acid and base log question

[medscholhopeful]

arrgg!! this is the part of gen chem i absolutely cannot stand... working those silly PH questions with no calculator.. i have found a lot short cuts with TBR but still some questions....

How do you solve for the H30 concentration when given the PH. Eg PH of so and so acid is 2.24 what is h30 conc..i know the set up eqn should be
H3O=10^-2.24 (now how do the heck do u break this down without a calculator???? n e shortcuts pls!!!). thank you

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[loveoforganic]

10^-2.24 = 1/10^2.24, so you're looking for a number a little smaller than 1/100

lots of rounding.

 

[kentavr]

or
1. 10^-2.24 = 10^-2 * 10^-0.24 = 0.01* 10^-0.24
2. 10^-0.24 = 1/10^0.24
3. 0.24 ~ 0.25 = 1/4 ==> 10^0.24 ~ 10^1/4
4. estimating 10^1/4: 2^4 ~16>10 too much but close then
Ans ~ 0.01 /2 = 0.005

May be too long, but that's how i would do it.

 

[ThirdEye]

Memorize what I have on the left. What is on the right is only for verification

10M strong acid is pH -1 ........ 10^-(-1) = 10
1M strong acid is pH 0 ....... 10^-0 = 1
.1M strong acid is pH 1 ....... 10^-1 = .1
.01M strong acid is pH 2 ........ 10^-2 = .01
.001M strong acid is pH 3 ....... 10^-3= .001

pH of 2.24 has to be smaller than .01 but larger than .001 and I doubt the MCAT would have more than one answer in this range.