Physical Chemistry Nonideal Systems Chapter 11 Reaction Equilibrium in Nonideal Systems
1 Chapter 11 Reaction Equilibrium in Nonideal Systems Physical Chemistry Nonideal Systems
Physical Chemistry Nonideal Systems s The Equilibrium Constant For the ideal-gas reaction aA+becc+dD (4.36) Lyu=0 the equilibrium condition ∑vA=0 - RT (11.1) u;=u:+RT In a (11,2) ∑v4+Rr∑vha1a=0 (11.3
2 The Equilibrium Constant For the ideal-gas reaction aA+bB cC+dD (4.36) = the equilibrium condition i i i 0 i o i = i + RT ln a (11.2)* RT i o i i a e − (11.1) = i i i,eq 0 + = i i i eq i o i i RT ln a , 0 (11.3) Physical Chemistry Nonideal Systems
Physical Chemistry Nonideal Systems s The Equilibrium Constant ∑v+Rr∑vha=0 (11.3) △G+RhnI(a1)y=0 △ rT In K° (11.4) △G ∑ (11.5) K°≡∏ (11.6) Standard equilibrium constant Activity equilibrium constant Equilibrium constant
3 The Equilibrium Constant (11.4)* i o i i o G + = i i i eq i o i i RT ln a , 0 (11.3) + ln( , ) = 0 i i i eq o G RT a o o G = −RT ln K i i i eq o K a ( ) , (11.5)* (11.6)* Standard equilibrium constant Activity equilibrium constant Equilibrium constant Physical Chemistry Nonideal Systems
Physical Chemistr Nonideal Systems Reaction equilibrium in nonelectrolyte solutions K°≡I[(a1) K°=I(nx)G=∑"Am=RThK am=ymm/m°(i≠A Km=( rX)∏ 1.m i≠A △G°=-RThK° (118) △C +∑v i≠A
4 Reaction Equilibrium in nonelectrolyte solutions / ( ) a , , m m i A o m i = m i i i i i eq o K a ( ) , (11.6)* i i II i i o K x ( ) = , x i o i II i o Gx , = −RT ln K (11.7) A o i i A x A A m i i o Km x m m ( ) ( / ) , , = (11.8) o m o Gm = −RT ln K + i A o i m i o A x A o Gm , , (11.9) Physical Chemistry Nonideal Systems
Physical Chemistr Nonideal Systems Reaction equilibrium in nonelectrolyte solutions K°≡I[(a1) K°=I1(nx)G=∑ rT In K m /m°(i≠A) yc1/c(i≠A) Km=(yAx1)1(m1m)△CGm=≡vA+ i≠A ≠A K=(7x)" △G2=vA+∑v i≠A ≠A
5 Reaction Equilibrium in nonelectrolyte solutions / ( ) a , , m m i A o m i = m i i i i i eq o K a ( ) , (11.6)* i i II i i o K x ( ) = , x i o i II i o Gx , = −RT ln K A o i i A x A A m i i o Km x m m ( ) ( / ) , , = + i A o i m i o A x A o Gm , , + i A o i c i o A x A o Gc , , A o i i A x A A c i i o c K x c c ( ) ( / ) , , = / ( ) a , , c c i A o c i = c i i Physical Chemistry Nonideal Systems
Physical Chemistr Nonideal Systems Reaction equilibrium in electrolyte solutions Many ionic reactions in solution are acid-base reactions e Bronsted definition of acidbase Acid: a proton donor Base: a proton acceptor water: amphoteric, either a proton donor or a proton acceptor H,O+HO台H2O++OH (11.10) K°=∏ (11.6) K a(hOa(OH) [a(H2O)2 The standard state of the solvent H2O is pure H2O a(h,O) pure
6 Reaction Equilibrium in electrolyte solutions Many ionic reactions in solution are acid-base reactions. + − H2 O + H2 O H3 O + OH (11.10) Brønsted definition of acid/base Acid: a proton donor Base: a proton acceptor water: amphoteric, either a proton donor or a proton acceptor i i i eq o K a ( ) , (11.6)* 2 2 3 [ ( )] ( ) ( ) a H O a H O a OH K o w + − = (11.11) The standard state of the solvent H2O is pure H2O. a(H2 O) pure =1 Physical Chemistry Nonideal Systems
Physical Chemistr Nonideal Systems Reaction equilibrium in electrolyte solutions In aqueous solutions a(H,O)=r(HO)x(H,O) e for dilute aqueous solutions a(H2O)≈1,a1=ym1/m K=a(Ho a(oh) Lr(H3O)m(H3o)/mr(oh )m(OH)/m] Omission of the solvent's activi For the ho ionization V+=l=V, 2+=rr Kp=rim(Hgo )m(OH)/(m) dilute aqueous solution(11. 12yo
7 Reaction Equilibrium in electrolyte solutions In aqueous solutions [ ( ) ( )/ ][ ( ) ( )/ ] ( ) ( ) 3 3 3 o o o w H O m H O m OH m OH m K a H O a OH + + − − + − = = For the H2O ionization Omission of the solvent’s activity. ( ) ( ) ( ) a H2 O = x H2 O x H2 O For dilute aqueous solutions o a(H2 O) 1,ai = i mi / m (11.12)* 2 3 2 ( ) ( )/( ) o o Kw m H O m OH m + − = dilute aqueous solution + = = − = + − 2 1 , Physical Chemistry Nonideal Systems
Physical Chemistr Nonideal Systems Reaction equilibrium in electrolyte solutions For the ionization of the weak acid hX in aqueous solution Hx+H2O分HO++X K r(HO)m(HO)/mlr(x)m(X )/m (11.14 y(HX)m(H/m° In dilute solution m(hO)m(X dilute solution 11.15) m(Hr) The pair of ions HO/X-
8 Reaction Equilibrium in electrolyte solutions For the ionization of the weak acid HX in aqueous solution + − HX + H2 O H3 O + X (11.13) o o o o a HX m HX m H O m H O m X m X m K ( ) ( )/ [ ( ) ( )/ ][ ( ) ( )/ ] 3 3 + + − − = (11.14) In dilute solution dilute solution (11.15) ( ) ( ) ( ) 3 2 m HX m H O m X Ka + − = The pair of ions H3O+/XPhysical Chemistry Nonideal Systems
Physical Chemistr Nonideal Systems Reaction equilibrium in electrolyte solutions For an aqueous solution of the weak acid hX with stoichiometric molality m, the degree of dissociation a (X n(X C≡ m m(X )+m(HX) 1+(m(Hr)/m(r)1+rm(H3o)/K K=2m10)m(x dilute solution 11.15) m(HX) K has a dimension of m
9 Reaction Equilibrium in electrolyte solutions For an aqueous solution of the weak acid HX with stoichiometric molality m, the degree of dissociation m HX m X m H O Ka m X m HX m X m m X 1 ( )/ 1 1 ( )/ ( ) 1 ( ) ( ) ( ) ( ) 3 2 + − − − − + = + = + = dilute solution (11.15) ( ) ( ) ( ) 3 2 m HX m H O m X Ka + − = Physical Chemistry Nonideal Systems Ka has a dimension of m
Physical Chemistr Nonideal Systems Reaction equilibrium involving pure solids or pure liquids Many reactions involve one or more pure solids or liquids Caco(s)eCao(s)+Co2(8) equilibrium condition I, eq (11.13) K°≡I(a u,=u:+RTIn a RTIna,=A,A' pure solid or liquid (11.20) du=dGm=smdT+vn,dP at const T du;=Vm dP 10
10 Reaction Equilibrium involving pure solids or pure liquids Many reactions involve one or more pure solids or liquids. ( ) ( ) ( ) CaCO3 s CaO s +CO2 g = (11.13) i i i,eq 0 i i i eq o K a ( ) , equilibrium condition i o i = i + RT ln a (11.2)* o RT ai = i − i ln pure solid or liquid (11.20) d = dGm = −Sm dT +Vm dP at const. T di =Vm,i dP Physical Chemistry Nonideal Systems
