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+//Chemical Engineering Thermodynamics

+//Chapter 14

+//Thermodynamics of Chemical Reactions

+

+//Example 14.6

+clear;

+clc;

+

+//Given

+//SO2 + (1/2)O2 - SO3

+//Basis: 1 Kgmole of SO2

+n_SO2 = 1;// SO2 fed in Kgmole

+//From table 14.1 (page no 301)

+//alpha values for the following components are given as

+a_SO2 = 7.116;

+a_O2 = 6.148;

+a_SO3 = 6.077;

+//beta values for the following components are given as

+b_SO2 = 9.512*10^-3;

+b_O2 = 3.102*10^-3;

+b_SO3 = 25.537*10^-3;

+//Standard enthalpy of the following components at 25 deg cel in Kcal/Kgmole are given as

+H_SO2 -70960;

+H_O2 = 0;

+H_SO3 = -94450;

+//Standard free energy of the following components at 25 deg cel in Kcal/Kgmole K are given as

+F_SO2 = -71680;

+F_O2 = 0;

+F_SO3 = -88590;

+n_O2 = n_SO2;//O2 fed in Kgmole; since 50 mole percent mixture of SO2 & O2 is fed

+n_SO3 = n_SO2;//SO3 formed in Kgmole

+n_O2_e = n_O2-(n_O2/2);//Kgmoles of O2 in exit gas

+n_O2_r = n_O2/2;//Kgmoles of O2 reacted

+R = 1.98;//gas constant in Kcal/Kgmole K

+

+//To show  the variation of the standard heats of reaction with temperature and the equilibrium constant with temperature graphically in the  given temperature range

+//(i)Variation of the standard heats of reaction with temperature

+del_H = (n_SO3*H_SO3)-(n_O2_r*H_O2)-(n_SO2*H_SO2);// in Kcal/Kgmole

+del_F = (n_SO3*F_SO3)-(n_O2_r*F_O2)-(n_SO2*F_SO2);// in Kcal/Kgmole

+//From equation 14.10 (page no 301)

+del_a = (n_SO3*a_SO3)-(n_O2_r*a_O2)-(n_SO2*a_SO2);

+del_b = (n_SO3*b_SO3)-(n_O2_r*b_O2)-(n_SO2*b_SO2);

+//In equation 14.11 (page no 302), substituting del_H at

+T = 298;//in deg cel

+I = del_H - del_a*T - (del_b*(T^2)/2);// integrating constant

+mprintf('(i)The standard heat of reaction at any tempperature can be calculated by the relation:');

+mprintf('\n    del_Ht = %fT + %fT^2 %f',del_a,del_b/2,I);

+

+//(ii)Variation of the equilibrium constant with temperature

+//K1 = lnKa (say)

+K1 = -del_F/(R*T);

+//From equation 14.42 (page no 316); M1 = M/R (say)

+M1 = K1-(del_a/R)*log(T)-(del_b/(2*R))*T+(I/(T*R));

+//Let us assume the temperature in the range 800K to 1500K as

+Ta = [700 800 825 850 900 1000 1100 1300 1500];

+for i = 1:9

+    Ka(i) = %e^((del_a/R)*log(Ta(i))+(del_b*Ta(i)/(2*R))-(I/(Ta(i)*R))+M1);

+end

+clf;

+plot(Ta,Ka);

+xtitle(" ","Temperature in K","equilibrium constant K");

+mprintf('\n\n(ii)From the graph it can be seen that as temperature increases Ka decreases exponentially,so the reaction is exothermic.');

+//end
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