1. Stoichiometry

2. The Stoichiometric Table aA + bB  cC + dD rewrite in terms of limiting specie A + (b/a)B  (c/a)C + (d/a)D = -1, -b/a, c/a, d/a

3. Stoichiometric Table Species Feed Rate Change Effluent Rate A F A0 -1 F A0 X F A0 (1-X) B F B0 B F A0 X B F A0 X F B0 + B F A0 X C F C0 C F A0 X C F A0 X F C0 + C F A0 X D F D0 D F A0 X D F A0 X F D0 + D F A0 X I F I0 --- Total F T0  j F A0 X F T0 +  j F A0 X

4. Let’s simplify a bit: Define  j ≡ F j0 /F A0  ≡  j = -1 - b/a + c/a + d/a  ≡ y A0  = (F A0 /F T0 ) 

5. Stoichiometric Table Species Feed Rate Change Effluent Rate A F A0 - F A0 X F A0 (1 - X) B F A0  B B F A0 X B F A0 X F A0 (  B + B X) C F A0  C C F A0 X C F A0 X F A0 (  C + C X) D F A0  D D F A0 X D F A0 X F A0 (  D + D X) I F A0  I --- Total F T0  j F A0 X F T0 (1 +  X)

6. Comparing Moles Reacted Let’s use a real reaction: CO + 3H 2  CH 4 + H 2 O A + 3B  C + D 10 mol CO/min 20 mol H 2 /min 5 mol H 2 O/min 15 mol N 2 /min T = 200 o C P = 2 atm

7. Species jjjj j CO H2H2H2H2 CH 4 H2OH2OH2OH2O N2N2N2N2

8. Species jjjj j CO1 H2H2H2H22-3 01 H2OH2OH2OH2O0.51 N2N2N2N21.50

9. Methane Synthesis Stoichiometric Table Species Feed Rate Change Effluent Rate CO F A0 - F A0 X F A0 (1 - X) H2H2H2H2 2 F A0  F A0 X F A0 (  - 3 X) CH 4 0 F A0 X H2OH2OH2OH2O 0.5 F A0 F A0 X F A0 (  + X) N2N2N2N2 1.5 F A0 --- F A0  Total F T0  F A0 X F T0 (1 - 0.4 X)

10. Uh, oh – negative flow rate!

11. H 2 + 1/3 CO  1/3 CH 4 + 1/3 H 2 O A + 1/3 B  1/3 C + 1/3 D 10 mol CO/min 20 mol H 2 /min 5 mol H 2 O/min 15 mol N 2 /min T = 200 o C P = 2 atm

12. Methane Synthesis Stoichiometric Table Species Feed Rate Change Effluent Rate H2H2H2H2 F A0 CO CH 4 H2OH2OH2OH2O N2N2N2N2 Total

13. Methane Synthesis Stoichiometric Table Species Feed Rate Change Effluent Rate H2H2H2H2 F A0 - F A0 X F A0 (1 - X) CO 0.5 F A0  F A0 X F A0 (  – 1/3 X) CH 4 0 1/3 F A0 X H2OH2OH2OH2O 0.25 F A0 1/3 F A0 X F A0 (  + 1/3 X) N2N2N2N2 0.75 F A0 --- F A0 0.75 Total F T0  F A0 X F T0 (1 - 0.267 X)