO}_2 + 1 \: \text{CaC}_2 \rightarrow 1 \: \text{Si} + 1 \: \text{CaO} + 2 \: \text{CO}_2 \][/tex]
Therefore:
- First box: 1
- Second box: 1
- Third box: 1
- Fourth box: 1
- Fifth box: 2
