Question

The irreversible elementary gas-phase reaction is carried out isothermally at 305 K in a packed-bed reactor with 100 kg of catalyst. The entering pressure was 20 atm and the exit pressure is 2 atm. The feed is equal molar in A and B and the flow is in the turbulent flow regime, with FA0 10 mol/min and CA0 0.4 mol/dm3. Currently 80% conversion is achieved. What would be the conversion

Answer 1

0.856.

Step-by-step explanation:

Lets represent the irreversible elementary gas phase equation of reaction as

A + B -----------------------------------> C + D

We have that the percentage of conversion is 80%.

The pressure, p from the ratio of exit pressure and entering pressure is p = 2/20 = 1/10 = 0.1.

Therefore, n = 1 - p^2/ weight of the catalyst = 1 - 0.1^2/ 100 = 9.9 × 10^-3 kg cat^-.

Now, let's make use of the equation below;

J/ 1 - J = kb^2/ u [ w - nw^2/2] ----------(1).

0.8 / 1- 0.8 = k ( 0.4)^2/ 10 [ 100 - (9.9× 10^-3 × 100^2/ 2] .

k = 4.95 dm^6/ kg.cat .mol.min

The turbulent flow= 1/2 × 9.9 × 10^-3 = 4.95 × 10^-3 kg cat^-.

Thus, making use of the equation (1) again, we have that;

{4.95 × 10^-3 × 0.4}/ 10 × [ 100 - (4.95 × 10^-3 × 100^2)] / 2 = 5.964.

Therefore, a/1 - a = 5.964.

5.964( 1 - a) = a.

5.964 - 5.964a = a.

5.964 = a + 5.964a.

5.964 = 6.964a.

a = 5.964/ 6.964 = 0.856.