To determine if the mixture is at equilibrium, we need to examine the given reaction and the stoichiometry involved:
[tex]\[ 2 \text{NOCl} (g) \rightleftharpoons 2 \text{NO} (g) + \text{Cl}_2 (g) \][/tex]
1. Stoichiometric Ratios:
- According to the balanced chemical equation, for every 2 moles of NOCl that react, the reaction produces:
- 2 moles of NO,
- 1 mole of Cl₂.
- Therefore, the total moles of products produced are:
[tex]\[ 2 \, \text{moles of NO} + 1 \, \text{mole of Cl}_2 = 3 \, \text{moles of products} \][/tex]
2. Given Data:
- We are given that 2 moles of NOCl react.
- The reaction produces 3 moles of products (2 moles NO and 1 mole Cl₂).
3. Checking the Ratios:
- We need to check if the ratio of moles of reactants (NOCl) to the total moles of products matches the stoichiometric ratio provided by the reaction.
- The ratio of moles of NOCl reacted to the total moles of products is:
[tex]\[
\frac{\text{moles of NOCl reacted}}{\text{total moles of products}} = \frac{2}{3}
\][/tex]
- Since the reaction indicates that 2 moles of NOCl produce 3 moles of products, this ratio of [tex]\( \frac{2}{3} \)[/tex] is indeed what we expect based on the stoichiometry.
4. Conclusion:
- As the ratio given by the reaction matches the calculated ratio ([tex]\( \frac{2}{3} \)[/tex]), this suggests the system is at equilibrium. This is because the stoichiometry of the reaction is being exactly followed, indicating no net change in the concentrations of reactants and products over time.
Therefore, the mixture is at equilibrium because the ratio of the moles of NOCl reacting to the moles of products formed adheres to the stoichiometric requirements of the balanced equation.
