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type=NAT · page=37–38 · marks=2 · content_conf=0.7999999999999999 · math_conf=0.814

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file: GATE CH 2020 (with Solutions).pdf

pages: 37–38

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An exothermic, aqueous phase, irreversible, first order reaction, Y→Z is carried out in an ideal continuous stirred tank reactor (CSTR) operated adiabatically at steady state. Rate of consumption of Y (in mol liter⁻¹ minute⁻¹) is given by

−r_Y = /frac{10^9e(−6500)}{ᵗC_Y} /text{Where} C_Y /text{is} /text{the} /text{concentration} /text{of} Y (/text{in} mol /text{liter}^{-1}) , and T is the temperature of the reaction mixture (in K) . Reactant Y is fed at 50⁰ C. Its inlet concentration is 1.0 mol liter⁻¹,and its volumetric flow rate is 1.0 liter minute⁻¹.

In addition, use the following data and assumptions

• /text{Heat} /text{of} /text{the} /text{reaction} = −42000Jmol^{-1}

• /text{Specific} /text{heat} /text{capacity} /text{of} /text{the} /text{reaction} /text{mixture} = 4.2g^{-1}K^{-1}

• /text{Density} /text{of} /text{the} /text{reaction} /text{mixture} = 10000 /text{gliter}^{-1}

• Heat of the reaction, specific heat capacity and density of the reaction mixture do no vary with temperature • Shaft work is negligible If the conversion of Y at the exit of the reactor is 90 %, the volume of the CSTR (in liter) is ____(round off to 2 decimal places).

Options

none

Answer

2.8

Solution

−r_y = /frac{10^9(−6500)}{e^ᵗc_y}

T_0 = 323.15K

.

(−r_y) Energy balance

.

1 /times 1000 /times 4.2(323.15-0)-1 /times 1000

×4.2 /times (T_2-0) = 1 /times 1 /times (−42000)

T_2 = 332.15K

−r_y = /frac{10^9(−6500)}{e^ᵗc_y}

−r_y = 3.1702c_y

1 /times 0.9

.

(3.1702)c_y\cdot(1-x_y_0)

V = 2.8 /text{liter}

Hence, the correct answer is 2.8

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

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