1 DECOMPOSITION OF METHANOL TO CH3 + OH MASTER EQUATION SOLUTION FOR FALL-OFF AND LOW PRESSURE REGIMES LATEST UPDATE: Sept 1994 ERROR FOR TRUNCATION OF MATRIX 1.0E-03 EIGENVALUE TOLERANCE 1.0E-03 ERROR FOR TRUNCATION OF P(E,E') 1.0E-03 NUMBER OF REACTION CHANNELS 1 FULL ANGULAR MOMENTUM CONSERVATION USED (SMITH-GILBERT METHOD) COLLISION DIAMETER = 3.58 ANGSTROMS MASS OF REACTANT= 32.04 A.M.U. MASS OF BATH GAS = 39.95 A.M.U. LENNARD JONES COLLISION FREQUENCY USED WELL DEPTH = 227.0 K NO. OF PRESSURES = 1 INITIAL GRAIN SIZE = 200 CM-1 NO. OF VALUES OF ALPHA = 1 NO. OF TIMES,+1,GRAIN SIZE HALVED = 2 CUTOFF PARAMETER FOR H(E)=1 0.50 NUMBER OF REACTION CHANNELS = 1 TEMPERATURE = 1000.0 KELVINS ALPHA = 500. CM-1 PROBABILITY FUNCTION IS R(E-E')/N(E'), WHERE R(E-E')=(X** 0) EXP(-X** 1), WHERE X=E-E'/ALPHA NUMBER OF INPUT MICROSCOPIC RATES = 323 NUMBER OF INPUT DENSITIES OF STATES = 590 MAXIMUM ENERGY CONSIDERED 168.7 KCAL MOL-1 = 705.9 KJ MOL-1 CRITICAL ENERGY 76.37 KCAL MOL-1 = 319.53 KJ MOL-1 ENERGY (KJ/MOL) DELTA E TOTAL (CM-1) SQRT(DE**2) EQUILIBRIUM POPULATION 188.8 -161.5 613.3 1.40E-08 200.8 -162.8 612.6 5.21E-09 212.7 -164.9 612.3 1.91E-09 224.7 -166.6 611.8 6.89E-10 236.6 -167.4 611.3 2.44E-10 248.6 -170.2 611.3 8.57E-11 260.5 -171.2 610.8 2.96E-11 272.5 -172.1 610.4 1.01E-11 284.4 -173.6 610.2 3.40E-12 296.4 -174.4 609.9 1.13E-12 308.3 -175.5 609.7 3.74E-13 320.3 -177.1 609.6 1.23E-13 332.2 -177.0 609.3 3.96E-14 344.2 -177.9 609.0 1.27E-14 356.1 -178.3 608.8 4.05E-15 368.1 -179.8 608.8 1.28E-15 380.0 -180.4 608.7 4.03E-16 392.0 -180.9 608.4 1.26E-16 403.9 -182.1 608.4 3.90E-17 415.9 -182.6 608.3 1.20E-17 427.8 -182.9 608.1 3.67E-18 439.8 -182.8 607.8 1.12E-18 451.7 -183.7 607.9 3.39E-19 463.7 -184.2 607.8 1.02E-19 475.6 -184.4 607.6 3.06E-20 487.6 -185.1 607.6 9.12E-21 499.5 -185.5 607.5 2.71E-21 511.5 -185.8 607.4 8.01E-22 523.4 -185.2 607.1 2.35E-22 535.4 -186.7 607.1 6.93E-23 547.3 -187.6 607.3 2.03E-23 559.3 -187.4 607.1 5.88E-24 571.2 -187.4 607.0 1.70E-24 583.2 -188.2 607.0 4.93E-25 595.1 -188.3 606.9 1.42E-25 607.1 -188.6 606.8 4.07E-26 619.0 -188.9 606.8 1.17E-26 631.0 -189.1 606.7 3.32E-27 642.9 -189.3 606.6 9.45E-28 654.9 -189.6 606.6 2.68E-28 666.8 -190.1 606.6 7.60E-29 678.8 -190.2 606.0 2.14E-29 690.7 -195.2 597.5 6.01E-30 702.7 -324.3 592.3 1.69E-30 VALUES OF R(X) (FOR LARGEST GRAIN SIZE): 1.00E+00 6.70E-01 4.49E-01 3.01E-01 2.02E-01 1.35E-01 9.07E-02 6.08E-02 4.08E-02 2.73E-02 1.83E-02 1.23E-02 8.23E-03 5.52E-03 3.70E-03 2.48E-03 1.66E-03 THE FOLLOWING IS FOR THE LOW PRESSURE LIMIT NO. NOT DELTA BAND- MATRIX TOTAL NO.OF REACTING E WIDTH SIZE RATE (K0) ITERATIONS 79 200. 17 158 1.28E+02 23 158 100. 34 316 1.27E+02 3 ******************************* LOW PRESSURE K0 = 1.27E+02 CM3 MOL-1 S-1 BETA = 3.34E-01 -------FALL-OFF CALCULATION------- PRESSURE = 1.00E+02 TORR (= 1.33E+04 PASCAL) OMEGA = 4.25E+08 SEC-1 EXACT (EIGENVALUE) RATE STRONG COLLISION TOTAL DELTA BAND- NO.NOT NUMBER K1 K2,3 TOTAL K1 K2,3 DIMENSION E WIDTH REACTING ITERATIONS 3.41E-05 0.00E+00 3.41E-05 7.4E-05 0.0E+00 176 200. 17 133 23 3.36E-05 0.00E+00 3.36E-05 7.1E-05 0.0E+00 352 100. 34 267 3 * * * * * * * * * * * * * * * * * * * * * * * * * FINAL RESULT: AT PRESSURE = 1.00E+02 TORR, OMEGA = 4.25E+08 S-1 Kuni (S-1) = 3.36E-05 (CHANNEL 1) (BY NUMERICAL INTEGRATION) = 493.2 CM-1 TOTAL K(INF) = 2.96E-04 S-1 K(TOT)/K(INF) = 1.13E-01 STRONG COLLISION K0*[M] = 6.09E-04 S-1 WEAK COLLISION K0*[M] = 2.04E-04 S-1 WEAK COLLISION K0*[M]/K(INF)= 6.88E-01 BETA = 3.34E-01 FLH = 4.07E-01,FSC = 4.49E-01,FWC = 6.20E-01 *******************************