Correct Answer:

(a) A & R are both true and A is due to R

Explanation:

In filtration processes, particularly in plate and frame filters, the filtrate flow rate decreases over time when operated under constant pressure. This phenomenon is primarily due to the buildup of a filter cake on the filter membrane. Let’s break down both the Assertion A and the Reason R to understand why the correct answer is (a).

Assertion A: “In a plate & frame filter operated under constant pressure, the filtrate flow rate declines with time.”

• This is true. In a plate and frame filter, as the filtration process progresses, the particles that are being filtered accumulate on the membrane, forming a filter cake. Over time, this filter cake obstructs the flow of the liquid through the membrane, causing the filtrate flow rate to decline. The filter cake increases resistance to filtration, which reduces the flow of liquid through the system.

Reason R: “In a plate & frame filter operated under constant pressure, the filtrate cake builds up on the filter membrane.”

• This is also true. As the filtration process continues, particles in the feed liquid accumulate on the filter membrane, forming a filter cake. The buildup of the cake is a natural consequence of the filtration process, and it leads to increased resistance to flow. The cake’s resistance causes the flow rate to decline, as stated in Assertion A.

Why is the answer (a) correct?

• The decline in filtrate flow rate (Assertion A) is due to the formation of the filter cake (Reason R). The increasing resistance from the cake impedes the movement of the filtrate, thus causing the flow rate to reduce over time when pressure is kept constant. Hence, Assertion A is correct because it directly follows from Reason R.

Why are other options incorrect?

• (b) A & R are both true but A is NOT due to R:
  This option is incorrect because Assertion A is directly caused by Reason R. The buildup of the filter cake is the primary reason for the decline in flow rate, so Assertion A is definitely due to Reason R.

• (c) A is false but R is true:
  This option is incorrect because Assertion A is actually true. The flow rate does decline with time due to the formation of the filter cake, so Assertion A is true.

• (d) A is true but R is false:
  This option is incorrect because Reason R is also true. The formation of the filter cake is indeed a key factor in the decline of the filtrate flow rate.

Conclusion

In a plate & frame filter operating under constant pressure, the filtrate flow rate declines over time due to the buildup of the filter cake on the membrane. This is why Assertion A is true, and it is directly caused by Reason R. The correct answer is therefore (a) A & R are both true and A is due to R.