ReactionUra

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1 years, 57 days

MaplePrimes Activity


These are replies submitted by ReactionUra

@vv 

Oh, this seems quite difficult to me. I can go through your way. But is there any possibility how all variables get nonnegative? 

 

@Carl Love 

Okay, but still remains the problem that the result is wrong...
If I want to check the numeric results for example for eq4 and eq5, they are totally wrong.

@Carl Love 

Yeah, thanks for this command. However all variables should be nonnegative... but when I use allowed range, maple just subtitutes numerical constants into equations.

Does that mean that there is not any solution with all nonnegative variables?

Problem is also that in your solution when variable ionic is negative, u_Cl should be positive so the numerical result seems wrong to me.


 

@Carl Love 

okay here is my whole problem

eq1:=K_1=(((n_Cl-x)*u_Cl)*(n_H*u_H))/(n_HCl*m);
eq2:=K_2=(((n_Na-x)*u_Na)*(n_OH*u_OH))/(n_NaOH*m);
eq3:=K_w=(n_H*u_H/m)*(n_OH*u_OH/m);
eq4:=(n_NaCl-x)=(n_Na-x)+n_NaOH;
eq5:=(n_NaCl-x)=(n_Cl-x)+n_HCl;
eq6:=(n_Na-x)+n_H=(n_Cl-x)+n_OH;
eq7:=2*ionic=(n_H/m)+((n_Cl-x)/m)+((n_Na-x)/m)+(n_OH/m);
eq8:=u_H=0.4077*ionic^2-0.3152*ionic+0.9213;
eq9:=u_Na=0.0615*ionic^2-0.2196*ionic+0.8627;
eq10:=u_OH=0.1948*ionic^2-0.1803*ionic+0.8887;
eq11:=m=r*V;
eq12:=u_Cl=(1.417625986641341e-01)*exp(-ionic/2.199955601666953e-02)+2.369460669647978e-01*exp(-ionic/3.756472377688394e-01)+5.859738096037875e-01;
 

constants

K_1:=10^(8);K_2:=10^(-0.2);K_w:=10^(-13.995);n_NaCl:=1.2*10^(-4);V:=5*10^(-8);r:=997.0;x:=0;
 

command

res:=solve({eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12},{n_Cl,n_H,n_HCl,n_Na,n_OH,n_NaOH,ionic,m,u_H,u_Na,u_OH,u_Cl});
 

@Carl Love 

oh, you are right, but the problem is the same, when I rewrite it... I have more similar systems. Answer from Maple is Warning, solutions may have been lost

 

yeah few of them are constants, it is 13 variables and 13 eq

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