# confusion about pH of a substance

Let's take an acid, $\ce{HCl}$;

Now what do you mean by the $p\ce{H}$ of $\ce{HCl}$? Does $\ce{HCl}$ have free floating ions in it like water does?

Also, why can't the $p\ce{H}$ value of a substance be less than $0$? Like can't a substance have $10^1~\rm M$ of $\ce{H+}$ ions? In that case won't the $p\ce{H}$ be $-1$?

And when we talk about $p\ce{H}$ values, then are we talking about Arrhenius acids and bases or Brønsted–Lowry acids and bases?

• I would like to point out the fact that, in aqueous solutions, there is natural limit to pH, because you can only have 55.39 moles of water per L at 25 degree Celsius. Hence, there would be a limit to how much of HCl can dissociated. – jaspreet Jul 31 '16 at 15:15
• A "substance" doesn't have a pH. In general it is aqueous solutions of substances that have a pH. You can have pH values in other solvents, but water is by far the most common. – MaxW Jul 31 '16 at 15:49

Dissociation of ions

Water, as you probably know, is highly polar and has a very high dielectric constant. When ionic compounds are added to the water, the electrostatic force of attraction between the ions get very weak and hence will result in dissociation of the compound.

The percentage of dissociation of a compound depends on various factors such as solvent, strength of ionic bond, etc.

$\ce{HCl}$ is a polar molecule and hence it dissociates into its constituent ions, namely, $\ce{H+}$ and $\ce{Cl-}$ ions.

Your initial question "what is the pH of HCl" is not quite right. More about it in the next section.

What is pH?$\space$ Can pH be negative?

pH by definition is a measure of hydrogen ion concentration.

$\mathrm{pH} = -\log[\ce{H+}]$ where $[\ce{H+}]$ denotes the active hydrogen ion concentration.

Hence, $\mathrm{pH}$ of $\ce{HCl}$ in an arbitary context won't make any sense since the $\mathrm{pH}$ of $\ce{HCl}$ would depend on its concentration.

The $\mathrm{pH}$ of a substance can be negative. $10\ \mathrm M$ solution of $\ce{HCl}$ would have a $\mathrm{pH}$ of $-1$.

The stronger the acid, the smaller is the value of $\mathrm{pH}$. $\ce{HCl}$ is a strong acid because it ungergoes almost 100 % dissociation.

Theory of acids and bases and their relation with pH

The theory of acids which you are refering to were developed to classify acids and bases rather not to measure the strength of the acids and bases.

However, one can arrive at the strength of the acid/base according to the theory by logical reasoning. For example, if someone were to ask you which one of the two compounds is an Lewis acid, you would investigate both the molecules and find out which one has a higher tendency to accept electrons to find the stronger acid.

Therefore, the theory of acids proposed by Arrhenius and Brønsted–Lowry are in no way related to $\mathrm{pH}$.

pH on the other hand, is a measure of strength of an acid and is indepdent of the above theories.

It is quite easy to compare $\mathrm{pH}$ with Arrhenius/Brønsted–Lowry theory of acids since according to the theory, the molecule which is willing to donate free $\ce{H+}$ ions will be considered an acid. A claim that higher the concentration of $\ce{H+}$ will be a stronger acid is reasonable, understandable and acceptable.

Bonus: In case of bases, we have a strength measurement scale similar to the pH. We make use of hydroxide ion concentration in place of hydrogen ion concentration to find the strength of the base. We call it $\mathrm{pOH}$.

These two are related by the following formula when the acid/base are dissolved in water at room temperature.

$14 = \mathrm{pH} + \mathrm{pOH}$

• if you google pH of HCl then it says "3.01". What does that mean? – MartianCactus Aug 1 '16 at 9:18
• Firstly, Google is a computer and hence isn't intellegent enough. It simply gathers information from websites and tries to compile it into a neat table. Secondly, if you click on the link from where the Google obtained the information, you will find that at the top of the page, the concentration of the solutions have been mentioned. – Yashas Aug 1 '16 at 9:49
• So it means that if we dissolve 1mM of HCl on water, then it will have a pH of "3.01" ? How many moles of H+ ions will we have then? – MartianCactus Aug 1 '16 at 10:17
• By "it" I mean HCl – MartianCactus Aug 1 '16 at 10:29
• If you dissolve 1mM of HCl, you get the pH to be 3.0. HCl is a very strong acid or is highly ionic and hence dissociates completely in water. Therefore, 1mM of HCl will produce 1mM of $H^+$ ions and hence when you calculate the pH, $-log (10^{-3}) = 3.0$. – Yashas Aug 1 '16 at 11:15

Water is a weak electrolyte, which means that it can act either as an acid or base. The ionisation reaction is 2H$_2$O = OH$^-$ + H$_3$O$^+$ and is highly endothermic, and the equilibrium constant
$K_w$ = [OH$^-$][ H$_3$O$^+$] increases rapidly with temperature. This equilibrium exists in solution no matter what other solutes are present. At 298 K, $K_w=10^{-14}$ and we define $p$K$_w$= -log$_{10}K_w$ = 14

The pH is usually defined in a similar manner as

$p$H = -log$_{10}$[H$^+$],

where [H$^+$] is used instead of [H$_3$O$^+$]. Similarly $p$OH is defined as $p$OH = -log$_{10}$[OH$^-$].
Thus it is possible to have negative $p$H when [H$^+$] > 1, and negative $p$OH when [OH$^-$] > 1. In neutral solution $p$H = 7, [H$^+$] = [OH$^-$] = 10$^{-7}$ M.

However, the definition of $p$H above is only correct at low concentrations, formally the definition is $p$H = -log$_{10}(a_{H^+})$ where a is the activity. Activity is related to mole fraction X of a solute as $a = \gamma X$ where $\gamma$ is the activity coefficient and is effectively a correction to relate concentration to activity. (Activity arises because of the way the chemical potential is defined and it is the true property to use when using thermodynamics equations)

At low concentrations the activity and concentration are effectively equal, hence $\gamma \approx 1$ as here solutions behave ideally, but as concentration increases real solutions deviate from their ideal behaviour but the correct properties are calculated when the activity is used, in this case $\gamma >1$. Thus in concentrated acid solutions (for HCl > 2 M) the $p$H measured may not be that expected from a given acid concentration and this deviation will vary between different acids thus bear in mind that the actual [H$^+$] may not be what the $p$H indicates.
( Additionally, some very concentrated or pure acids may not dissociate completely, for example pure sulphuric and nitric acids are liquids, and thus for this reason also the $p$H may not be what one might expect.)