6.6 Weak Acids and Bases - log calculations

[bonga1]

Thanks for the response; I understand that.

But I still dont understand the relevance of the wording in the book: "The wording says "....once you know the squares of all numbers between 1 and 15. the root of 1.69 (a fair estimate of 1.75) is thus 1.3...."

Am I correct that this information is irrelevant to the calculation and should really be deleted?

[goldstanda3269]

Am I correct that this information is irrelevant to the calculation and should really be deleted?

Not so much deleted, but perhaps reworded:

....once you know the squares of all numbers between 1 and 15, the root of 1.75 can be adjusted to 17.5 (a fair estimate of 16) and thus provides a result that is a bit higher than 4 ...."

[tom.greato8362]

Re calculation of -log (4.18 x 10^-4)= 3.38. Does anyone have any advice on how to hand calculate this? most ways i have found do not come close to getting a answer as precise as the one documented.

[goldstanda3269]

Re calculation of -log (4.18 x 10^-4)= 3.38. Does anyone have any advice on how to hand calculate this? most ways i have found do not come close to getting a answer as precise as the one documented.

There is no way to "hand calculate" 3.38. Perhaps we should have made it more clear: We tried to explain in 6.6.1 (page CHM-149, Masters Series) that a question based on that calculation would have, as an example, 4 multiple-choice answers sufficiently far apart such that your calculation only needs to determine if the pH is between 2 and 3, or between 3 and 4, or between 4 and 5, etc.

The key is to use log rules to reduce:

-log (4.18 x 10^-4)

to

4 - log 4.18

...which must result in a number between 3 and 4 (as shown at the end of CHM 6.6.1).

Suggestions: The practice questions at the end of the chapter (especially questions 20, 21, 22, 23, 26) and, of course, the Spoiler Alert section which also has a few similar calculations using ACER's materials.

FYI, our next free webinar will be next weekend: https://www.gamsat-prep.com/GAMSAT-free-online-seminar/

[sarah.pl.a8144]

Hi ,
Please could you explain how we arrive to the answer of pH = 3.4 from -log 4.2 x 10^4 - example used on CHM147 & 148 to explain the application of ICE . Many thanks

[goldstanda3269]

Hi ,
Please could you explain how we arrive to the answer of pH = 3.4 from -log 4.2 x 10^4 - example used on CHM147 & 148 to explain the application of ICE . Many thanks

-log (4.2 x 10^-4) = -[log (4.2 x 10^-4)] = -[log(4.2) + log10^-4)] = -[log(4.2) - 4)] = -log(4.2) + 4

And so we have: 4 - log(4.2)

We can reason that log(4.2) is a number between log 1 (which is 0) and log 10 (which is 1), thus log(4.2) is a fraction. The expression "4 - log(4.2)" means that we are subtracting a fraction from the number 4.

Thus we can confidently say that -log (4.2 x 10^-4) is a number between 3 and 4. This is enough information for a multiple choice exam since ACER would normally only have one reasonable response.

Note that the log rules used above are needed to solve ACER's GAMSAT Practice Test 3, Section 3, Questions 109 and 110.