MCAT Math

[spyderracing32]

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Now I know the general math topics that the MCAT wants you to be familiar with, however as I do content review with the Princeton review book it got me to wondering just how far they are expecting you to take it. For instance:

Given the pKa of HCN is 9.22, what is the pH of a 0.10M solution of HCN?

Now this isn't too hard to figure out with a calculator, but when it comes down to it you have to take the square-root of 6.02*10^-11. Are we expected to be able to do this?

 

[engineeredout]

Yes. Its actually not that difficult. The square root means raise the entire thing to the 1/2th. Convert it to 60.2*10^-12 so the square root will involve (10^-12)^1/2 = 10^-6. You can also estimate that the square root of 60 ~ 8, so you can approximate the answer as 8 X 10^-6. There should be an answer choice close enough to that number that you'll know.

By the way the calculator says 7.8 X 10^-6, so its pretty damn close.



Definitely make sure you get practice with multiplying and dividing exponential numbers.

 

[spyderracing32]

Nice haha that's pretty nifty.

 

[Turtlespeed]

Can somebody explain how to do this problem from the start??

 

[Turtlespeed]

bump

 

[anbuitachi]

Given the pKa of HCN is 9.22, what is the pH of a 0.10M solution of HCN?

correct me if im wrong, but HCN is a weak acid, so the pH of that is approximately

9.22/2 - (log .1)/2 = 4.61 - (-1)/2 = 4.61 + .5 = 5.11

Where did the 6.02*10^-11 come from?

 

[Turtlespeed]

You are correct, and the sqrt of 6.02e-11 corresponds to ph5.1, but what was the formula to get that

 

[fullset]

pH = (0.5 pKa) - (0.5 log [HA])

Thanks to Berkeley Review, and their practice passages, I am able to do these problems in <30 seconds! By the way, I looked up similar problems in my G.Chem text I used in undergrad, and most of them have solutions ~1.5 pages!