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 NOT 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

a)

[H3O+] = sqrt(Kw) = sqrt(2.5*10^-14) = 1.5811*10^-7

pH = -log(H+) = -log(1.5811*10^-7) = 6.801040

b)

dG° = -RT*lnK

dG° = -8.314*(37+273)*ln(2.5*10^-14) =  80722.03 J/mol

c)

Kw at 4°C = 0.182*10^-14

[H+] = sqrt(Kw) = sqrt(0.182*10^-14) = 4.2661*10^-8

pH = -log(H) = -log(4.2661*10^-8) = 7.36996

d)

if we add HCl --> 1.5 microM = 1.5*10^-6

[H+] increases to 1.510^-6

this will favour dG to form H+

e)

the lowest chemical equilbirium in such example is OH- ions