To analyze what happens when more [tex]\( O_2 \)[/tex] is added to the reaction at equilibrium:
[tex]\[ 2 H_2 + O_2 \rightleftharpoons 2 H_2O \][/tex]
we need to apply Le Chatelier's Principle. This principle states that if a change is imposed on a system at equilibrium, the system will adjust itself to counteract that change and re-establish equilibrium.
### Step-by-Step Analysis:
1. Addition of [tex]\( O_2 \)[/tex] to the System:
- The addition of [tex]\( O_2 \)[/tex] increases the concentration of one of the reactants.
2. Shift in Equilibrium:
- According to Le Chatelier's Principle, the system will try to oppose the increase in [tex]\( O_2 \)[/tex] concentration by shifting the equilibrium to the direction where [tex]\( O_2 \)[/tex] is consumed. This is the direction of the forward reaction (producing [tex]\( H_2O \)[/tex]).
- Therefore, the equilibrium will shift to favor the production of [tex]\( H_2O \)[/tex].
3. Reaction Rates:
- As the system shifts to favor the forward reaction, the rate at which [tex]\( H_2 \)[/tex] and [tex]\( O_2 \)[/tex] react to form [tex]\( H_2O \)[/tex] will increase. This increased reaction rate helps to consume the added [tex]\( O_2 \)[/tex] and produce more [tex]\( H_2O \)[/tex].
### Conclusion:
Based on the principles above, we can identify the two events that will happen if more [tex]\( O_2 \)[/tex] is added to this reaction at equilibrium:
1. The equilibrium will shift to favor the production of [tex]\( H_2O \)[/tex].
2. The rate at which [tex]\( H_2 \)[/tex] and [tex]\( O_2 \)[/tex] react will increase.
These correspond to options:
- [tex]\( \mathbf{B} \)[/tex] The equilibrium will shift to favor the production of [tex]\( H_2O \)[/tex].
- [tex]\( \mathbf{D} \)[/tex] The rate at which [tex]\( H_2 \)[/tex] and [tex]\( O_2 \)[/tex] react will increase.
Final Answer: [tex]\( B \)[/tex] and [tex]\( D \)[/tex]
