To determine how many moles of [tex]\( C_6H_{12}O_6 \)[/tex] (glucose) are consumed when 6.0 moles of [tex]\( O_2 \)[/tex] (oxygen) are used, you can follow these steps using the balanced chemical equation:
[tex]\[
C_6H_{12}O_6 + 6 O_2 \rightarrow 6 CO_2 + 6 H_2O
\][/tex]
1. Understand the stoichiometry of the reaction:
- The balanced equation indicates that 1 mole of glucose [tex]\( (C_6H_{12}O_6) \)[/tex] reacts with 6 moles of oxygen [tex]\( (O_2) \)[/tex].
2. Set up the stoichiometric relationship:
- According to the equation, the ratio of moles of glucose to moles of oxygen is 1:6.
- This means that 1 mole of glucose requires 6 moles of oxygen.
3. Determine how many moles of glucose are consumed using the given moles of oxygen:
- You are given that 6.0 moles of [tex]\( O_2 \)[/tex] are used.
- Using the stoichiometric ratio (1 mole of [tex]\( C_6H_{12}O_6 \)[/tex] per 6 moles of [tex]\( O_2 \)[/tex]), you can set up the relationship:
[tex]\[
\text{moles of glucose} = \frac{\text{moles of oxygen}}{6}
\][/tex]
4. Calculate the moles of glucose consumed:
- Substitute the given amount of moles of oxygen:
[tex]\[
\text{moles of glucose} = \frac{6.0 \text{ moles } O_2}{6} = 1.0 \text{ mole }
\][/tex]
Therefore, 1.0 mole of glucose [tex]\( (C_6H_{12}O_6) \)[/tex] is consumed when 6.0 moles of [tex]\( O_2 \)[/tex] are used.
