Ionic Strength In dilute solutions, the ions that are present behave independently of each other. However, as the concentration of ions in solution increases, the activity of the ions decreases because of ionic interaction. The ionic strength may be determined using the following equation (Lewis and Randall, 1921) I = ionic strength of solution, mole/L Ci = concentration of species i, mole/L Z = Charge

212 i i

iI C Z= ∑

Ionic Strength If the concentration of individual species is not known, the ionic strength may be estimated from the total dissolved solids concentration using the correlation. TDS = mg/L Quiz) try to calculate the ionic strength for ocean seawater

I = 2.5×10−5( )(TDS)

Activity is a tendency to react or “effective concentration” and is used to account for nonideal Activity of substance: standard state conditions of the substance and is based on commonly used standard conditions. The standard reference conditions for zero free energy are: 1 atm of pressure a temperature of 298.15 K (25C), elements in their lowest energy level, and 1 molal hydrogen ion (1 mole of hydrogen ion per 1000 g of water).

Activity is a tendency to react <= to account for nonideal Ac#vity  coefficient  of  a  chemical  in  water  may  be  given  by      {i}  =  γi  [i]  for  ions  and  molecules  in  solu#on      where  {i}  =  ac#vity  of  ionic  species,  mole/L    γi    =  ac#vity  coefficient  for  the  ionic  species  [i]=  molar  concentra#on  of  the  ionic  species  in  solu#on,  mole/L      General  defini#on  of  ac#vity  coefficient:  γi  >1.0  for  non-­‐electrolytes    γi  <  1.0  for  electrolytes   •  fresh  water,  γi    =  1.0  for  non-­‐electrolytes  •  a  solvent  in  a  solu#on,  {i}  =  γi  xi  where  xi  is  the  mole  frac#on  •  pure  solids  or  liquids  in  equilibrium  with  a  solu#on,  {i}  =  1  •  gases  in  equilibrium  with  a  solu#on,  {i}  =  γi  Pi  where  Pi  is  the  par#al  pressure  

of  the  gas  in  atmosphere  •  mixtures  of  liquids  {i}  =  xi  where  xi  is  the  mole  frac#on  

I < 0.005 M, the activity coefficient can be estimated from the Debye-Hückel limiting law   I < 0.1 M (less dilute solution) modification of the DeBye-Hückel equation which is known as the Davies equation can be applied with acceptable error (Davies, 1967). Accurate to within 10% up to 0.5 M The constant A for water: 0.49 @ 0°C 0.5 @ 15°C 0.51 @25°C

log10 γ i =− AZi

2 I1/2

1+ I1/2 −0.3I1/2⎛⎝⎜

⎞⎠⎟

log10 γ i =− AZi2 I1/2

A = 1.29×106 2

DεT( )1.5

Exercise  1    Calculate  the  ac0vity  coefficient  of  Na+,  Ca2+,  Al3+  at  ionic  strengths  of  0.001  M  and  0.005  M  at  25°C      

γ c[C]( )cγ d[D]( )d

γ a[A]( )aγ b[B]( )b =

C{ }cD{ }d

A{ }aB{ }b = K

Equilibrium constant based on the activities:  

Ionic  strength  <  0.005  mole/L  for  most  water  supplies    Ionic  strength  ~  0.7  mole/L  for  seawater    Ionic  strength  ~  0.001-­‐0.005  mole/L  for  lake  and  river  water  Ionic  strength:  0.001-­‐0.005  mole/L  for  potable  ground  water    Ionic  strength:  >  5  for  oil  field  brines    

Influence of Ionic Strength on Activity of Molecules For  nonelectrolyte,  γA  is  a  func0on  of  ionic  strength  and  can  be  calculated  using  the  following  empirical  equa0on:    log10  γA  =  Ks  ×  μ  where  Ks  =  Setschenow  or  “sal0ng-­‐out”  constant,  1/mol  μ  =  ionic  strength  of  the  water,  mol/L  

Influence  of  Ionic  Strength  on  Henry’s  Constant  

Gases or VOCs in water supplies high in dissolved solids have higher volatility (or have an higher apparent Henry’s law constant) than those with low dissolved solids. This results in a decrease in the solubility of the volatile component (i.e., salting-out effect), which can be represented mathematically as an increase in the activity coefficient of component A, γA in aqueous solution. γA will increase with increasing ionic strength and this in turn causes the apparent Henry’s law constant, Happ, to be greater than the thermodynamic value of H. For most water supplies, the ionic strength is less than 10 mM and the activity coefficient is equal to one. Significant increases in volatility and the apparent Henry’s constant are only observed for very high ionic strength (0.7 mole/L) waters such as seawater.

Thermodynamics  of  Chemical  Reac#ons    Principles  from  equilibrium  thermodynamics  provide  a  means  for  determining  whether  reac0ons  are  favorable,  and  are  also  used  in  process  design  calcula0ons  to  determine  the  final  equilibrium  state.      To  determine  whether  a  reac0on  will  proceed,  two  fundamental  thermodynamic  criteria  must  be  considered.  1.  Change  in  entropy  of  the  system  and  its  surroundings  must  be  greater  than  zero  

for  a  reac0on  to  proceed.    When  evalua0ng  chemical  reac0ons,  the  entropy  requirement  generally  does  not  need  to  be  considered  because  it  is  typically  sa0sfied,  especially  when  heat  is  produced  by  the  reac0on.  

2.  Requirement  that  the  change  in  free  energy  of  the  reac0on  must  be  less  than  zero.    This  is  because  the  change  in  free  energy  is  defined  as  the  final  state  minus  ini0al  state  and  the  final  state  must  be  lower  than  the  ini0al  state.      

It  is  useful  to  examine  the  total  free  energy  of  reac0on  as  a  func0on  of  the  reac0on  extent.    Because  the  absolute  free  energy  of  reac0on  cannot  be  easily  determined  it  is  most  common  to  determine  the  change  in  free  energy  of  a  reac0on.    Accordingly,  the  free  energy  of  reac0on  curve  is  compared  to  convenient  standard  condi0ons.      

Thermodynamics  of  Chemical  Reac#ons    

The convenient standard conditions: 1)  Elements in their natural state at 25°C and 1 atm of pressure 2)  The reference temperature is 25°C 3)  The reference temperature for gases is 1 atm of pressure 4)  The reference concentration for ions and molecules in solution is 1

molal hydrogen ion.

For most applications, molar concentration equals molal concentration and a 1 molal solution is 1 mole per 1000 g of solvent. It is noted that some are not stable such as Na or K

Free  Energy  of  Forma#on  

The  expression  for  free  energy  was  developed  by  J.W.  Gibbs  and  is  oden  referred  to  as  Gibbs  free  energy,  G.    The  free  energy  change  of  forma0on  of  a  substance,  i,  is  given  by  the  following  expression.        

ΔGF ,i = Free  energy  change  of  the  forma0on  of  species  i,  kJ/mol   ΔGF ,i =ΔGF ,i

° + RT ln{i}

ΔGF ,i

° = Free  energy  change  of  the  forma0on  of  species  i,  kJ/mol,  at  standard  condi0ons  

R  =  universal  gas  law  constant,  8.314  x  10-­‐3  kJ/mol  K    T  =  absolute  temperature,  K    {i}  =  ac0vity  of  species  i  

Free  Energy  of  Forma#on  

A+ b

aB! c

aC + d

aD

Exercise:  calculate  the  free  energy  change  of  reac0on  for  the  following  reac0on  

Free  Energy  of  Reac#on  

Free  Energy  at  Equilibrium  

Temperature  Dependence  of  Free  Energy  Change    

Temperature  Dependence  of  Free  Energy  Change    

Exercise  1      

Calculate  the  pH  of  neutrality  and  free-­‐energy  change  of  the  reac0on  at  10  degree  Celsius  assuming  that  the  enthalpy  of  reac0on  does  not  change  with  temperature  

Exercise  2    Can  MTBE  be  degraded  anaerobically  (i.e.,  in  groundwater)  in  the  presence  of  nitrate?  

Energy  Equivalences    Standard  units  for  expressing  this  energy  input  are:  Electron  volts,  Cell  poten0al,  Wavelength  of  light  Band  gap    

Energy  =  eV  =  E° × number of electrons transfer   -19

-19

1.60×10 coulomb Joule1eV=1electron× ×1Volt×electron coulomb•volt

=1.60×10 Joules

Energywhere

wavelength

h

c

ν

λν

=

=

-3410

-19

6.26×10 J•sec 3.0 10 cm/secEnergy 1.60×10 J

1172

c h c

nm

λν

= = × = × ×

=

What  is  the  equivalent  wavelength  for  this  energy?