Question

This is the problem that I was given:

Use ∆H˚ and ∆S˚ for autoionization to calculate ∆Gº at body temp (37ºC). What is Kw at this temperature? What is the pH of pure water at body temp?

I have the Kw, ∆H˚, and ∆S˚ values for water at 25ºC but how do I do this problem at 37ºC?

Answer 1

So, first, just on notation, thermodynamically, it is incorrect to say ∆Gº at 37 ºC as the index zero states that the value is calculated at standard temperature which is 25 ºC. For any other temperature you say ∆G and may specify the temperature in the upper corner.

So, you can calculate ∆Gº from the enthalpy and enthalpy, right?

Afterwards, you use the GIbbs-Helmholtz equation

\[\frac{ \Delta G }{ T _{1} } = \frac{\Delta G ^{ o}}{T} + \frac{ \Delta H ^{o} }{ T _{1} -T }\]

Answer 2

Then, for the pH, you need to recalculate the Kw at 310 K (37 ºC).

Use the Van't Hoff equation,

\[\ln (\frac{ K }{ Kw })=\frac{ \Delta H }{ R }\left( \frac{ 1 }{ T _{1} } - \frac{ 1 }{ T } \right)\]

Answer 3

You can find the neutral pH at a higher temperature using the new equilibrium constant for water you just calculated. Note that even though the value will not be equal to 7 but slightly less than that, it still means equal concentration of the ions.

Answer 4

Let me know if you need further details or if you want me to calculate it for you.