Let's balance the chemical equation:
[tex]\[ \square \, \text{CO}_2 + \square \, \text{H}_2\text{O} \rightarrow \square \, \text{C}_6\text{H}_{12}\text{O}_6 + \square \, \text{O}_2 \][/tex]
1. Step 1: Start with carbon (C):
- On the left side, we have CO\(_2\). The coefficient for CO\(_2\) is currently unknown.
- On the right side, we have C\(_6\)H\(_{12}\)O\(_6\), which contains 6 carbon atoms.
Therefore, the coefficient for CO\(_2\) must be 6 to balance the carbons:
[tex]\[ 6 \, \text{CO}_2 + \quad \text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + \quad \text{O}_2 \][/tex]
2. Step 2: Next, balance hydrogen (H):
- On the left side, we have H\(_2\)O. The coefficient for H\(_2\)O is currently unknown.
- On the right side, we have C\(_6\)H\(_{12}\)O\(_6\), which contains 12 hydrogen atoms.
Therefore, the coefficient for H\(_2\)O must be 6 to balance the hydrogens:
[tex]\[ 6 \, \text{CO}_2 + 6 \, \text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + \quad \text{O}_2 \][/tex]
3. Step 3: Finally, balance oxygen (O):
- On the left side, we have 6 CO\(_2\) which gives 6 \(\times\) 2 = 12 O atoms and 6 H\(_2\)O which gives 6 \(\times\) 1 = 6 O atoms. This totals 12 + 6 = 18 oxygen atoms.
- On the right side, we have C\(_6\)H\(_{12}\)O\(_6\) which contains 6 oxygen atoms and O\(_2\).
Therefore, the coefficient for O\(_2\) must be 6 to balance the oxygens:
[tex]\[ 6 \, \text{CO}_2 + 6 \, \text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + 6 \, \text{O}_2 \][/tex]
So, all the coefficients are balanced correctly:
[tex]\[ \boxed{6} \, \text{CO}_2 + \boxed{6} \, \text{H}_2\text{O} \rightarrow \boxed{1} \, \text{C}_6\text{H}_{12}\text{O}_6 + \boxed{6} \, \text{O}_2 \][/tex]
Remember, a coefficient of "1" is understood and we choose the option "blank" if the coefficient is "1".
