A continuous stirred tank reactor is used to convert A to R. How will the space time of the reactor change if the diameter of the reactor is increased by 30%? Assume all other conditions remain constant.

A. $ T_2 = 1.69 T_1 $
B. $ T_1 = 1.69 T_2 $
C. Space time stays the same
D. $ T_2 = 0.59 T_1 $

The space time in a Continuous Stirred Tank Reactor (CSTR) will increase if the diameter of the reactor is increased by 30%, assuming all other conditions remain constant. This is due to the increased volume that results from the larger diameter. Therefore, the reactants will spend more time in the reactor.

Explanation:

In the context of a Continuous Stirred Tank Reactor (CSTR), the space time (τ) is defined as the reactor volume (V) divided by the volumetric flow rate (Q), expressed mathematically as τ = V/Q. If the diameter of the reactor is increased by 30%, the volume of the reactor, which is proportional to the cube of the diameter, will increase by approximately 120%. Therefore, the space time of the reactor will also increase assuming the flow rate and other conditions remain constant. It signifies that the reactants will spend more time in the reactor, allowing for more conversion of A to R. Visually, if we assume T₁ is the original space time, then after the diameter increase, the new space time T₂ will be approximately 2.2 times T₁, i.e., T₂ ≈ 2.2 T₁.

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