> restart:#"m07_p21"

Determinar la masa molar de la hemoglobina humana sabiendo que a 20 ºC y en una centrifugadora de g=105g0 se ha medido Di=63×10-12 m2/s, Vsedim=0,44×10-6 m/s y r=1330 kg/m3.

Datos:

 > su1:="H2O":su2:="Hemoglobina":dat:=[T0=(273+20)*K_,gnew=1e5*g,D[i]=63e-12*m_^2/s_,V[infinity]=0.44e-6*m_/s_,rhoH=1330*kg_/m_^3];

Esquema:

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Eqs. const.:

 > g1dat:=get_gas_data(su1):l1dat:=get_liq_data(su1):dat:=op(dat),g1dat,l1dat,Const,SI2,SI1:

 > eqBF:=m*diff(V(t),t)=-m*g+m*g*rho[m]/rho-3*Pi*mu*D*V(t);dsolve({eqBF,V(0)=0},V(t));V[infinity,i]:=subs(rho[m]=rho+Drho,solve(0=rhs(eqBF),V(t)));Dt[infinity,i]:=m/(3*Pi*mu*D);eqBMi:='V[infinity,i]'*c[i]=D[i]*dc[i]/dz;eqGD:=0=S*dT-V*dp+Sum(n[i]*dmu[i],i);

 > eqEq1:=T=cte;eqEq1:=dT/dz=0;eqEq2:=v=cte;eqEq2:=dv/dz=0;eqEq3:=mu[i]+M[i]*g*z=cte;eqEq3:=dmu[i]/dz+M[i]*g=0;

 > eqEH:=0=0-V*dp-Sum(n[i]*M[i]*g*dz,i);eqEH:=0=-Vdp-n*M[m]*g*dz;eqEH:=0=-dp-rho*g*dz;

 > eqEquilHydr[i]:=Diff(mu[i],p)*Diff(p,z)+Diff(mu[i],x[i])*Diff(x[i],z)+M[i]*g=0;eq1:=Diff(mu[i],p)=Diff(V,n[i]);eq1:=Diff(mu[i],p)=V/n;eq2:=Diff(p,z)=-(n*M[m]/V)*g;eq3:=Diff(mu[i],x[i])=R[u]*T/x[i];

 > eqEquilHydr[i]:=subs(eq1,eq2,eq3,eqEquilHydr[i]);eqEquilHydr[i]:=dlnx[i]/dz=(M[m]-M[i])*g/(R[u]*T);

Pero al ser mezcla líquida hay que pasar a densidades.

 > eqEquilHydr[i]:=dlnx[i]/dz=(m[m]-m[i])*g/(k[B]*T);

 > eqBMi:='V[infinity,i]'=-D[i]*dlnc[i]/dz;eqBMi:='V[infinity,i]'=-D[i]*dlnx[i]/dz;eqBMi:=subs(eqEquilHydr[i],V[infinity]/D[i]=-dlnx[i]/dz);

 > eqmpart:=Mi=rho[H]*Vpart*N[A];eqBMi_:=(subs(m[m]=rho*Vpart,m[i]=rho[H]*Vpart,eqBMi));eqmpart_:=subs(Vpart=solve(eqBMi_,Vpart),eqmpart);eqmpart__:=subs(g=gnew,Const,rho[H]=rhoH,T=T0,dat,eqmpart_);

Puede compararse con el método del P-7.11.

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