interactions in an electrolyte sähkökemian peruseet ke-31.4100 tanja kallio [email protected]...
TRANSCRIPT
Solvent – ion interactions
Solvent – ion interactions
ion neutral1
2
3
vacuum
solvent
a
ez
a
qdqdqqVw
zeze
0
22
0 00
1 84)(
a
ezw
r0
22
3 8
W2 = cavity formation + surface tensionW2 ~ negligible
W1 = discharging an ion
W3 = charging a molecule
r
el a
ezGw
11
8 0
22
IS
total
Experimental values for hydration energy
Kationit Säde/pm / hydG
kJ mol 1
/ hydH
kJ mol 1
/ hydS
J mol 1 K 1
/mV
cm3 mol 1
H+ 1055 1090 131 5,5
Li+ 69 475 530 161 6,4
Na+ 102 365 415 130 6,7 K+ 138 295 330 93 3,5 Rb+ 149 275 305 84 8,6 Cs+ 170 250 280 78 15,8 NH4
+ 148 285 325 131 12,4 Me4N
+ 280 160 215 163 84,1 Et4N
+ 337 130 205 241 143,6 Mg2+ 72 1830 1945 350 32,2 Ca2+ 100 1505 1600 271 28,9 Fe2+ 78 1840 1970 381 30,2 Ni2+ 69 1980 2115 370 35 Fe3+ 65 4265 4460 576 53 Anionit F
– 133 465 510 156 4,3
Cl– 181 340 365 94 23,3
Br– 196 315 335 78 30,2
I– 220 275 290 55 41,7
OH– 133 430 520 180 0,2
NO3
– 179 300 310 95 34,5
ClO4
– 250 205 245 76 49,6
Ion – ion interactions
Debye length (1/2)
)()(
)( rzbi
RT
rFzbii
i
i
ececrc
Spatial distribution of ions around the central ion obeys Boltzmann distribution
(2.32)
rr
counterion 273 K
Debye length (2/2)
i
bii
i
ibii
i
rzbii
iii cz
RT
rF
RT
rFzFczeFczFczr i 2
2)( )()(
1)(
i
bii
rr
czRT
F 2
0
2222
0
2 ;
Charge density around the central ion is obtained by summarizing charge densities of all the ions
first term of Taylor series
electroneutrality
(2.33)
(2.34)
k-1 = Debye length = thickness of the double layer
Dependence of potential on charge density is given by Poisson equation
rr
Electrostatic potential falloff
ra
eezr
ar
r
c 1
14)(
)(
0
(2.36)
rCerr )(
a
cezdrrrC )(4 2
General solution for the previous equation in spherical coordinates is (f(r) = 0 when r → )
Integration constant is determined taking into account that the total charge density around the central ion is equal but opposite that of the central ion
After calculus we obtain
distance of closest approach
Debye-Hückel limiting law (1/3)
a
ezaVaadqaNw
r
cezc
14
)()()(;)(0
atm0
atmionion A
Electrostatic work done to move the central ion inside the ion cloud
r
ezrV
r
c 1
4)(
0
potential distribution around the central ion (2.36)
potential field created by the central ion at distance a (2.37)
a
ezNw c
r
18
2
0
Aionion
ra
eezr
ar
r
c 1
14)(
)(
0
Consequently
(2.39)
Debye-Hückel limiting law (2/3)
Comparison of (2.39) and (2.40) gives us
akT
ez
RT
w
r
ii
18ln
0
2ionion
g2 = 1 (infinite dilution)
(2.41)
ion-ionosm1
2
1
2
1
2dil lnlnln wwRT
c
cRT
a
aRTw
activity coefficients origins from electrostatic interactions between ions
(2.40)
When diluting the solution from concentration c1 to c2 (infinite dilute) work is done
Debye-Hückel limiting law (3/3)
i
iiii czIIBa
IAz 22
2
1;
1log
ion strength
Sifting to log system
2/12/32/11
2/1
8
2/32/32/12/3
6
Kdmmolcm1029,50
Kdmmol108246,1
TB
TA
r
r
IBa
IAzz
1log
Utilizing definition of mean activity:
(2.42)
(2.43)
experimentalD-H lawD-H limiting law
Ionpairs
1
1
AB
BBAA c
c
ccKd
g± = 1 → Kd = a2c/(1 a)
Equilibrium constants for ion assosiation/dissosiataion
Bjerrumin theoryIons around the central ion obey Maxwell-Bolzman distributionPotential profile immediately around the central ion obeys (2.37)Hypothesis: ions form ion pair when distance is smaller than q
Fouss theoryIons must be in contact to form an ionpairProbability of forming an ion pair depends on number of ions, solvent volume, space occupied by the species and electrostatic energy on the surface of the ion
bx
ra dxex
kT
ezzNK
2
4
3
0
2
A 44000
akTaE KeaN
c
/)(33
4A2
10001
Super acids and Hammett acid function
M.A. Paul and F.A. Long, Chem. Rev. 57 (1957) 1-45
Hammett acid function H0 for 0.1 M HCl-solutions. Abscissa: content of the organic component in mol-%
B + H+ BH+
very acidic acids extension to the conventional pH scale is needed
a weak indicator base B is added into the acid solution
equilibrium constant for the indicator acid
BH
BH
B
BH
BH
B0 log)log(log
c
clog
ca
acH H
measurable
measurable
O][Hlog)1(][OHlog 2 npKH w
for super basisBH + OH−(H2O)n B− + (n + 1)H2O
unknownconcentration depends on the pH of the super aid
Hammet acid function is defined so that it becomes equal to pH in ideally diluted aqueous solutions
Summary
Interaction in electrolyte solutions
r
el a
ezGw
11
8 0
22
IS
solvent – ion interactions
ion neutral1
2
3
vacuum
solvent
ion – ion interactions
i
bii
r
czRT
F 2
0
22
Debye length
IBa
IAzz
1log
Debye – Hückel law
0][BH
[B]log HpKd
superacids
O][Hlog)1(][OHlog 2 npKH w