To analyze how the system responds to a change in volume, we need to apply Le Chatelier's Principle. This principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.
Here is the step-by-step breakdown:
1. Identify the number of moles of gas on each side of the equilibrium:
The chemical equation is:
[tex]\[
PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)
\][/tex]
- On the left side (reactants), we have 1 mole of [tex]\( PCl_5 \)[/tex].
- On the right side (products), we have 1 mole of [tex]\( PCl_3 \)[/tex] and 1 mole of [tex]\( Cl_2 \)[/tex]. Therefore, there are a total of 2 moles of gas on the right side.
2. Consider the initial conditions:
- The system is initially at equilibrium in a 2.0 L container.
3. Determine the change in conditions:
- The volume of the container is reduced from 2.0 L to 1.0 L.
4. Analyze the effect of the volume change on the system:
- Reducing the volume of the container increases the pressure of the system.
- According to Le Chatelier's Principle, the system will shift to the side with fewer moles of gas in order to reduce the pressure.
5. Compare the moles of gas on each side:
- Left side (reactants): 1 mole of gas ([tex]\( PCl_5 \)[/tex])
- Right side (products): 2 moles of gas ([tex]\( PCl_3 \)[/tex] and [tex]\( Cl_2 \)[/tex])
6. Predict the direction of the shift:
- Since there are fewer moles of gas on the left side (1 mole) compared to the right side (2 moles), the system will shift towards the left (reactants) in order to produce fewer moles of gas and thereby reduce the pressure.
In conclusion, when the container is shrunk to 1.0 L, the system responds by shifting to the left (towards the reactants) to produce fewer moles of gas, thus decreasing the pressure in the new, smaller volume.
