Question

For biological and medical applications we often need to consider proton transer equilibria at body temperatue (37o C). Water itself can undergo a proton transfer reaction to form hydronium and hydroxide ions in a process known as autoionization. The equilibrium constant for this reaction, also known as KW, at body temperature is 2.5x10-14.

(You can assume that H+ (aq) is equivalent to H3O+ (aq) )

a) What is the concentration of hydronium ions in neutral water at body temperature? Calcluate the pH of water under these conditions, recalling that: pH = -log[H3O+ ]

b) Calculate ΔGo for this reaction at this temperature.

c) Calculate the pH of water at 4o C.

d) Use a Gibbs eenrgy calculation to determine whether the autoionization reaction would go forwards or backwards at body temperature upon additon of HCl to a final concentration of 1.5 µM.

e) Which species in the autoionization reaction has the lowest chemical potential at equilibrium? Explain your answer in one sentence.

Answer 1

Kw   = 2.5*10^-14

[H3O+][OH-]   = 2.5*10^-14

in water [H3O+] = [OH-]

   {H3O+][H3O+]   = 2.5*10^-14

    [H3O+]² = 2.5*10^-14

    {H3O+]    = 1.58*10^{-7 M}

PH = -log[H3O+]

       = -log1.58*10^-7

         = 6.8

G    = -RTlnKw

          = -8.314*310*ln2.5*10^-14

            = -8.314*310*-31.319   = 80719.7J