For the equilibrium
`PCl_5(g)hArr PCl_3(g) +Cl_2`, the value of the equilibrium constant decreases on additions of `Cl_2 ` gas.

Answer

To analyze the statement regarding the equilibrium of the reaction:

\[ \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \]

and the claim that the equilibrium constant \( K_c \) decreases upon the addition of \( \text{Cl}_2 \) gas, we will follow these steps:

### Step 1: Understand the Concept of Equilibrium Constant
The equilibrium constant \( K_c \) for a reaction at a given temperature is defined by the expression:

\[ K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]} \]

where \([\text{PCl}_3]\), \([\text{Cl}_2]\), and \([\text{PCl}_5]\) are the molar concentrations of the respective species at equilibrium.

### Step 2: Analyze the Effect of Adding \( \text{Cl}_2 \)
According to Le Chatelier's principle, if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust to counteract that change and restore a new equilibrium.

- When \( \text{Cl}_2 \) is added, the concentration of \( \text{Cl}_2 \) increases.
- The system will respond by shifting the equilibrium to the left to reduce the concentration of \( \text{Cl}_2 \), producing more \( \text{PCl}_5 \).

### Step 3: Determine the Effect on \( K_c \)
It is crucial to note that the equilibrium constant \( K_c \) is only affected by changes in temperature. The addition of \( \text{Cl}_2 \) does not change the temperature of the system.

- Therefore, while the concentrations of the reactants and products may change momentarily, the value of \( K_c \) remains constant at a given temperature.

### Step 4: Conclusion
The statement that the equilibrium constant \( K_c \) decreases upon the addition of \( \text{Cl}_2 \) is **false**. The equilibrium constant is not affected by changes in concentration or the addition of reactants or products; it is only affected by temperature.

### Summary
- The equilibrium constant \( K_c \) is defined by the concentrations of the species at equilibrium.
- Adding \( \text{Cl}_2 \) shifts the equilibrium to the left but does not change \( K_c \).
- The value of \( K_c \) is only influenced by temperature.