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Answer:
Explanation:
From the information above:
The equation for the reactor volume of CSTR is given by the formula:
[tex]V = \dfrac{C_{Ao}V_o - C_A V_o }{-rA}[/tex]
[tex]V = \dfrac{C_{Ao}V_o (1 - 0.01)}{KC_A^2}[/tex]
The reaction rate of A is:
[tex]-r_A = kC_A^2[/tex] and k = 3 dm³/mol.h
replacing the values in the above equation to solve for v;
∴
[tex]V = \dfrac{(0.5 \ mol/dm^3) (10 \ dm^3/h) (1 - 0.01)}{ ( 3 \ dm^3/mol.h) (0.01 \times 0.5 \ mol/dm^3)^2}[/tex]
V = 66,000 dm³
Thus, the reactor volume of CSTR is 66000 dm³
Taking the differential mole balance equation for PFR is as follows:
[tex]\dfrac{d(C_AV_o)}{dV} = -r_A[/tex]
[tex]\dfrac{d(C_AV_o)}{dV} = Kc^2A[/tex]
Taking the integral between initial and final concentrations;
[tex]\dfrac{v_o}{k} \int ^{C_A}_{C_{Ao}} \dfrac{dC_A}{C^2A}= - \int ^V_o \ dV[/tex]
[tex]V = \dfrac{V_o}{K} \Big [\dfrac{1}{C_A}- \dfrac{1}{C_{Ao}} \Big ][/tex]
replace the values in the above equation;
[tex]V= \dfrac{(10 \ dm^3/h) }{(3 \ dm^3/mol.h)}\Big [ \dfrac{1}{0.01(0.5 \ mol/dm^3)} - \dfrac{1}{0.5 \ mol/dm^3} \Big ][/tex]
[tex]\mathbf{V = 66 0 \ dm^3}[/tex]
Thus, the reactor volume of PFR is 660 dm³