In the following system,
$$PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$$ at equilibrium, upon addition of xenon gas at constant T & p, the concentration of

The equilibrium in the gaseous phase is
$$PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$$

For this reaction the equilibrium constant (in terms of pressure) is
$$K_p = \frac{P_{PCl_3}\,P_{Cl_2}}{P_{PCl_5}}$$  $$-(1)$$
At a fixed temperature $$K_p$$ has a fixed value.

Step 1 : What happens immediately after adding xenon (inert gas)?
The total pressure is kept constant but the total amount of gas (moles) increases. Because $$P_i = y_i\,p$$ (where $$y_i$$ is the mole-fraction and $$p$$ is the constant total pressure), every $$y_i$$ decreases when inert gas is added. Hence the partial pressures $$P_{PCl_5},\;P_{PCl_3},\;P_{Cl_2}$$ all drop at that instant, so the mixture is no longer at equilibrium.

Step 2 : Direction of the shift
In equation $$(1)$$, the numerator involves the product gases while the denominator involves the reactant gas. After dilution, the numerator $$P_{PCl_3}\,P_{Cl_2}$$ decreases more than the denominator $$P_{PCl_5}$$, making the ratio smaller than the required constant value of $$K_p$$.
To raise this ratio back to $$K_p$$, the reaction must produce more product gases, i.e. it must shift to the right. (Le-Châtelier’s principle also predicts this: at constant $$T$$ and $$p$$, increasing volume favours the side with the larger number of moles; here $$\Delta n = +1$$.)

Step 3 : Final concentrations
Because the equilibrium has shifted to the right:
• extra $$PCl_3$$ and $$Cl_2$$ are formed, so their amounts increase.
• some $$PCl_5$$ is consumed, so its amount decreases.
Although the volume of the system is larger than before, the increase in moles of $$PCl_3$$ is sufficient to make its final concentration higher than the original equilibrium concentration. (On the other hand, the concentration of $$PCl_5$$ definitely falls, and the behaviour of $$Cl_2$$ depends on the initial composition; it is not guaranteed to decrease universally.)

Step 4 : Choosing the correct option
The only statement that must be true after the system re-establishes equilibrium is: “$$PCl_3$$ will increase”.

Hence, the correct choice is Option D.