Temperature effects on pKa and pKw

Question

I am an industrial electrician apprentice who needs to learn more about pH-measurements and how the temperature effects the measurement itself (I am in charge of all the pH measurements on the powerplant I work at and I have no one to ask about this stuff as no one knows a thing about pH measurements).

So far I have learned how the temperature affects the electrochemical and physical properties of the combination electrode and how this can easily by adjusted for by incorporating an automatic temperature compensation that keeps the NERNST equation updated in real time.

So far so good.

I have, however, also read about the auto-ionisation of water and the constant pKw and how a change in temperature affects the span of the pH scale: With a change in temperature comes a change in hydronium content due to a shift in equilibrium as predicted by Le Chatelier's Principle. However, with a change in hydronium content comes an equal change in hydroxide content and so a change in this constant DOES NOT change the acidity of a solution. In other words, this particular constant decides the SPAN of the pH scale and because of this also the point of neutrality (7 at 25 degree celcius in pure water and less at higher temperatures).

And then there is the so called pKa that says something about the strength of an acid via the acids point of equilibrium in water. This dissociation constant is also temperature dependent although it is my understanding that this constant have nothing to do with the location of the neutrality point. It's simply a constant that changes with temperature and so the solution (unlike with pKw) DOES become more/less acidic as the temperature changes.

Is this correct?

If so, could you please give me an answer to the following questions I have?

1. Why does a solution become less temperature dependent the more acidic it is? Basic solutions are extremely temperature sensitive, neutral solution still significant sensitive, but highly acidic solutions don't seem give a damn about temperature. Why is that?

2. It is my understanding that pKw is only important in pure water and highly diluted solutions. But what am I to make about this? If I have a tank of an acidic solution (say pH 1) and the temperature is 50 degrees celcius, does this mean that the point of neutrality hasn't shifted as much away from pH 7 as it would had done in pure water? Or is it because there is simply so much hydronium present that the pKa constant takes up proportionally more importance than pKw and so the autoionisation becomes a non issue to consider in every practical sense?

Thanks in advance for any help you may provide me with

Answer 1

The background of the topic is, that for the function

$$y = \frac {a(T)}{x}$$

$y$ does depend on $T$, but $x$ does not.

$\mathrm{pH}$ of basic solutions is temperature dependent via $\mathrm{p}K_\mathrm{w}$ temperature dependance.

Additionally, $\mathrm{pH}$ of weak acid/base solutions is temperature dependent via $\mathrm{p}K_\mathrm{a}$ or $\mathrm{p}K_\mathrm{b}$ temperature dependance.

There is also additional, difficult to quantify factor of temperature dependency of activity coefficients.

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The $\mathrm{pH}$ of strong acid solutions ( like hydrochloric or sulphuric acids ) of molar concentration $c \pu{[ mol/L]}$ is approximately(*)

$$\mathrm{pH}=-\log{c}$$

( For sulphuric acid, it is more complicated due 2 acidic hydrogens, where the second one is not strongly acidic ( in sense it has considerable $\mathrm{p}K_\mathrm{a}$ )).

The $\mathrm{pH}$ of strong base solutions ( like sodium hydroxide) is approximately

$$\mathrm{pH}=\mathrm{p}K_w(T) + \log{c}$$

because concentration of hydroxide ions $\ce{[OH-]}$ is the same as the concentration of e.g. sodium hydroxide. Concentration of hydronium ions $\ce{[H3O+]}$ then follows the above $y = \frac {a(T)}{x}$, i.e. $\ce{[H3O+]} = \frac {K_\mathrm{w}(T)}{\ce{[OH-]}}$

The $\mathrm{pH}$ of weak acid solutions ( like acetic acid ) is approximately

$$\mathrm{pH}=0.5 \cdot (\mathrm{p}K_\mathrm{a}(T) - \log(c))$$

The $\mathrm{pH}$ of weak base solutions ( like ammonia or sodium carbonate ) is approximately

$$\mathrm{pH} = \mathrm{p}K_\mathrm{w}(T) - 0.5 \cdot (\mathrm{p}K_\mathrm{b}(T) - \log {c})$$

The neutral $\mathrm{pH}$ is then

$$\mathrm{pH}_\mathrm{neutral}=\frac {\mathrm{p}K_\mathrm{w}}{2}$$

Note that if there was an OH- electrode, situation would be the opposite. Strongly acidic solutions would have temperature dependent pOH and strongly bases would not.

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For the strong acid/base $T$ dependency, see the table:

t[deg C]	pKw	Solution	pH	pOH
25	14	0.1 M HCl	1	13
25	14	0.1 M NaOH	13	1
50	13.27	0.1 M HCl	1	12.27
50	13.27	0.1 M NaOH	12.27	1

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(*): The equations are not exact, as there plays the role also the ionic strength, activity coefficients and for weak acid/base cases the simplification of $\ce{pH}$ calculation.

Answer 2

Why does a solution become less temperature dependent the more acidic it is? Basic solutions are extremely temperature sensitive, neutral solution still significant sensitive, but highly acidic solutions don't seem give a damn about temperature. Why is that?

Is this statement based on theory or on your own experience?

It is my understanding that pKw is only important in pure water and highly diluted solutions.

No. It is certainly important in solutions of strong bases, where hydroxide is a major species and the hydronium concentration (or activity) depends on the pKw.

If I have a tank of an acidic solution (say pH 1) and the temperature is 50 degrees celcius, does this mean that the point of neutrality hasn't shifted as much away from pH 7 as it would had done in pure water?

Are you asking whether the pH of an acidic solution is less temperature-dependent than that of pure water? Without knowing which acids and bases are in that solution it would be difficult to say. If you have 100 mM of a strong acid at room temperature and heat it up, the amount of hydronium would not change. The concentration would change because the volume of the solution changes a bit. The activity would change more because the activity coefficient would also change.

Or is it because there is simply so much hydronium present that the pKa constant takes up proportionally more importance than pKw and so the autoionisation becomes a non issue to consider in every practical sense?

For a solution of a weak acid, the pKa makes a big difference. For a solution of a strong acid, neither pKa nor pKw makes a big difference.

[OP in comments] With no solution temperature compensation it could mean millions of dollars due to unoptimized control loops and unoptimized dosing of chemicals.

If I were about to waste millions of dollars, I would not trust the answers in an online forum, I would hire a chemist. They would ask what the role of the pH is in the reactions you want to sustain or avoid, and then figure out how temperature and pH play a role in this (e.g. is the the hydronium or the hydroxide activity relevant for the process, or maybe both).

Answer 3

Well, it works both ways...

t[deg C]	pKw	Solution	pH	pOH
25	14	0.1 M HCl	1	13
25	14	0.1 M NaOH	13	1
50	13.27	0.1 M HCl	1	12.27
50	13.27	0.1 M NaOH	12.27	1