Certainly! Let's solve this step-by-step to determine if the given reaction is at equilibrium in the container.
### Given Information:
- Moles of [tex]\( O_3 \)[/tex]: 2 mol
- Moles of [tex]\( O_2 \)[/tex]: 2 mol
- Balanced chemical equation: [tex]\( 2 O_3 (g) \rightleftharpoons 3 O_2 (g) \)[/tex]
### Steps to Determine Equilibrium:
1. Understand the Mole Ratio:
According to the balanced chemical equation:
[tex]\[
2 O_3 (g) \rightleftharpoons 3 O_2 (g)
\][/tex]
This means 2 moles of ozone ([tex]\( O_3 \)[/tex]) produce 3 moles of oxygen ([tex]\( O_2 \)[/tex]).
2. Calculate the Expected Moles of [tex]\( O_2 \)[/tex]:
If 2 moles of [tex]\( O_3 \)[/tex] react, we use the ratio from the balanced equation to find the expected moles of [tex]\( O_2 \)[/tex]:
[tex]\[
\text{Ratio of } O_3 \text{ to } O_2 = \frac{3}{2}
\][/tex]
Hence,
[tex]\[
\text{Expected moles of } O_2 = 2 \text{ moles of } O_3 \times \frac{3}{2} = 3 \text{ moles}
\][/tex]
3. Compare the Expected Moles with Actual Moles:
The actual moles of [tex]\( O_2 \)[/tex] given are 2 moles.
[tex]\[
\text{Actual moles of } O_2 = 2 \text{ moles}
\][/tex]
4. Determine if Equilibrium Exists:
For equilibrium to exist, the actual moles of [tex]\( O_2 \)[/tex] should match the expected moles of [tex]\( O_2 \)[/tex]:
[tex]\[
3 \text{ moles (expected)} \neq 2 \text{ moles (actual)}
\][/tex]
Since the expected amount of [tex]\( O_2 \)[/tex] (3 moles) does not equal the given amount of [tex]\( O_2 \)[/tex] (2 moles), we conclude that the system is not at equilibrium.
### Conclusion:
No, equilibrium does not exist in the container because the expected moles of oxygen ([tex]\( O_2 \)[/tex]) do not match the given moles of oxygen. The balanced equation suggests that 2 moles of ozone should produce 3 moles of oxygen, but only 2 moles of oxygen are present.
