山东大学：《物理化学》课程教学资源（讲义资料）7.4 Activity coefficient-for students

87.4 Activity and activity coefficient Out-class extensive reading ra n. Levine, pp 294-300 Section 10.6 solutions of electrolytes Section 10. 7 determination of electrolyte activity coefficients

§7.4 Activity and activity coefficient Out-class extensive reading: Ira N. Levine, pp. 294-300 Section 10.6 solutions of electrolytes Section 10.7 determination of electrolyte activity coefficients

87.4 Activity and activity coefficient Some facts of strong electrolytes solution present species 0.52 mol- 3KCI 95%K++5%KCl 0. 25 mol,SO4 76% Na*+ 24%NaSO4 0.1 mol dm-3 CuSo 44% CuSO Effective concentration is rather different from the actual concentration Activity coefficient is essential for quite dilute solutions

solution present species 0.52 mol·dm-3 KCl 95% K+ + 5% KCl 0.25 mol·dm-3 Na2SO4 76 % Na+ + 24% NaSO4 ¯ 0.1 mol·dm-3 CuSO4 44% CuSO4 Some facts of strong electrolytes Effective concentration is rather different from the actual concentration Activity coefficient is essential for quite dilute solutions §7.4 Activity and activity coefficient

87.4 Activity and activity coefficient 1. Concepts For ideal or dilute non-electrolyte solution AB=uR(T)+RTIn m For nonideal solution of non-electrolytes uB=UR(T)+RtIn a Bm aB,m rBh e For electrolytic solution such as dilute Hcl solution HCI(aHci=h(au+)+cl(a) y+ a=y-6

For ideal or dilute non-electrolyte solution B B B ( ) ln m T RT m   = + For nonideal solution of non-electrolytes B B B,m   = + ( ) ln T RT a B B,m B,m m a m =  1. Concepts For electrolytic solution such as dilute HCl solution: HCl H Cl HCl( ) H ( ) Cl ( ) a a a + − + − = + m a m  + + + = m a m  − − − = §7.4 Activity and activity coefficient

87.4 Activity and activity coefficient 1. Concepts H=uH(T)+RTinayt Hcr=f- (t)+rTinaci HCI HCI CI=FHCI+RT in(qH.ac) WHCI=AHCI (T)+rT In aHcI Therefore: a Because solution only containing single ion does not exist, the activity of individual ion is unmeasurable, therefore, we use mean activity instead mean activity a=a,a=at a,Va=(a,a)

HCl HCl HCl   = + ( ) ln T RT a Therefore: HCl H Cl a a a =  + − Because solution only containing single ion does not exist, the activity of individual ion is unmeasurable, therefore, we use mean activity instead. mean activity 2 + − =  a = a a a 2 1 ( ) a = a = a+ a− H H H   + + + = + ( ) ln T RT a Cl Cl Cl   − − − = + ( ) ln T RT a HCl H Cl    = ++ − HCl H Cl    = ++ − HCl HCl H Cl   = +  RT a a ln( ) + − 1. Concepts §7.4 Activity and activity coefficient

87.4 Activity and activity coefficient 1. Concepts For a salt with general formula Mu x M X vM+yX 1=V+H4+v 4=+ rTIn a4=12+ RTIn ym=4°+RTna=°+ RTIn y-m u=(vux+vu+RTInyr'+rtInm m Definition: b+=y+ m*=mm-Iv=v++v u=(vur+v_u)+vRTIn++vRTInm Molality-scale mean ionic activity coefficient C. Levine pp 295-297

For a salt with general formula Mv+Xv-  = + + + − − v v     RT a RT m ln ln + + + + + + = + = +     RT a RT m ln ln − − − − − − = + = + ( ) ln ln v v v v      v v RT RT m m + − + − = + + + + + − − + − + − Definition: + −  = + − v v v    + −  = + − v v v m m m = + + − v v v     = + + + ( ) ln ln v v vRT vRT m + + − −   Cf. Levine pp. 295-297 Molality-scale mean ionic activity coefficient 1. Concepts §7.4 Activity and activity coefficient

87.4 Activity and activity coefficient 1. Concepts MX二vM+X m =v m mn三vm m+=m+mm,=(v+v)m mean ionic molality ri=r+r-n=(r+r) mean ionic activity coefficient a=(ata mean ionic activity y Mean ionic molality can be expressed in term of the molality of the solution, mean ionic activity coefficient can be measured experimentally, and then mean ionic activity can be determined

m+ = v+ m m− = v− m m v v v m v v 1 ( ) + −  = + − v v v 1 ( ) + −  = + −    mean ionic molality mean ionic activity coefficient  + −   = =  + − a a a m  v v v 1 ( ) mean ionic activity Mean ionic molality can be expressed in term of the molality of the solution, mean ionic activity coefficient can be measured experimentally, and then mean ionic activity can be determined. v a = a 1. Concepts §7.4 Activity and activity coefficient + −  = + − v v v m m m + −  = + − v v v   

8 7.4 Activity and activity coefficient 3. Influential factors 1)Concentration-dependence Discussion HCI 1.0 Nacl 0.8 0.6 Mg(NO3 )2 0.4 0.2 ZnsO4 00.10.20.30.40.50.6 m/ mol kg-I

3. Influential factors 1) Concentration-dependence Discussion: 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.2 0.4 0.6 0.8 1.0 HCl NaCl Mg(NO3 ) 2  m / mol·kg-1 ZnSO4 §7.4 Activity and activity coefficient

8 7.4 Activity and activity coefficient 3. Influential factors activity coefficient of LiBr in water 30 at 25oC and 1 atm 2.5 0.001 0.965 20 0.01 0.905 0.1 0.797 15 0.5 0.754 0.803 10 5 2.70 10 20.0 0.5 20 486 了 Levine p.299

Activity coefficient of LiBr in water at 25 oC and 1 atm m  0.001 0.965 0.01 0.905 0.1 0.797 0.5 0.754 1 0.803 5 2.70 10 20.0 20 486 Cf. Levine p.299 3. Influential factors §7.4 Activity and activity coefficient

87.4 Activity and activity coefficient 3. Influential factors 2)temperature Table Dependence of yi on temperature for 1: 1 type electrolytes T/°C 10 20 5 KCI 0.768 0.769 0.770 0.769 KOH 0.795 0.798 0.798 0.798 Naoh 0.767 0.768 0.766 0.766

2) temperature T/℃ 0 10 20 25 KCl 0.768 0.769 0.770 0.769 KOH 0.795 0.798 0.798 0.798 NaOH 0.767 0.768 0.766 0.766 Table Dependence of ± on temperature for 1:1 type electrolytes 3. Influential factors §7.4 Activity and activity coefficient

8 7.4 Activity and activity coefficient 3. Influential factors 4)ionic strength 3)Valence types and concentration In 1921. Lewis. who noted that the type electrolyte 0.1 m 0.2 m 1.0 m nonideality observed in electrolytic RbNO3 0.734 0.658 0.430 solutions primarily stems from the total NHCIO 0.7300.6600.482 concentration of charges present rather than from the chemical nature of the Bacl2 0.50804500.401 Individual ionic species, Introduced 1:2 CaCI 0.510 0.457 0.419 ionic strength 0.3140.2740.342 1:3 FeCl30.3250.2800.270 4z8 ar

3) Valence types and concentration 3. Influential factors =  i mi Zi I 2 2 1 type electrolyte 0.1 m 0.2 m 1.0 m 1:1 RbNO3 0.734 0.658 0.430 NH4ClO4 0.730 0.660 0.482 1:2 BaCl2 0.508 0.450 0.401 CaCl2 0.510 0.457 0.419 1:3 LaCl3 0.314 0.274 0.342 FeCl3 0.325 0.280 0.270 In 1921, Lewis, who noted that the nonideality observed in electrolytic solutions primarily stems from the total concentration of charges present rather than from the chemical nature of the individual ionic species, introduced ionic strength. 4) ionic strength §7.4 Activity and activity coefficient 2 0 1 2 4 r q q F  r  =