OUWB Acid base question

The e-mail:

Hi Dr. Topf,

We were going through the acid-base study guide and Prince Harry has us all out of sorts. His scenario is this: 

Your first mistake. It is Prince William not Harry. Know your Royals. (Though I do not think royal genealogy is a board eligible topic.)

7.42 | 32 | 76
Na – 148
Cl – 98
K – 5.8
HCO3 – 28 

For the primary acid-base disturbance, I would think it is respiratory alkalosis because the pH is elevated, the PCO2 is decreased, and the HCO3 is elevated.  

You are correct

Then for the second acid base disturbance, I thought it would be metabolic alkalosis. His PCO2 is 32, which is down about 10. So, his bicarb should go down either 2 if acute or 4 if chronic, to either 22 or 20. Instead it is 28 which means he has excess HCO3 (base) and so has an additional alkalosis. 

Correct again

I tried doing the anion gap (22) and the bicarb before (38) but my understanding is that a bicarb before of 38 would also be metabolic alkalosis.  

Yes

In the answers, it says that if you have an AG with alkalosis or a primary acid-base disorder, that it would be an acidosis.  

If you have time, can you help me understand why his primary disorder is metabolic alkalosis, and how to apply the anion gap and bicarb before formulas to this case?  

Thanks for your time. 

Best regards,

This refers to this question in the handout:
There is an error in the ABG. Using the Henderson Hasselbalch equation it is obvious that this ABG is impossible, as pointed out by +MedCalc on twitter:

@kidney_boy Threw @medcalc at it. Don’t know how HCO3 could be 28 as Henderson (The Law) says it should be 21. pic.twitter.com/ilqD1l3Qec
— MedCalc (@MedCalc) August 23, 2014

So the actual pH should be 7.51. But that doesn’t change the rest of the answer or the calculations.
To get this problem right, it breaks one of the rules I established and uses another rule that was not discussed. This is failure on my part and I will fix this.
The rule that it breaks is the rule that compensation is always in the same direction as the primary disorder. Obviously with a pCO2 of 32 and bicarbonate of 28 the two independent Henderson-Hasselbalch variables are moving in discordant directions.
This is a great guideline, it just isn’t always true. In cases where patients have two primary disorders the pCO2 and bicarbonate can move in opposite directions. This is not the typical finding but when it occurs it is simple to interpret:
If the pCO2 falls it is respiratory alkalosis and if it rises it is respiratory acidosis. If the bicarbonate falls it is metabolic acidosis and if it rises it is metabolic alkalosis. So in the case of Prince William, his bicarb is up and pCO2 is down so he has both a metabolic and respiratory alkalosis. The reason I do not include this is that it is an additional complexity that if you follow the algorithm that I taught you will get the right answer without knowing this exception. I choose to streamline the teaching rather than teach this shortcut.
The rule that was not discussed is in regards to the anion gap. In my booklet I never discuss that the presence of an anion gap regardless of the pH or serum bicarbonate always indicates a metabolic acidosis. The hierarchy of acid interpretation that I showed in the booklet should include that right at the top and has been updated to reflect that:
So Prince William is rocking an anion gap of 22, this means he has an anion gap metabolic acidosis. If you use the bicarbonate before formula you see that his bicarbonate was 38 excluding his anion gap metabolic acidosis indicating a truly wicked metabolic alkalosis.