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 http://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 http://leah4sci.com/MCATMath. You can find additional MCAT videos including

Physics, Chemistry, Biology and Organic Chemistry on my website http://leah4sci.com/MCAT

Are you stuck on a specific MCAT topic? I offer Private Online Tutoring where I focus

on your needs to strengthen your individual weaknesses. Tutoring details can be found

using the link below or by visiting my website leah4sci.com/MCATTutor.

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nice. Its really helpful for my future MCAT exam.

where is you video on buffers?

Great video. May I recommend, for continuity with the previous video (MCAT Math Vid 8,) that at 3:40 you flip the table? i.e. in the previous video, the "#.1" was on the bottom, though in this video, it is on the top. That made this video a bit more challenging to follow (since I just watched the previous before this.) Thank you again for all of your help.

Your videos have been very helpful, thank you! Can you help me understand how you decided that the x exponent would equal 5 at 3:53. Please advise, thanks!!

im confused on why it is to the -5th power not -4th

@Leah4sciMCAT Hi Leah! I love your videos! I was a bit confused in this video around 4:04. You didn't mention how you determined that the exponent is going to be -5 and not -4 or some other number. Thanks!

I realize this question has been asked before, but I don't think you gave a satisfactory answer. Since our desired number has the exponent lying between 4 and 5, why did you pick 5 instead of 4 as the exponent? In other words, why didn't you pick our value ranges to be between: 5 x 10^-4 and 8 x 10^-4? How did you know to go with -5 instead of -4 as the exponent?

Around 4:04….same question most other people have.

Same question Jennifer, Natalie, and meowismeify asked below. You do not explain how you arrived at the exponent 5 instead of 4. I'm not sure how else to ask the question. What part of my questions don't you understand? The desired value lies between two exponents (4 and 5), and you picked 5. However, you do not provide a rationale for why you picked 5 instead of 4 or why you did not pick 4. As mentioned. the same question has been asked by 3 other people, but you haven't yet answered the question.

You are the best online teacher I ever known.Thank you.You really helped me

Omg i got so confused , your previous video was clearer…

how did u round to X10^-5 …. ?????

4.19 is closer to X10^-4

Hi Leah, I really like your video very much and they help a lot! But I just have one question toward the end of the video: isn't 6.46 x 10^-5 actually closer to 5 x 10^-5 instead of closer to 8 x 10^-5 (I think you said it's closer to 8 x 10^-5)? In this case if there are 2 answer choices between 5 x 10^-5 and 8 x 10^-5 how do I know which one it is?

Hello, love your videos, but I am very confused. I get up to the point where the Ka is in the range between 1×10^-4 and 1×10^-5 and am confused with the final answer you get. Isn't 6.46×10^-5 larger than 1×10^-5 therefore being out of the range??

Basically what people are asking (I think), and which I'm also a little confused by, is at 4:27 where the answer is somewhere between 5×10^5 – 8×10^-5. I would have reasoned the range to instead be 5×10^4 – 8×10^4. I know this isn't right, but I don't see a logic behind why you chose the former (and correct) answer.

Hello, how can I approximate 1×10^-5.4 or any 10 to a negative decimal? the answer is 3.9 x10^-6 but how?

Hey +Leah4sciMCAT,

Great video! one question though. At 5:02 you fine tune your answer saying it should be closer to 8×10^-5, because .19 is closer to # .1 than to # .3, however the answer is actually closer to 5 x 10^-x. What there a mistake?

Hello, I know you have tried to explain this before but I do not understand it. Why do you choose an answer between 5X10^-5 – 8X10^-5 instead of 5X10^-4 – 8×10^-4 ?

this is amazing for gamsat prep!!

At 4:15 mark I believe you misspoke when you said "point 1 gives me an 8 and point 5 gives me a 5". I think you meant to say "point 1 gives me an 8 and point 3 gives me a 5". Due to the fact that you rounded 4.19 to 4.2 and (.2) lies half way between (.1) and (.3), which would then give the (8 x 10^-x) and (5 x 10^-x) values you use later in the problem.

is nice this tips improve my math

this video is very confusing last one is very clear

kindly explain once again please

Your videos are amazing, what a huge help. Thank you Leah 🙂

Goes a little off the rails in the second half.

This video got confusing after 5:02

Thank you seriously so much. This was unbelievably helpful

i understood the first part now am confused how to calculate negative log of 5,7 or any decimal am not able to fig out

please explain

Thanks you are great!

Allthough I hope you can make worksheets with practice questions, to further aid us 🙂

Get the gist thanks, just got confusing at the end

Hey Leah, I think you should delete this video and remake an updated version to cover some important points that you might have left out

Log has never been this easy for me

Hi Leah, why did you end up going for 10^-5 for the pH= 4.19 problem? We had two options of 10^-4 and 10^-5 when you explained that we need to round down and up to 4 and 5, respectively. but it wasn't explained why -5 was a better answer choice. Why did we go for 5?

NICCCEEEE !!! Thank you.

(1) 4.19+ 0.15=4.33 (Always add constant of 0.15 to your pKa value)

(2) 5.00-4.33=0.67 (increase the given pKa to the whole next number and subtract from that whole number answer you get from step 1)

(3) 0.67 x10 = 6.7 (always multiply whatever number you get by 10)

(4) 10^-5 ( one thing to note your 10^- number will be alway one digit higher than given pKa value)

(5) 6.7×10^-5

Hope it helps everybody.

Calc: 6.46×10^-5 .

I think what people are confused is to why the -4 wasnt selected and why -5 was. Yes its because the pH would of have to been 3.19 but how can we calculate to know that? And eliminate -4.

Leah 3:58 please explain why you chose 8 x 10^-5 instead of 8x 10^-4. I watched all the other videos in this series and took notes based on your videos, but I don't understand why you chose -5 instead of -4.

I too was confused about the 10^5 thing but then I re-watched your last video again and it mostly makes sense.

3:45

Rounding Ka up to -4 and down to -5:

Ka of 5 gives a pKA of 1 x 10^-5

Ka of 4 gives a pKA of 1 x 10^-4 ——> but really we should look at it as 10 x 10^-5

So that's why we use 10^5, which is confusing because the Ka starts with a 4 (4.19)

Now since 4.19 is effectively 4.2, we don't have the pKa value for the Coeffient of .2 (again, the .2 is from 4.2), but we have the values for

.1 = 8 x 10^-x

.3 = 5 x 10^-x

So the final pKa answer would be between 5 x 10^-5 and 8 x 10^-5

which is a much more narrow range than 1 x 10^-5 and 10 x 10^-5

Confusing.

why did you go with the ^-5 and not ^-4?