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.
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
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.
For the strong acid/base $T$ dependency, see the table:
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.
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
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.
For the strong acid/base $T$ dependency, see the table:
I would say acidity is the same, but alkality grows. But there is the major effect caused by exponential growth of kinetic rates of chemical reactions with temperature, so it is rather a moot point. By other words, more diluted acid at higher temperature can have the same effect during given time intervals as more concentrated one at lower temperature.More
Thank you for an easily understandable answer. I am aware of the fact that pH is a concept concerning the activity of the hydronium ions and not the concentration itself - and that this discrepancy grows in magnitude that more acidic a solution becomes. One more question: Is a solution with pH 1 at 50 deg C less acidic than a solution with pH 1 at 25 deg C? I mean, because at 50 dec C a pH 1 is closer to being neutral than a pH 1 at 25 deg C. True?More
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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).
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).
Well, it works both ways...
Well, it works both ways...
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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.
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.
For the strong acid/base $T$ dependency, see the table:
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.
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.
For the strong acid/base $T$ dependency, see the table:
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Is this statement based on theory or on your own experience?
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.
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.
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.
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).
Is this statement based on theory or on your own experience?
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.
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.
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.
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).
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