By this point in time we have seen all the ps and all of the Ks. There are a lot of equations a ton of different possible calculations we can be asked to complete. To keep it all organized let’s briefly review the connection between the different values and look at some calculation logic.

Okay so there are a lot of arrows flying around on this concept map and it might be a bit intimidating at first but we are going to walk through each element step by step. Once you understand how each of the elements fits together this map makes a ton of sense and helps make acid-base problems much easier. Just take a couple moments to look the map over and get a general sense of what is going on.

To begin with, we will focus on the left-hand side of the map starting with the strong acids and bases. Since strong acids and bases completely dissociate their concentration is identical to the hydronium and hydroxide concentration in the solution. Once we have either of these we can calculate the other using Kw = [H^{+}][OH^{–}]. From here we can also calculate the pH or the pOH using pX= -log[X]. Or we can go the other direction from pH to concentration using [X] = 10^{-pX}. Here the X stands either for H or OH. Lastly, to convert between pH and pOH we can use 14 = pH + pOH.

If we now shift over to the right-hand side of the chart we will see a striking similarity between this and the strong acid side of the chart.

Starting at K_{a} and K_{b} the transition between the two is the same as between [OH^{–}] and [H^{+}]. K_{w} = K_{a} x K_{b} or 1×10^{-14} = K_{a} x K_{b}. Additionally interconverting between the K values and the pK values is the same as between OH and H and the pH and pOH. In both cases we will use the -log(K_{x}) to get to a pX and 10^{-pKx} to get back to the K_{x} values. Here x stands in for a or b. The one major difference between weak and strong acids is their inability to fully dissociate this means we need to use the Ka or Kb value of a weak acid or weak base plus its concentration to find the hydroxide or hydronium ion concentrations. From there we can find the pH or pOH of the solution depending on what the question asks for.

Now that we have a better handle on the concept map above lets trace out how we can solve several different questions using it. The specific workflows presented here aren’t meant to be comprehensive but give you an idea of the different ways that the concept map is useful when solving MCAT style acid-base problems.

For questions asking us to go from strong [Acid] to pH, we will need to first find the hydronium ion concentration. Since strong acids dissociate completely the strong acid concentration is identical to the hydronium ion concentration. From there we can use pH = -log([H^{+}]).

For questions asking us to calculate the pH of a strong base we will need to either end up at the hydronium ion concentration or the pOH. I prefer using the pOH method, but I have already presented it before so we will look at how to solve for the hydronium ion concentration. To begin we need to recognize that a strong base will completely dissociate so the hydroxide concentration and the strong base concentration are identical. From there we can use the Kw to calculate the hydronium ion concentration in solution. Sice Kw = [H^{+}][OH^{–}] and Kw = 10^{-14} the [OH^{–}] = 10-14/[H^{+}]. From there we can calculate the pH using pH = -log([H^{+}]).

For weak acid and weak base problems, we can no longer use the acid or base concentration in isolation in order to find the pH of the solution. Instead, we will need a K or pK value. For a weak acid we will need a Ka value and then can use the simplified equation to solve for the [H^{+}]. From there we convert the [H+] to pH using pH = -log([H^{+}]).

[latexpage]

\[

[H^+] = \sqrt{K_a \times [HA]_{initial}}\]

The acid base concept map is super helpful when working through a wide variety of acid base questions found on the MCAT. While first getting the hang of these types of questions have a copy with you so you can begin to see how all of the different concepts and calculations fit together.

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