To balance the chemical equation:
[tex]\[ \boxed{1} \ \text{SiO}_2 + \boxed{1} \ \text{CaC}_2 \rightarrow \boxed{1} \ \text{Si} + \boxed{1} \ \text{CaO} + \boxed{1} \ \text{CO}_2 \][/tex]
We assign coefficients to each compound in the reaction such that the number of atoms of each element is equal on both sides of the equation.
- For Silicon (Si): There is 1 Si atom on the left in SiO₂ and 1 Si atom on the right in Si. Therefore, the coefficient for SiO₂ and Si is 1.
- For Oxygen (O): There are 2 O atoms on the left in SiO₂ and a total of 2 O atoms on the right (1 in CaO and 2 in CO₂). Therefore, the coefficient for SiO₂ is 1 and for CaO and CO₂ are both 1.
- For Calcium (Ca): There is 1 Ca atom on the left in CaC₂ and 1 Ca atom on the right in CaO. Therefore, the coefficient for CaC₂ and CaO is 1.
- For Carbon (C): There are 2 C atoms on the left in CaC₂ and a total of 2 C atoms on the right (1 in CO₂). Therefore, the coefficient for CaC₂ is 1 and for CO₂ is also 1.
Thus, the balanced chemical equation is:
[tex]\[ 1 \ \text{SiO}_2 + 1 \ \text{CaC}_2 \rightarrow 1 \ \text{Si} + 1 \ \text{CaO} + 1 \ \text{CO}_2 \][/tex]
Or more simply:
[tex]\[ \boxed{1} \ \text{SiO}_2 + \boxed{1} \ \text{CaC}_2 \rightarrow \boxed{1} \ \text{Si} + \boxed{1} \ \text{CaO} + \boxed{1} \ \text{CO}_2 \][/tex]
