To determine which stress will shift the equilibrium system to the left for the reaction
[tex]\[ N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}, \][/tex]
we need to analyze the given options using Le Chatelier's Principle. Le Chatelier's Principle states that if an external stress is applied to a system at equilibrium, the system will adjust itself in such a way as to counteract that stress.
Let's go through each option one by one:
1. Adding more [tex]\( N_{2(g)} \)[/tex]:
- According to Le Chatelier's Principle, if we add more nitrogen gas ([tex]\( N_2 \)[/tex]), we are adding more reactants to the system. The equilibrium will shift to the right to produce more ammonia ([tex]\( NH_3 \)[/tex]) to counteract the change. Therefore, this action will not shift the equilibrium to the left.
2. Adding more [tex]\( NH_{3(g)} \)[/tex]:
- Adding more ammonia ([tex]\( NH_3 \)[/tex]) increases the concentration of the product. According to Le Chatelier's Principle, the system will respond by shifting the equilibrium to the left to reduce the concentration of ammonia by producing more reactants, [tex]\( N_2 \)[/tex] and [tex]\( H_2 \)[/tex]. Therefore, this action will shift the equilibrium to the left.
3. Reducing the volume of the container:
- Reducing the volume of the container will increase the pressure of the system. For gaseous reactions, the system will shift in the direction that has fewer moles of gas to counteract the increase in pressure. On the left side of the equation, we have 1 mole of [tex]\( N_2 \)[/tex] and 3 moles of [tex]\( H_2 \)[/tex], totaling 4 moles of gas. On the right side, we have 2 moles of [tex]\( NH_3 \)[/tex]. Since reducing the volume increases pressure and the system will shift to the side with fewer moles of gas, reducing the volume will shift the equilibrium towards the right (towards [tex]\( NH_3 \)[/tex]). Thus, this will not shift the equilibrium to the left.
4. Increasing the pressure of the system:
- Similarly, increasing the pressure of the system will cause the system to shift towards the side with fewer moles of gas to relieve the increased pressure. As explained above, this will shift the equilibrium towards the right (towards [tex]\( NH_3 \)[/tex]), not the left.
Therefore, based on this analysis, the stress that will shift the equilibrium system to the left is:
- Adding more [tex]\(\text{NH}_3\)[/tex]
So, the correct answer is Adding more [tex]\( NH_3 \)[/tex].
