(A): The degree of decomposition of `PC1_(5)` is more at low pressures.
(R) : In a reversible reaction, on increasing the pressure the equilibrium shifts in the direction in which decrease in volume takes place.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that "the degree of decomposition of PCl5 is more at low pressures."

- The decomposition reaction of phosphorus pentachloride (PCl5) can be represented as:
\[ \text{PCl}_5 (g) \rightleftharpoons \text{PCl}_3 (g) + \text{Cl}_2 (g) \]
- In this reaction, 1 mole of PCl5 decomposes into 1 mole of PCl3 and 1 mole of Cl2, resulting in a total of 2 moles of gas on the product side.
- Therefore, the volume increases when PCl5 decomposes.

### Step 2: Understand the Effect of Pressure on Equilibrium
According to Le Chatelier's principle:
- When the pressure of a system at equilibrium is increased, the equilibrium shifts in the direction that decreases the total number of gas moles (or volume).
- Conversely, if the pressure is decreased, the equilibrium shifts towards the side with more gas moles (or volume).

### Step 3: Conclusion on the Assertion
- Since the decomposition of PCl5 results in an increase in the number of moles (from 1 mole to 2 moles), it follows that at low pressures, the equilibrium will favor the decomposition of PCl5.
- Thus, the assertion is true: "the degree of decomposition of PCl5 is more at low pressures."

### Step 4: Analyze the Reason
The reason states that "in a reversible reaction, on increasing the pressure, the equilibrium shifts in the direction in which decrease in volume takes place."

- This statement is also true. In the case of the PCl5 decomposition, increasing the pressure will shift the equilibrium to the left (towards PCl5), which has a smaller volume compared to the products.

### Step 5: Conclusion on the Reason
- The reason correctly explains the assertion, as it describes the principle that governs the behavior of the system under pressure changes.

### Final Conclusion
Both the assertion and the reason are true, and the reason is a correct explanation for the assertion.

### Answer:
Both assertion (A) and reason (R) are true, and R is the correct explanation for A.

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