To determine the ratio between the energy released and the moles of oxygen involved in the given chemical reaction, let's break the problem down into a series of logical steps.
1. Chemical Reaction Analysis:
The balanced chemical equation provided is:
[tex]\[
\text{C}_2\text{H}_5\text{OH} + 2 \text{O}_2 \rightarrow 2 \text{CO}_2 + 3 \text{H}_2\text{O} + 1367 \text{ kJ}
\][/tex]
2. Energy Released:
From the equation, we see that 1367 kJ of energy is released for the entire reaction.
3. Moles of Oxygen:
The equation tells us that 2 moles of O[tex]\(_2\)[/tex] are needed for the combustion of ethanol (C[tex]\(_2\)[/tex]H[tex]\(_5\)[/tex]OH).
4. Energy per Mole of Oxygen:
To find the ratio of energy per mole of oxygen involved, we need to divide the total energy released by the number of moles of O[tex]\(_2\)[/tex].
[tex]\[
\text{Energy per mole of O}_2 = \frac{\text{Total Energy Released}}{\text{Moles of O}_2}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Energy per mole of O}_2 = \frac{1367 \text{ kJ}}{2 \text{ moles}}
\][/tex]
5. Final Calculation:
Performing the division gives:
[tex]\[
\text{Energy per mole of O}_2 = 683.5 \text{ kJ/mol}
\][/tex]
Thus, the ratio between the energy released and the moles of oxygen involved in the reaction is 683.5 kJ per mole of O[tex]\(_2\)[/tex].
