Question

The first-order reaction A--->B is carried out in a tubular reactor in which the volumetric flow rate is constant. deduce an equation that relates the volume of the reactor with the input and output concentrations of A, the velocity constant k and the volumetric flow rate. determine the volume of the reactor necessary to reduce the output concentration to 1% of the input concentration, when the volumetric flow rate is 10 dm ^ 3 / min and the specific reaction rate constant, k is 0.23 min ^ -1

Answer 1

INPUT OF A - OUTPUT OF A + GENERATION OF A - CONSUMPTION OF A = ACCUMULATION OF A

............. Eq1

At steady State, Accumulation of A = 0

Differentiate the eq1, we get

The conversion of A

Integrate the above equation

.......... Eq2

For first order reaction

-r_A = k C_A

In terms of conversion

-r_A = k C_A0 (1 - X)

Molar flow rate F_A0 = C_A0 * v₀

v₀ = volumetric flow rate

From eq2

V = C_A0 * v₀dX/[k C_A0 (1 - X)]

V = (v₀/k) dX/(1 - X)