CCL: pKa calculation of strong acid

 Sent to CCL by: "VITORGE Pierre 094605" [Pierre.VITORGE*cea.fr]
 Dave,
 pKa = -6 in aqueous solution, means it cannot be measured. We are both right:
 the value cannot be measured, but it might very well be the good value, which I
 am explaining below.
 pKa = -lgKa is a definition of pKa, where
 Ka = [H+] [Cl-] / [HCl]
 [X] is the concentration of species X, here X is an aqueous specie (H+, Cl- or
 HCl). For simplicity I am using concentrations meaning the (small) activity
 corrections are included in Ka.
 A first (chemical) meaning of pKa is (pH) half point reaction, namely for 50%
 dissociation [Cl-]_1/2 = [HCl]_1/2, where subscript _1/2 is to stress
 concentrations are for special (chemical) conditions. Consequently
 Ka = [H+]_1/2 equivalently
 pKa = -lg[H+]_1/2 and
 pKa° = pH_1/2 a well known formula in solution chemistry, where
 superscript° is for standard conditions (infinite dilution where -lg[H+]
 -> pH)
 In this respect pKa of strong acid has no finite value, since strong acid means
 completely dissociated in any chemical conditions, namely [HCl]=0; which is
 indeed not possible for finite values of Ka.
 However, Ka can directly be measured only when the dissociated form can be
 detected, typically if the detection limit is 1% only pKa > -2 can be
 directly measured, and "no finite value" actually means ">
 -2".
 (Partial) conclusion: do not write pKa of strong acid; it is chocking for those
 who currently measure or use pKas knowing the meanings of the concept.
 Another meaning of pKa is form thermodynamics: delta_rG = -RTlnK here applied to
 K = Ka. You can very well calculate
 delta_rGa = G(H+) + G(Cl-) - G(HCl)
 (again note they are aqueous species, especially not HCl(g)), where G(X) can be
 taken from thermochemical data bases (as G(X) = delta_fG(X)) or calculated by
 molecular modelling.
 Now imagine delta_rGa have been estimated in this way giving pKa=-6. This means
 that in the most favourable conditions to form HCl, typically 10 mol.L-1 total
 HCl concentration, the concentrations of the actual species in solution would be
 [H+] # 10 mol.L-1
 [Cl-] # 10 mol.L-1
 [HCl] = 10^-6 mol.L-1, which can probably not be detected, but might very well
 exist. The reasoning still stand even for concentrations less than Avogadro
 Number per litre, and the result is meaningful: the (Ka) reaction can be used in
 thermodynamic cycles, typically with another acid-base reaction to decide in
 which way the proton will be transferred.
 Conclusion: what is your actual problem? Do you really need the pKa of HCl in
 liquid water? Or is it only part of your calculations? In this later case can it
 be cancelled out by using other calculation strategies?
 This was actually the origin of my remark.
 Pierre Vitorge
 -----Message d'origine-----
 De : owner-chemistry+pierre.vitorge==cea.fr!=!ccl.net [mailto:owner-chemistry+pierre.vitorge==cea.fr!=!ccl.net] De la part de case
 case~!~biomaps.rutgers.edu
 Envoyé : mercredi 8 juillet 2009 16:44
 À : VITORGE Pierre 094605
 Objet : CCL: pKa calculation of strong acid
 Sent to CCL by: case [case##biomaps.rutgers.edu]
 On Tue, Jul 07, 2009, VITORGE Pierre 094605 Pierre.VITORGE^^cea.fr wrote:
 >
 > The pKa of a strong acid have no finite value, namely it does not exist.
 These values certainly exist.  For the HCl example that was in the
 original post, the pKa in aqueous solution is around -6, although this
 seems to have a big uncertainty.  You would have to spend some time to
 find the original determination -- a secondary reference to start from
 would be Albert and Serjeant, "The Determination of Ionization
 Constants",
 Chapman & Hall, 1984.
 ....dave case
 -= This is automatically added to each message by the mailing script =-http://www.ccl.net/cgi-bin/ccl/send_ccl_messageSubscribe/Unsubscribe:
 Job: http://www.ccl.net/jobs http://www.ccl.net/spammers.txt