Problem Statement
Rank the following 0.10 M solutions from lowest to highest pH:
a. b. c. d. e. f. g.
We have 7 compounds. To create a complete ordering, you could compare each compound to every other, making in total comparison. That’d be a brute-force approach. What you could also do is recall that inorganic compounds can be categorized into ~5 main groups (see notes on Arrhenius Theory of Acids and Bases), and here we have instances of 3 of those: acids, bases, and salts. In short, an acid must have as the cation, a base must have as the anion, and a salt is formed when an acid reacts with a base. Within Arrhenius, any acid has a lower pH than a base, so if we group compounds first into acids and bases we would reduce the number of comparisons required simply because we wouldn’t need to compare acids to bases; it’d be enough to compare acids to acids. It also helps to recognize that if salts are formed from acids and bases, they would have a pH that is somewhere in between the pH of an acid and a base.
Okay, so let’s categorize each compound:
- acids:
- bases:
- salts:
Acids have pH lower than salts, which in turn have pH lower than bases.
Good, now let’s do in-group comparisons.
Comparing Acids
Consider acids first. You have to know that both and are strong acids on first dissociation. Meaning that if you take 0.10 M of HCl and H2SO4, you’ll have in case of HCl and you’ll have in case of H2SO4. can dissociate further into and . The dissociation will not go completely, but even if it goes to a very tiny extent, you’ll get some extra from the second stage, let’s call it , and so your total . is greater than , so you’ll have more ions in H2SO4 than in HCl, and so the former will have a lower pH than the latter.
This establishes that the pH row goes as:
Comparing Bases
Let’s now look at bases. Both and are strong bases, meaning they dissociate fully. The only weak base in Arrhenius theory is . Thus, in the solution of NaOH and in the solution of Ba(OH)2. Thus, the latter has lower pOH than the former. Given an inverse relationship between pH and pOH, the latter should have a bigger pH.
This establishes that the pH row is:
Comparing Salts
How do we determine the pH of salts? We have to consider which acid and base formed that salt. There are 4 cases:
- a salt formed from a strong acid and a strong base. Example: ( is a strong base, is a strong acid). Such salts have a neutral pH of 7.
- a salt formed from a weak acid and a strong base. Example: ( is a strong base, is a weak acid). We could have a mnemonic rule that a stronger ion dominates, and so the acidity of the solution is determined by the stronger ion. Here, stronger ion is the as it comes from a strong base, so the solution will have a slightly basic pH . Chemically, it is considered that dissociates into ions , ; nothing happens to sodium while the acetate ion is weak and can partially deprotonate water:
which increases the concentration of $\ce{OH-}$, which means that pH increases. - a salt formed from a strong acid and a weak base. Example: ( is a weak base, is a strong acid). Mnemonically, a stronger ion is as it comes from a strong acid, so it dominates and the solution is slightly acidic, meaning . Chemically, the ion can dissociate:
which increases the concentration of $\ce{H+}$ ions and so decreases the pH. - a salt formed from a weak acid and a weak base. Such salts are actually quite often either insoluble, or unstable towards hydrolysis, so I’m not going to talk about them a lot.
Using the arguments above, we can conclude that the order of pH is:
Given that the pH of acids is lower than that of salts, and the pH of salts is lower than that of bases, the final order is: