In the folowing reactions, the system will shift towards the forward reaction by adding inert gas at constant pressure?
`PCl_5->PCl_3+Cl_2`

Explanation

To determine whether the system will shift towards the forward reaction by adding an inert gas at constant pressure for the reaction \( PCl_5 \rightleftharpoons PCl_3 + Cl_2 \), we can follow these steps:

### Step 1: Identify the number of moles of gas on both sides of the reaction.
- **Reactants:** \( PCl_5 \) has 1 mole of gas.
- **Products:** \( PCl_3 + Cl_2 \) has 2 moles of gas (1 mole of \( PCl_3 \) and 1 mole of \( Cl_2 \)).

### Step 2: Calculate the change in the number of moles of gas (\( \Delta N_g \)).
- \( \Delta N_g = \text{Moles of products} - \text{Moles of reactants} \)
- \( \Delta N_g = 2 - 1 = 1 \)

### Step 3: Understand the effect of adding an inert gas at constant pressure.
- When an inert gas is added to a system at constant pressure, the total pressure increases, but the partial pressures of the reacting gases remain unchanged. The equilibrium will shift towards the side with more moles of gas.

### Step 4: Determine the direction of the shift in equilibrium.
- Since \( \Delta N_g > 0 \) (1 in this case), the equilibrium will shift towards the side with more moles of gas, which is the forward direction (products).

### Conclusion
- Therefore, by adding an inert gas at constant pressure, the equilibrium for the reaction \( PCl_5 \rightleftharpoons PCl_3 + Cl_2 \) will shift towards the forward reaction.

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