Page 67 - Elements of Chemical Reaction Engineering Ebook

38 Conversion and Reactor Sizing Chap. 2

where C,, = entering concentration, mol/dm3
yAO = entering mole fraction of A
P, = entering total pressure, kPa
To = entering temperature, K

PA, = entering partial pressure, kPa
i
R = ideal gas constant e.g., R = 8.314 kPa * dm3; see Appendix B
mol K

Example 2-I Using the Ideal Gas Law to Calculate C,,

A gas mixture consists of 50% A and 50% inerts at 10 atm (1013 @a) and enters
the reactor with a flow rate of 6 dm3/s at 300°F (422.2 K). Calculate the entering con-
centration of A, CAO, and the entering molar flow rate, FA'. The ideal gas constant is
R = 0.082 dm3-atm/mol-K (Appendix B)

Solution
We recall that for an ideal gas:

YAOPO
c = - = - (E2- 1.1)
*' RT, RTo
where Po = 10 atm

yAO = 0.5
PA, = initial partial pressure = yAoP, = (OS)( 10 atm) = 5 atm
To = initial temperature = 300°F = 149°C = 422.2 K
0.82 dm3. atm
R=
mol. K
We could also solve for the partial pressure in term of the concentration
(E2- 1.2)
= CAORTO
Substituting values in Equation (E2- 1.1) yields
mol
0.3 10 atm) = 0.14442 -
= 0.082 dm3 atm/mol. K(422.2 K) dm3
Keeping only the significant figures gives us
C,, = 0.144 mol/dm3 = 0.144 kmol/m3 = 0.144 mol/L

The entering molar flow rate, FAo, is just the product of the entering concentration,
i CAo, and the entering volumetric flow rate, u,: