Alright, let's balance the chemical equation step-by-step:
The unbalanced equation is:
[tex]\[ \square \, \text{SiO}_2 + \square \, \text{CaC}_2 \rightarrow \square \, \text{Si} + \square \, \text{CaO} + \square \, \text{CO}_2 \][/tex]
1. Balance the silicon (Si) atoms:
- We have one Si atom in SiO\(_2\) on the left side.
- We have one Si atom on the right side.
- Therefore, the coefficient for both SiO\(_2\) and Si is 1.
2. Balance the calcium (Ca) atoms:
- We have one Ca atom in CaC\(_2\) on the left side.
- We have one Ca atom in CaO on the right side.
- Therefore, the coefficient for both CaC\(_2\) and CaO is 1.
3. Balance the carbon (C) atoms:
- We have two C atoms in CaC\(_2\) on the left side.
- We have one C atom in CO\(_2\) on the right side.
- Therefore, we need two CO\(_2\) molecules on the right side to balance the carbon atoms. The coefficient for CO\(_2\) is 2.
4. Balance the oxygen (O) atoms:
- We have two O atoms in SiO\(_2\) on the left side.
- We have a total of four O atoms on the right side (one in CaO and three in the 2 CO\(_2\) molecules).
- Since the counts of O atoms are already balanced with the given coefficients, no further adjustment is required.
So, the balanced equation is:
[tex]\[ 1 \, \text{SiO}_2 + 1 \, \text{CaC}_2 \rightarrow 1 \, \text{Si} + 1 \, \text{CaO} + 2 \, \text{CO}_2 \][/tex]
The coefficients to balance the equation are:
[tex]\[ \boxed{1} \, \text{SiO}_2 + \boxed{1} \, \text{CaC}_2 \rightarrow \boxed{1} \, \text{Si} + \boxed{1} \, \text{CaO} + \boxed{2} \, \text{CO}_2 \][/tex]
