Question

Design equation for varying volume system is ______

(a) t = \(\int_0^{XA} \frac{dXA}{-rA εA} \)

(b) t = \(\int_0^{XA} \frac{dXA}{CA0} \)

(c) t = \(\int_0^{XA} \frac{dXA}{NA0} \)

(d) t = CA0 \(\int_0^{XA} \frac{dXA}{-rA(1+XA εA)} \)

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I'd like to ask this question from Batch Reactor Design Equations topic in portion Ideal Reactors for a Single Reaction, Conversion and Reactor Sizing of Chemical Reaction Engineering

Answer 1

Correct answer is (d) t = CA0 \(\int_0^{XA} \frac{dXA}{-rA(1+XA εA)} \)

Explanation: The varying volume in a batch reactor is given as V = V0 (1+XA εA) where εA is called the fractional volume change of the system. The above equation is substituted in the general batch reactor design equation.