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file: GATE CH 2020 (with Solutions).pdf

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An elementary liquid phase reversible reaction P→Q is carried out in an ideal continuous stirred tank reactor (CSTR) operated at steady state. The rate of consumption of P, −rₚ(in mol literliter⁻¹ minute⁻¹), is given by

−r_p = C_p-0.5C_Q /text{Where} C_p /text{andC}_Q are /text{the} /text{concentrations} (/text{in} mol /text{liter}^{-1}) /text{of} P /text{and} Q , respectively. The feed contains only the reactant P at a concentration of 1 mol liter⁻¹, and conversion of P at the exit of the CSTR is 75 /\% of the equilibrium conversion. Assume that there is no volume change associated with the reaction, and the temperature of the reaction, and the temperature of the reaction mixture is constant throughout the operation. The space time (in minutes) of CSTR is ___ (round off to 1 decimal place).

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Answer

Solution

(−r_p) = C_p-0.5C_Q

C_{p_0} = /frac{1mol}{l}

Xₚ=75% of Xe (equilibrium conversion)

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Cₚ−0.5 C_Q

C_p = C_{p_0}(1-X_p)

C_Q=CₚXₚ

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2 = /frac{CP_0XP_e}{(C_p(1-X_{pe}))}

X_{pe} = /frac{⁰2}{3}

Actual conversion

X_p = /frac{0.75 /times 2}{3} = 0.5

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Source PDF: GATE CH 2020 (with Solutions).pdf

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