Chapter 11 – Chemical Equilibrium

Homework Assignment, Ch 8 (buffers) Problems 5,6,9,11,12,13,18,19,20 Due Fri, Nov 1

Exam 2 on Wed, Nov 6 Covers Chapters 5, 6, 7, 8 plus Gravimetric and Volumetric Chloride Determinations

Homework Assignment, Ch 12 (EDTA) Problems 1,8,10,12,17,23 Due Fri, Nov 8

Chapter 11 – Chemical Equilibrium Our understanding of the phenomena shown on the proceeding slide is that the inert salt increases the ionic atmosphere (environment), allowing each cation or anion to be surrounded by species of the opposite charge, but farther separated from the counter ion which caused its original precipitation.

Chapter 11 – Chemical Equilibrium This effect of the ionic environment within the solution is known as the ionic strength and may be represented as  (your author) or I (other authors).  = I = ½ (c 1 z c 2 z 2 2 +…) = ½  c i z i 2 The sum of terms includes all of the ions in solution. An example of this calculation is shown in Problem 1

What is the ionic strength of a solution that is M in KNO 3 and M Na 2 SO 4 ?  = ½  c i z i 2  = ½ {0.01(+1) (-1) (+1) (-2) 2 }  = ½ {0.08} = 0.04M

Activity Coefficients The “actual” or “effective” concentration of an ionic species in solution is known as the activity ; your author uses the symbol A (more commonly used is simply a lower case a); I will use the later symbol, so that his equation 11-2 is written as a C = [C]  C

Activity Coefficients The exact equilibrium constant K is then expressed in terms of the activities of the species involved instead of the more commonly concentrations. For the reaction aA + bB cC + dD K = (a c ) c (a D ) d / (a A ) a (a B ) b or K = ([C]  C ) c ([D]  D ) d / ([A]  A ) a ([B]  B ) b

Activity Coefficients The individual values for the activity coefficients  of each of the species is a function of the ionic strength as shown by the extended Debye-Huckel equation: log 10  = -0.51z 2   / {1 + (  /(305))} (Eq11-5) where  is the size of the ion in pm (picometers). Examples of  for the F - and I - ions are shown in the next slide.

Activity Coefficients A more general form of the extended Debye-Huckel equation is log 10  = z 2   / (1 +   ) * Although this equation is less exact, one does not need all of the parameters of the previous form. * From Hargis, “Analytical Chemistry: Principles and Techniques, p 19, Prentice-Hall, 1988.

Activity Coefficients The effects of ionic strength on activity for various charges of ions are shown in the next slide.

Figure 11-4  as a function of  for different values of z

What is the activity coefficent of Mg +2 in a 3.3 mM solution of Mg(NO 3 ) 2, using both the author’s equation 11-5 and the given simplified forms? In both, we first need the ionic strength  :  = ½ {(3.3mM)(+2) 2 + (6.6mM)(-1) 2 }  = ½ { } = ½{19.8} = 9.9 mM  = M

What is the activity coefficent of Mg +2 in a 3.3 mM solution of Mg(NO 3 ) 2, using both the author’s equation 11-5 and the given simplified forms? Using the author’s eqn 11-5, log  = (-0.51)(+2) 2 (0.0099) 1/2 / {1 +(800)(0.0099) 1/2 /305} log  = /1.261 =  = = 0.690

What is the activity coefficent of Mg +2 in a 3.3 mM solution of Mg(NO 3 ) 2, using both the author’s equation 11-5 and the given simplified forms? Using the simplified equation log  = (-0.509)(+2) 2 (0.0099) 1/2 / {1 +(0.0099) 1/2 } log  = /1.099 =  = = 0.654

What is the activity coefficent of Mg +2 in a 3.3 mM solution of Mg(NO 3 ) 2, using both the author’s equation 11-5 and the given simplified forms? In summary, the more exact equation 11-5 gives  = while the the simplified equation gives a value of  = In most cases the difference between the 2 values would not be important.

Activity Coefficients - Ignore activity coefficients for nonionic compounds.

Activity Coefficients Whenever the ionic strength is high (  > 1 M) the activity coefficient values we could calculate are not very meaningful because of the lower concentration of the solvent and the concentrations of the solutes increase.

Figure 11-5  of H+ in M HClO 4 as a function of [NaClO 4 ]

pH The response of the glass electrode for measurement of pH is dependent on the ionic strength of the solution. The technical definition of pH is pH = - log 10 (a H+ ) = log 10  H+ [H + ] Also, be aware that most glass electrodes show significant errors at pH > 12 because of the high concentrations of the counter ions such as Na + and K +.