Below is the written transcript of my YouTube tutorial video pH/pOH [H+]/[OH-] Wheel .
Leah here from leah4sci.com/MCAT and in this video I’ll take you through the pH pOH wheel to intraconvert between different acid base calculations. In the previous videos we looked at the basics, the logic for acids and bases and we also started with the calculations. We know that pH is equal to negative log of the H+ concentration and that pOH is equal to the negative log of OH concentration. We also looked at the kw which is equal to the concentration of H+ times OH- which is equal to one times ten to the minus fourteen at room temperature twenty five degrees Celsius. And then we took the p of this equation and got the pkw which is equal to pH plus pOH equals fourteen again at twenty five degree Celsius.
But let’s not forget our ka calculations and our kb calculations. Do you see where this starts getting overwhelming. You have to know the individual equations because if you’re given some data and ask to calculate something, you have to know how to do that on your MCAT. But then the question is, what if you’re given something that isn’t straightforward that you can’t simply pick out one of these calculations?
For example, if I give you an H+ calculation and I ask you to find the pOH? Or I give an OH minus calculation and ask you to find the pH? None of these equations have H+ to pOH or OH- to pH. So you have to ask yourself, which equation do I know that gives me part of the way. And then where can I take that data to give me rest of the way? But instead of thinking of these as unconnected facts, I wanna show you how to bring all these calculations together. And that brings me to the pH pOH wheel.
If you’re an H+ concentration you should know how to turn that into a pH. And if you’re given a pH you should know how to turn that into an H+ concentration. And that equation is that pH is equal to negative log of your H+ concentration, use it forwards or backwards depending on what you’re looking for. The same concept comes up if you have an OH- concentration and you’re asked for a pOH or if you’re given a pOH and asked for the OH minus concentration. And that equation of course is that pOH is equal negative log pOH minus concentration.
Now what ties the H+ and the OH- concentrations together? It’s the kw, one times ten to the minus fourteen. In other words, if I have the H+ concentration, using the kw I can find OH- and if I have the OH- concentration using kw, I can find H+. And what ties the pH and pOH together? that’s the pkw. The number 14. So if I have the pH, I’ll subtract it from 14 to get the pOH and if I have the pOH, I subtract that from 14 to get the pH.
Now here’s how you want to think of this, if you know individually how to go from one to the next, ask yourself, what am I given and what is the quickest or most efficient route around this wheel to get to where I need to go. So if you’re given an H+ concentration and you’re asked to find the pOH, I can go around the wheel clockwise or counter-clockwise. They’re both equidistant because it’s the exact opposite point of the wheel. But which one is more efficient? Which one will give you there faster and potentially with the least aggravation.
I don’t know about you but I don’t like using exponents and decimals and tiny numbers. I would much rather deal with big numbers. So if I’m given an H+ concentration, I find it easiest to go for the pH and then subtract that number from 14. Same thing if you’re given an OH- concentration and you’re asked for the pH. You can go around this way to go from OH- to H+ concentration and then find the pH or simply find the pOH and subtract it from 14 to find the pH.
Let’s keep this wheel on the corner as we try a couple of simply examples. So for example if you’re told to find the pOH of a one times ten to the minus three molar HCl solution, you have to ask yourself, which way do I want to go around this wheel? If I’m given a concentration of HCl knowing that it’s a strong acid and it breaks up nearly a hundred percent, my H+ concentration is equal to one times ten to the minus three and starting with the H+ concentration, I can go clockwise, or counter-clockwise. Let’s start with the more difficult method going clockwise first. And we’ll use the equation H+ concentration times OH- is equal to kw.
Since I’m solving for the OH- concentration, I want to divide both sides by the H+ concentration and that gives me an OH- concentration that is equal to one times ten to the minus fourteen divided by one times ten to the minus three. How do we solve this without the calculator? We simply subtract negative fourteen minus negative three which becomes negative fourteen plus three or negative eleven. And the OH- concentration is equal to one times ten to the minus eleven.
Now I specifically chose easy numbers to show you the process but imagine the numbers were more complicated and you had extra levels of calculation here, hopefully you’ll see how potentially complicated this process is and we’re not even done. Now we have to find the pOH which is equal to negative log minus concentration or negative log of one times ten to the minus eleven. We’ll use the trick that I teach in my Math series where take the exponent and negate it so negative eleven gives me a pOH that is equal to eleven. Now this was one way to do it.
The other method going counter-clockwise from H+ to pH to pOH is much easier because we’re limiting the calculations that have to do with scientific notations and exponents. If we know that the H+ concentration is equal to one times ten to the minus three then we can say that the pH is equal to negative log of the H+ concentration of one times ten to the minus three, the trick is negative three, negate it, pH is equal to three. And since pH plus pOH is equal to pk or 14 then 14 minus the pH of 3 is equal to 11 and that is equal to the pOH. Same calculations, same concept but not only this is faster, it’s so much simpler. And on the MCAT the more you can limit your stress the more you can keep your confidence for the remainder of the exam.
Let’s try another example. Here you’re told to find the pH when 0.07 mol of NaOH are dissolved in 700 ml of H2O. So let’s see how we’re going to approach this. We’re told to find the pH, so that’s our destination. But we’re given a number of mols of base dissolved in water which we can use to find the concentration of OH-. It’s completely opposite on the wheel so let’s go the more difficult route first where we’ll go from the OH- to the kw to find the pH. But first we have to find the molarity. If we have 0.07 mols of the strong base that means that’s the number of mols of OH- dissolved in 700 milliliters or simply 0.07 liters of solution. We use this to find molarity because molarity is equal to mols per liter. I’m dealing with decimals, I’m dealing with fractions way too complicated.
Let’s simplify this by moving the decimals ones to the right for the numerator and denominator, again another trick I teach in the MCAT Math series and this gives me 0.7 divided by 7 mols per liter or molar and I can simplify further by saying that 7 over 7 cancels out, that gives me point one over one or simply 0.1 molar OH-. Now that I have the OH- concentration I wanna use the kw to find the H+. If H+ times OH- equals kw, then I have to divide both sides by the OH- concentration to isolate the H+. And this gives me an H+ concentration that is equal to kw divided by the OH- concentration. H+ is equal to one times ten to the minus fourteen divided by 0.1.
Typically I don’t like dealing with scientific notation but if we’re dividing something that has an exponent, ideally we want an exponent in the denominator as well. This way we can subtract the exponents to get the answer. Point one molar is one times ten to the minus one which means when we subtract negative fourteen minus negative one or negative fourteen plus one we get an H+ concentration of one times ten to the minus thirteen. And if this is the H+ concentration, we know that the pH is equal to negative log of one times ten to the minus thirteen, take your exponent, negate the sign and pH is equal to 13. Simple, straightforward but potentially too much work.
Let’s see if we can do this a faster way. And when I use to recognize that the other direction is the faster way. We want to go from OH- to pH. The OH- concentration is equal to point one molar which is equal to one times ten to the minus one. It’s important for you to recognize that this is the same thing because then when I setup the equation of pOH is equal negative log the OH- concentration. When I plug it in in scientific notation I just pull the exponent, negate the sign and the poH is equal to one. If pH plus pOH is equal to 14, then 14 minus 1 equals thirteen and that is equal to my pH. Same answer, same number of sets but it’s so much faster when you’re minimizing the use of exponents.
Be sure to join me in the next video where we look at the acid base properties of salt solution. You can find this entire series along with the reference Math videos, a practice quiz and cheat sheet by visiting my website leah4sci.com/MCATAcidBase.
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