PH of Water at Various Temperatures

[CheesyPeeps]

Homework Statement

If the text is too small, it reads:
'A student measured the pH of water at various temperatures using a pH meter and obtained the following results:
(table showing pH decreasing as temperature increases)
The student was unsure whether the results were accurate or if the pH meter was faulty.
Using your knowledge of chemistry, discuss possible reasons for the results obtained.'

From SQA Advanced Higher Chemistry 2013 Exam

Homework Equations

n/a

The Attempt at a Solution

I took this question to my teacher after seeing it in a past exam paper, and neither of us could come up with much of an explanation (in fairness, the teacher I asked specialises in practical rather than theory). We wondered if it was to do with entropy, as entropy increases with temperature. Looking at it again, I'm also thinking that maybe it's to do with the dissociation constant, as that would also be affected by temperature.
The level I am currently studying is roughly equivalent to first year degree.
Any help is appreciated.

 

[Nidum]

The question is full of holes but assuming pure water and that a simplistic answer is required this might help : Link

 

[Ygggdrasil]

You are definitely on the right track thinking about the dissociation constant and entropy.

The pH of water is due to the autoionization of water into hydrogen ions and hydroxide:
H₂O --> H⁺ + OH^-

which is governed by the equilibrium constant Kw

There are two relevant equations to consider:

1) Kw = exp(-ΔG°/RT)

and

2) ΔG° = ΔH° - TΔS°

For the autoionization of water, what sign do you expect for the change in enthalpy (ΔH) and change in entropy (ΔS). When you increase temperature (T), what effect will that have on the change in free energy (ΔG) and the equilibrium constant (Kw)?

 

[CheesyPeeps]

The question is full of holes but assuming pure water and that a simplistic answer is required this might help : Link

Thank you! That link definitely helped. I hadn't realized that the dissociation of water was endothermic.

My country's exam board calls these 'open ended questions'. They are always full of holes and the marking schemes are so vague that it can be very difficult to know how to answer them properly. They're meant to simulate a real life scenario in which you'd have to apply your knowledge of chemistry to explain something, which is a good idea for an exam in theory, but the effectiveness of them is debatable...!

 

[CheesyPeeps]

You are definitely on the right track thinking about the dissociation constant and entropy.

The pH of water is due to the autoionization of water into hydrogen ions and hydroxide:
H₂O --> H⁺ + OH^-

which is governed by the equilibrium constant Kw

There are two relevant equations to consider:

1) Kw = exp(-ΔG°/RT)

and

2) ΔG° = ΔH° - TΔS°

For the autoionization of water, what sign do you expect for the change in enthalpy (ΔH) and change in entropy (ΔS). When you increase temperature (T), what effect will that have on the change in free energy (ΔG) and the equilibrium constant (Kw)?

Thanks! From ΔG° = ΔH° - TΔS° I can see how ΔG° would decrease as temperature increases, making the ionisation more spontaneous.

 

[epenguin]

#2 was a lot of help - you find the same figures as in your question!
Your conjecture that the dissociation constant K_w changes is right - to be more precise it increases, meaning there is more H⁺ and OH^- as temperature increases. The dissociation. Is endothermic so this is Le Chatelier's principle. You can't hiwever say it becomes more acid on warming since H⁺ and OH^- concentrations remain always equal.

You're sure you understand this also from the formula? - it is easy to get confused. Well I find so.
Note that Ygggdrasil's formula in (3) can be written

$$K_{W}=exp\left( -\dfrac {\Delta H^{0}}{RT}+\dfrac {\Delta S^{0}}{R}\right)$$

The large ΔH⁰ is giving a large negative in the bracket and thence a small K_w. ΔS⁰ must be relatively unimportant at ordinary temperatures. As T increases the ΔH⁰/T term becomes smaller in absolute value - less negative! - so actually greater K_w. So more [H⁺]. So smaller pH! And entropy was not the thing changing but energy.

Clearer now, at least for me.