CH5010 CRT. Total Marks: 25 Quiz I 02.Sep.2013 1. (3 marks) The following data are available for a reaction. Determine the activation energy and the pre exponent for the rate constant, assuming Arrhenius temperature dependency.

Temp (K) 450 320

Rate Const (s-1) 5 x 10-3 4.8 x 10-6

2. (5 marks) A liquid phase first order reaction A� B is carried out in a batch reactor of 200 lit size, at 70˚C. The rate constant at the operating conditions is 0.02 min-1. Initially, the reactor is charged with 50 moles of pure A. Determine the time necessary to obtain a conversion of 70% 3. (10 marks) A gas phase reaction 2A � B is carried out in a PFR. The following data are available. Incoming total molar flow rate is 150 mol/min, and the volumetric flow rate = 30 lit/min. The reaction is first order with respect to A. The rate constant is k = 0.01 min-1. Mole percentage of A in the feed is 40% and the rest are inert gases.. The operation is at constant temperature and pressure and that the pressure drop is

negligible. The desired conversion is 50%. Determine (i) the parameter epsilon (ε) (ii) flow rate at the outlet and (iii) volume of the reactor. 4. (7 marks) Consider the liquid phase reaction A� B occurring at constant temperature in a recycle reactor. The fresh feed contains pure A at a concentration of 10 mol/lit, and is coming at a flow rate of 25 lit/min. The reaction is first order with a rate constant of 0.05 min-1. The conversion required is 30%. Determine the volume of the reactor needed, when the recycle ratio R= 2.

R

0 1 2 3

Quiz -1 Answer:

1. Using Arrhenius equation, 0

E

RTk k e−

=

1/(RT1) = 2.67286772 × 10-4. 1/(RT2) = 3.758720231 × 10-4

ln(k1) = -5.298317367 , ln(k2)=-12.24689464 -Slope = -(y2-y1)/(x2-x1) = E = 63991.9 ≃ 64 kJ/mol Intercept = 11.80857 � k = 134037 s-1. 2. Given that V = 200 lit, k = 0.02 min

-1, x = 0.7,

For a first order reaction, CA = CA0 e

-kt. CA /CA0 = 0.3, Hence t = -ln(0.3)/k = 60.2 min ≃ 1 h 3. Given that Inerts = 60%, Rest is A (i.e. 40%), all in mole %; At 100% conversion,

for 1 mole of feed, we will have 0.6 inert, 0.2 B and no A. Hence ε = -0.2 At 50% conversion, we will have 0.6 inert, 0.2 A and 0.1 B, i.e. 0.9 total for 1 mole of feed. Isothermal, isobaric conditions, no phase change. Hence, Q /FT = RT/P is a constant. Hence, if inlet flow rate is 30 lit/min, outlet flow rate is 27 lit/min, since Q =

Qin(1+εx), Q in = 30 lit/min, epsilon = -0.2, x = 0.5. In terms of molar flow rate, total outlet flow rate = 135 mol/min

The volume of the reactor is 0.5 0.5

0 0

1 0.2

1A in

A in

A A in

Fdx xV F dx

kC kC x

−

−

−

−= =

−∫ ∫

FA-in = 150 × 0.4 = 60 mol/min, CA-in = 2 mol/lit

0.5 0.5

0 0

60 1 0.2 1 0.23000

0.01 2 1 1

x xV dx dx

x x

− −= =

× − −∫ ∫

( )0.50.5

0 0

4 1 1 43000 3000 ln 1

5 1 5 5 5

xV dx x

x

= + = − − +

− ∫

( )0.5

0

43000 ln 1 1964

5 5

xV x

= − − + =

lit

4. For a recycle reactor ( )

( )

0

1

1o

x

A

A in

Rx A

R

dxV R F

r−

+

= +−∫

( )( )

( )0.3

0.3

0.20.2

0.82 1 250 1500 ln 1 1500ln

0.05 10 1 0.7A

dxV x

x

= + = − − =

× − ∫ ≃ 200 lit