Consider the following reaction scheme A B rightarrow C 2A

Consider the following reaction scheme: A + B rightarrow C 2A rightarrow D The reactions are carried out in a constant volume batch reactor at 42 degree C. At this temperature, the reactions have the following kinetics: r_1 = k_1 C_A C_B r_2 = k_2 C_A The rate equations are based on per mole of reaction, and at 42 degree C, k_1 = 0.82 L/mol middot min and k_2 = 0.04 min^-1. Initially, the reactor contains only A and B at 1.2 mol/L each. If a final overall conversion of 95% is desired for A, determine: (a) final concentrations of all species (b) overall selectivity of C over D (S_c/d = C_c/C_D) (c) yield of C produced to A fed initially (Y_C/A = C_c/C_AD)

Solution

GIVEN:- At 42C, k1 = 0.82 mol/L.min, k2 = 0.04 mol/L.min,

Initially reactor contains only A and B at 1.2 mol/L each. (Let us assume, there is 1L of A & B each),

so Ca0=1.2 and Cb0=1.2

TO FIND:- (a) Final concentrations of all species, (b) Overall selectivity of C over D (Sc/d = Cc/Cd)

(c) Yield of C produced to A fed initially (Yc/a = Cc/Ca0)

SOLUTION:-

r1 = k1.Ca0.Cb0 yields r1 = 0.82 x 1.2 x 1.2 = 1.181 and (For first reaction of A + B = C)

r2 = k2.Ca0 = 0.04 x 1.2 = 0.048 (For second reaction of 2A = D)

Since overall conversion of 85% of A is desired, the number of moles of A converted = 0.85 x 1.2 = 1.02moles/L

PART(a)--

Since reaction rate r1 is more than r2, maximum amount of A will get converted to C than D.

By Percentage 96.1% reactions will be for conversion to C and remaining 3.9% will be for conversion to D.

96.1% of 1.02 of A = 0.98 moles and remaining of A = 0.04 moles

So for reaction-1, 0.98 (moles of A) + 0.98 (moles of B) = 0.98 (moles of C)

For reaction-2, 2(0.04 moles of A) = 0.04 (moles of D)

Final concentration of unreacted species A (Ca) = 1.2-1.02= 0.18 moles/L (ANSWER)

Final concentration of species B (Cb) = 1.2-0.98 = 0.22 moles/L (ANSWER)

Final concentration of species C (Cc) = 0.98 moles/L (ANSWER)

Final concentration of species D (Cd) = 0.04 moles/L (ANSWER)

Part(b)--

Sc/d = Cc / Cd = 0.98 / 0.04 = 24.5, So Sc/d = 24.5 (ANSWER)

Part(c)--

Yc/a = Cc / Ca0 = 0.98 / 1.2 = 0.82, So Yc/a = 0.82 (ANSWER)