Addition of inert gas at constant pressure favours forward reaction in the case of

${\mathrm{PCl}}_5\left(\mathrm{g}\right)\stackrel{ }{\rightleftharpoons }{\mathrm{PCl}}_3\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right),\mathrm{\Delta n} >0 ;$ 

Addition of inert gas at constant pressure favours reaction involving increase in the number of gaseous moles.

This phenomenon can be explained using Le Chatelier’s Principle, which states that a system at equilibrium will adjust to counteract any changes imposed on it.

When an inert gas is introduced at constant pressure, the total volume of the system increases to maintain the same pressure. This causes the partial pressures of the reacting gases to decrease. Since equilibrium is dependent on the ratio of partial pressures or concentrations of the reactants and products, the system shifts in the direction that compensates for this change.

In reactions where there is an increase in the number of gaseous moles on the product side, the shift occurs toward the products. This is because the reaction attempts to restore equilibrium by producing more gas molecules, thus increasing the total pressure. 

It’s important to note that the addition of an inert gas does not directly participate in the chemical reaction or alter the equilibrium constant (K). Instead, it changes the conditions under which equilibrium is established, influencing the direction of the shift in reactions involving gases.