Physical Chemistry Chapter 10 Nonideal Solutions
Chapter 10 Nonideal Solutions Physical Chemistry
Physical Chemistry Nonideal Solutions Models for Nonelectrolyte Activity Coefficients Simple solution RTInyiB =Wxc, RTInylc =WxB,(10.31 w depends on Tand p but not on the mole fractions let z be the number of nearest neighbors of each molecule in the array. The intermolecular-interaction energy is approximated as the sum of nearest-neighbor interactions If &BB, Eco, and aBc are the interaction energies for adjacent B-B, C-C, and B-c pairs, respectively The energy of mixing mixu=2Nalebc 2 BB+EcC/nBnc/(ng+ nc)=WnBnc/(nB+nc
Simple Solution Models for Nonelectrolyte Activity Coefficients Nonideal Solutions W depends on T and P but not on the mole fractions. let z be the number of nearest neighbors of each molecule in the array. The intermolecular-interaction energy is approximated as the sum of nearest-neighbor interactions. ( ) ] /( ) /( ) 2 1 [ mix A B C B B CC nB nC nB nC WnB nC nB nC U = zN − + + + ln , ln , 2 , 2 R T I,B = WxC R T I C = WxB (10.31) If BB, CC, and BC are the interaction energies for adjacent B-B, C-C, and B-C pairs, respectively. The energy of mixing Physical Chemistry
Physical Chemistry Nonideal Solutions Models for Nonelectrolyte Activity Coefficients where W=ENAEBC-(EBB+Ecc) For two liquids b and c whose molecules have similar sizes and shapes △ma≈0,SO△mH=△m2U E SOSE=△S-△ nUX mIX G=H-TS≈H=△AH=△U ux GE=nB CW(T P n+n
Nonideal Solutions where For two liquids B and C whose molecules have similar sizes and shapes, mixV 0, so mixH = mixU ( )] 2 1 [ A BC BB CC W zN − + , = − = 0 i d mix mix i d E mixS mixS so S S S G H TS H mixH mixU E E E E = − = = W (T, P) n n n n G B C E B C + = Models for Nonelectrolyte Activity Coefficients Physical Chemistry
Physical Chemistry Nonideal Solutions Models for Nonelectrolyte Activity Coefficients G C-W(T,P) PStn aGE RT yii an, )T,P, lj# (Problem 10.4 simple solution model RTInyig=Wxc, RTInyic=WxB,(10.31 Redlich-Kister equation Margules equation) G n+n =xBxCRT[A4+A2(x2-xc)+A3(x2-xc)2+…+A(x2-xc)" (103)
Nonideal Solutions T P n j i i E I i n G RT = , , , ln simple solution model (10.32) (Problem 10.4) W (T, P) n n n n G B C E B C + = Models for Nonelectrolyte Activity Coefficients [ ( ) ( ) ( ) ] 2 1 1 2 3 − = + − + − + + − + n B C B C B C n B C B C E E m x x RT A A x x A x x A x x n n G G Redlich-Kister equation (Margules equation) Physical Chemistry ln , ln , 2 , 2 R T I,B = WxC R T I C = WxB (10.31)
Physical Chemistry Nonideal Solutions Models for Nonelectrolyte Activity Coefficients Redlich-Kister equation Margules equation) E G E n+r x3xR0+A1(x1-x)+4(x2-xc)2+…+41(x2-x)y (10.32 B C w(T, P) simple solution model n+n
Nonideal Solutions simple solution model (10.32) Models for Nonelectrolyte Activity Coefficients [ ( ) ( ) ( ) ] 2 1 1 2 3 − = + − + − + + − + n B C B C B C n B C B C E E m x x RT A A x x A x x A x x n n G G Redlich-Kister equation (Margules equation) W (T, P) n n n n G B C E B C + = Physical Chemistry
Physical Chemistry Nonideal Solutions Solutions of electrolytes N on-electrolyte solutions The solute is not present as ions Electrolyte solutions The solute is ionized and the ions generally interact strongly with each other MX→vM+vM (10.33) Vs Numbers of ions in the chemical formula(integers) zs Charges of ions in the chemical formula Ba(NO3)2>Ba+2NO3 2: 1 electrolyte MaSO,→2Na++SO 1: 2 electrolyte BaSoa>Ba2++S0 2: 2 electrolyte
Solutions of Electrolytes Nonideal Solutions Non-electrolyte solutions The solute is not present as ions Electrolyte solutions The solute is ionized and the ions generally interact strongly with each other. + + − − + − → + z z M X M M (10.33) 's Numbers of ions in the chemical formula (integers) z's Charges of ions in the chemical formula + − → + 3 2 Ba(NO3 ) 2 Ba 2NO + − → + 2 Na2 SO4 2Na SO4 + − → + 2 4 2 BaSO4 Ba SO 2:1 electrolyte 1:2 electrolyte 2:2 electrolyte Physical Chemistry
Physical Chemistry Nonideal Solutions s Chemical Potentials in Electrolyte Solutions MⅩ→vM++vM (10.33 G 10.34 G an, T,P,nj*+ an 7,P,n G an T P Since u+ and u are not measurable, define u, (the chemical potentials of the electrolyte as a whole) in solution G W;\On, T,P,mA (10.35)
Chemical Potentials in Electrolyte Solutions Nonideal Solutions Since + and - are not measurable, define i (the chemical potentials of the electrolyte as a whole) in solution + + − − + − → + z z M X M M (10.33) T P n j i i i n G , , + + + T P n j n G , , − − − T P n j n G , , T P nA i i n G , , (10.35) (10.34) Physical Chemistry
Physical Chemistry Nonideal Solutions Chemical Potentials in Electrolyte Solutions G (10.35) T Pn Similar definition for other partial molar properties of the electrolyte as a whole T Pn dG=-sdT+vaP+uana +u,dn++u_dn(10.36 fror MX→M2+vM (10.33 n =v n
Chemical Potentials in Electrolyte Solutions Nonideal Solutions T P nA i i n G , , (10.35) T P nA i i n V V , , Similar definition for other partial molar properties of the electrolyte as a whole. dG = −SdT +VdP+ A dnA + + dn+ + − dn− (10.36) + + − − + − → + z z M X M M (10.33) from n+ = + ni n− = − ni Physical Chemistry
Physical Chemistry Nonideal Solutions s Chemical Potentials in Electrolyte Solutions MX→vM2++vM (10.33 dG=-sdr+vaP+u,dn +u, dn, +u dn(10.36 G=-S+tP+pm+(4+v)dm(1037) Keep T, P, and n constant and using G (10.35 T.P.n 1=v+H4+V1 (10.38) On the mole-fraction scale, the chemical potential of solvent p1=AA(T,P)+ RThnyxx,(7x)=1(10.39)
Chemical Potentials in Electrolyte Solutions Nonideal Solutions dG SdT VdP A dnA dni ( ) = − + + + + + + − − (10.37) + + − − + − → + z z M X M M (10.33) Keep T, P, and nA constant and using n+ = + ni n− = − ni dG = −SdT +VdP+ A dnA + + dn+ + − dn− (10.36) T P nA i i n G , , (10.35) i = + + + − − (10.38)* ( , ) ln , , ( , ) 1 * = + = A A x A A x A T P RT x (10.39) On the mole-fraction scale, the chemical potential of solvent Physical Chemistry
Physical Chemistry Nonideal Solutions s Chemical Potentials in Electrolyte Solutions 4=A(T,P)+ RTInyxdx4,(y)=1(10.39 mole-fraction activity coefficient infinite dilution a On the molality scale, the chemical potentials of electrolyte 44=1C+RTm(ym4/m2°) (10.40) u_=uY+RTIn(- m/m) m=l mol/kg, n=r=l (10.41 1=v+14+v (10.38) u:=vui+v_uo+v RTIn(ym/m)+v RTIn(r-m_/m) 4l,=v,A+vAo+v, RT n(r )"(r_)"(m, /m")"(m I m)1 (1042)
Chemical Potentials in Electrolyte Solutions Nonideal Solutions ( , ) ln , , ( , ) 1 * = + = A A x A A x A T P RT x (10.39) mole-fraction activity coefficient infinite dilution On the molality scale, the chemical potentials of electrolyte 1 / , 1 ln( / ) ln( / ) = = = + = + − + − − − − + + + + m mol k g RT m m RT m m o o o o o (10.40) (10.41) i = + + + − − (10.38)* ln( / ) ln( / ) o o o o i = + + + − − + + RT + m+ m + − RT − m− m (10.42) ln[( ) ( ) ( / ) ( / ) ] + − + − = + + + − − + + + − + − o o o o i RT m m m m Physical Chemistry
