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# 8.2 pH and pOH of Strong Acids and Bases

Dylan Black

## pH and pOH Explained

pH and pOH are topics in unit 8, and AP Chemistry as a whole, that are extremely important. So then, what is pH? pH simply is a measure of the concentration of protons in a solution.

### pH

Essentially, pH is measured by the concentration of H+ ions, meaning it measures how acidic a solution is. A higher pH means a lower concentration of H+, implying a more basic solution and vice versa (I know, that's really annoying). So we get why there's the H in pH - H means hydrogen, pH measures the concentration of hydrogen ions - but what's that p? In chemistry, 'p' is a symbol that means negative log. p(anything) = -log(anything). Thus, pH = -log([H+]). For example, if we had a solution that had 0.01M H+, that would mean pH = -log(1 * 10^-2) = -(-2) = 2 (note that log() implies log base 10).

### pOH

If pH = -log([H+]), then one can logically find that pOH = -log([OH-]) and is in essence the opposite of pH. Where pH is measured with the concentration of H+, pOH is measured with the concentration of OH-. pOH measures how basic a solution is. A low pOH means a highly basic solution and vice versa.

## The Autoionization of Water

Let's suggest we had the reaction OH- + H+ --> H2O. This can be described as the protonation of OH-, or the autoionization of water. This is an important reaction, as it also serves as the net ionic for a strong acid-strong base interaction. This reaction can further be described using equilibrium by flipping the reaction to say that H2O ⇌ OH- + H+. The K value for this reaction is a constant called Kw. Kw = 1 * 10^-14.
Let's think about this reaction a little bit. From Kw that we were given before, we can write that Kw = [OH-][H+]. Therefore, 10^-14 = [OH-][H+]. Now, let's take the negative log of both sides:
14 = -log([OH-][H+]) = -log([OH-]) + -log([H+])
From here it is clear then that pH + pOH = 14.

## pH/pOH of Strong Acid and Strong Base Solutions

### Finding the pH of Strong Acid/Base Solutions

For these examples, we're going to be looking just at pH since that's the most common measure of acidity, but remember, pOH can be easily calculated from this. When dealing with strong acids (and by extension strong bases), what's important is that these reactions go fully forwards. That is to say, they have a K value so high that to call it an equilibrium is negligable. Therefore, all of the acid/base will dissociate. Let's take a look at an example.
Suppose we have a 1M solution of HCl. The dissolution of HCl looks like: HCl --> H+ + Cl- (we're gonna stick with the Arrhenius definition of acids to make things simpler). Because this reaction goes completely forward, we know that 1M of HCl will dissolve into 1M of H+ and 1M of Cl-. To find pH, we take the -log([H+]).
pH = -log(1) = -0 = 0. Therefore a 1M solution of HCl has a pH of 0.
The same idea applies to strong bases. Suppose we had 1M NaOH. NaOH --> Na+ + OH-, so pOH = -log([OH-]) = -log(1) = 0.
To find pH we then plug into pH + pOH = 14, which tells us that the pH of a 1M solution of NaOH is 14.

## The List of Strong Acids

There are 7 strong acids you need to memorize for AP Chemistry. Luckily, they're not that bad and they become second nature after a while. Here is the list:

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