For biological and medical applications we often need to consider proton transer

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 Go 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.

Explanation / Answer

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

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