# Effect of Temperature on pH of Water

The $K_\mathrm w$ is a function of temperature. It is $10^{-14}$ at $25\ \mathrm{^\circ C}$. When the temperature is $50\ \mathrm{^\circ C}$, the $K_\mathrm w$ can be calculated to be somewhere around $10^{-12}$ using Vant Hoff's equation, but this is so weird.

MY ATTEMPT

If we will solve for $K_\mathrm w=10^{-12}$, we get $\rm pH=6$. Will the water become acidic due to increase in temperature?

• The effect is correct; however your estimated $\mathrm{pH}$ is a bit low. The actual $\mathrm{pH}$ of neutral water at $50\ \mathrm{^\circ C}$ and normal pressure is about $\mathrm{pH} = 6.6$; i.e. the autoprotolysis constant of water is about $K_\mathrm w \approx 5\times10^{-14}$. – Loong Oct 25 '15 at 18:26
• People in this discussion don't understand the difference between "neutrality" and solution acidity. It is best to think of the Bronstead definition of acidity in discussions like this one. In that context it is known that methanol is more acidic than water and a solution of pure acetic is neutral, as well as more acidic than either methanol or water. (yes acetic acid has an autoprotolysis constant that happens to be about 14. So does methanol, ammonia, sulfuric acid and any other compound that self dissociates to a solvated hydrogen ion and the conjugate base form of the solvent) – Bill Tindall Mar 16 '17 at 21:57
• A solution of hot water is more acidic than cold water because it has a higher activity of dissociated hydrated hydrogen ions, yet it is neutral. For more reasons that I can easily type you can not test these facts with pH paper. – Bill Tindall Mar 16 '17 at 21:57

# TL;DR

$\rm pH=6$ is the neutral pH at $\rm 50\,^{\circ} C.$

# Long Version

Actually there is nothing wrong with your calculations. It seems that you are confused about the definition of a solution being acidic. If something is acidic, this means that the concentration of $\ce{H+}$ ions (technically $\ce{H3O+}$ ions) is greater than the concentration of $\ce{OH-}$ ions. At room temperature (25 degrees Celsius) a solution is neutral if its pH is 7. This means that for a solution to acidic, its pH must be lower than 7 at 25 degrees.

When we increase the temperature to 50 degrees, the pH of a neutral solution is actually 6, not 7. You can check this as if you were find the total concentration of $\ce{H+}$ ions and $\ce{OH-}$ ions, you will find that they both equal $10^{-6}$. Since there concentration is equal, the solution must be neutral. So for a solution to be acidic at a temperature of 50 degrees, its pH must be lower than 6, not 7.

## Explanation

Now you might wonder what the reason for this. Consider the following equation which is the auto-disassociation of water $$\ce{2H2O + heat \leftrightharpoons H3O+ + OH-}$$ As you can see, this reaction is actually endothermic. This means that when you increase the temperature, due to Le Chatelier's principle, the equilibrium will shift to the right; hence the concentration of $\ce{H3O+}$ and $\ce{OH-}$ ions will increase. This is indicated by the increase in the $\rm K_w$ value, as more products are formed.

Therefore since there is a greater of concentration of $\ce{H3O+}$, a solution which is neutral will have more $\ce{H3O+}$ ions at 50 degrees than it would when it is 25 degrees. Therefore its pH will be lower than 7 despite being neutral.

• So we can conclude that when we increase the temperature as there is increase in Kw both H3O+ and OH- ions concentration increases making it neutral. One more doubt. Why do we write H3O+ and H+ interchangeably as if both mean the same? – Ali Hasan Oct 25 '15 at 4:54
• @AliHasan H+ is easier to write but H3O+ is the actual form of H+ in water – TanMath Oct 25 '15 at 5:37
• Yes, we just use H+ for convenience, however is reality it is the hydronium ion, H3O+, that exists. Also higher hydrated protons do exists in solutions such as $\ce{H5O2+}$ and $\ce{H9O4+}$ – Nanoputian Oct 25 '15 at 8:07
• S0 we get pH=6. That means if we are boiling water and at that time we put a litmus paper in it, it's colour will change. Ph=6 at 50C and at 100C it will become more less. And as we increase temperature the pH value will tend 1 being more and more acidic. What I think is that water will still remain neutral as OH and H+ concentration will be same but a pH paper should most probably turn red. But that does not happen. – Ali Hasan Oct 26 '15 at 15:25
• @AliHasan That is because that the pH would not linearly decrease with temperature, but is rather like an exponential curve. Meaning that if heating the water to 50C decreases the pH, heating it by another 50C won't decrease the pH to 5 but to something like 5.5 (I don't exactly). So for the litmus paper to actually become red, the temperature has to extremely high (but the water would have evaporated to steam well before you could even reach the required temperature). – Nanoputian Oct 28 '15 at 4:59