Below is the transcript of my tutorial video MCAT Math Video 9 – Antilogs
Leah here from Leah4sci.com/MCAT and in this video, I’ll show you how to solve MCAT style Antilogs questions without a calculator. This video picks up from my last video where I show you how to solve logarithm based questions and you can find this video alongwith my entire series on solving MCAT Math without a calculator by visiting my website https://leah4sci.com/MCATMATH.
In the last video I showed you a trick on how to find a pH, pOH or pKa value when given a concentration or ka. The trick showed you that when you have a number times ten to a negative power, that power becomes your pka, your pH or your poH.
But what if now you are faced with a question where the actual pH, poH or pka value is given and you’re ask to find the concentration or the ka? For example you maybe given a question that says:
Find the ka of an acid whose buffer has a pH of 4.19 in a solution containing equal moles of acid and conjugate base.
I’ll cover the Science portion of this question in my Chemistry videos at leah4sci.com/MCATCHEMISTRY but for this video let focus just on the Math. Since we’re dealing with a buffer we’ll use the Henderson–Hasselbalch equation which says that pH is equal to pka plus the log of Conjugate base over acid.
You’ll also see this written as A minus over HA. Even though we have equal moles of acid and conjugate base or fifty-fifty, whatever number we have for conjugate base is the number for acid and that means we have a ratio of some number over itself or one.
The log of one is zero and that means this entire portion of the equation drops out telling me that the pH is equal to the pka. Knowing that the pH is equal to 4.19 equals the pka we know the pka is also equals to 4.19. But how do we use this to find the ka value of this acid? 4.19 is not a clean and easy number to calculate so let’s break it down:
The first thing you want to do is check how close your answer choices are to each other to see how much you can simplify and how quickly you can come up with the answer. Here’s the equation we’ll use. If pka is equal to negative log of ka (pka= -log ka), since log stands for log base ten, to solve for ka we have to have ten to the power of negative log to cancel out and that means we need ten to the power of negative pka. So the ka value is equal to ten to the minus pka which is equal to ten to the minus four point one nine (ka = 10^pka = 10^-4.19).
A nice and clean number like four would give us a ka value of one times ten to the minus four. But we also have to account for that 4.19 so we don’t know we’re looking for the number close to one times ten to the minus four. If this is not enough to isolate your answer, you then want to find the range where your ka will fall out.
We’ll take the number 4.19 and round it down to 4 and up to 5. A pka of 4 has a ka of one times ten to the minus four, a pka of 5 has a ka of one times ten to the minus five. That means the number we’re looking for is somewhere in this range. But if this is still not enough, then you wanna go back to the trick where I showed you how to recognize the different numbers that give you different ranges. In review, if we have a number point one we get an eight time ten to the minus x. And I put x instead of the number because if we have 4.19 our exponent will be a number times ten to the minus five. So if we had 4.1 it will be eight times ten to the minus five.
A number point three will be five times ten to the minus that power. In this case, if we have 4.19, let’s round that to 4.2, remember on the MCAT you are allowed to round because it will be close enough. If point one gives me an eight and point five gives me a five then our answer has to be somewhere between eight and five so all you have to recognize is that the number is somewhere between five and eight. So it’ll be five times ten to the minus five to eight times ten to the minus five.
Even if we haven’t narrowed in on a specific number, for the MCAT this is close enough. In fact, punching ten to the negative four point one nine in the calculator I get an answer of 6.46 times ten to the minus five which on the MCAT is close enough. If you wanna narrow this down a little more, 4.19 is closer to 4.1 than it is to 4.3 and that means we’ll be closer to the 8 than to the 5 as is evident by 6.46.
This concludes my video series on MCAT Math Without a Calculator. You can find this entire series on my website at https://leah4sci.com/MCATMath. You can find additional MCAT videos including Physics, Chemistry, Biology and Organic Chemistry on my website https://leah4sci.com/MCAT
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Watch the Video Here: MCAT Math Video 9 – Antilogs