Ok, so here is a trick you can use for all the logs. Ex: say the concentration of H is 4*10^-3 and we want to know the PH. use those 3 quanitities:
1*10^ -2...........PH= 2
3.16* 10 ^-3...........PH= 2.5
1*10^-3...............PH=3
now, our question was 4*10^-3. so, 4 is between 3.16*10^-3 which had PH= 2.5 and 1*10^-2 which had PH= 2. Our answer is between 2 and 2.5
You always use the format above: 1. 1*10^ (- one less than your given power)...........PH= some number
2. 3.16 * 10 ^(- power given in the problem).......PH= some number.5
3. 1* 10 ^(power given in the problem)..............PH= some number+1
For your question, we work backwards. so we have 6.6 meaning the PH we work with based on what I explained are 6, 6.5, and 7
in other words: 1*10-6...........ph= 6
3.16*10^ -7............ph= 6.5
1*10^ -7..............ph=7 our answer is 6.6 so our choice is something between 1*10^ -6 and 3.16*10^ -7 but closer to the latter, so its closer to 3.16 and the correct choice of 2.5 is close enough.
I know it's not intuitive but once you get the hang of it, its awesome! so lets work backwards again on your same question, what is the PH of 2.5*10^ -7
our options are 1*10^(-6) or if it helps you more, write it as 10*10^ -7...,PH=6
3.16 *10^ (-7).....................................................................PH= 6.5
1*10^ (-7)............................................................................PH= 7
Now, ignore the power, just look at the number it is 2.5. our options are 1, 3.16 and 10. 2.5 is between 1 and 3.16 but closer to 3.16 so our options are the 3.16*10^(-7) and 1*10^(-7) so the [H] is somewhere between those, thus 6.6 is correct.
hope that made any sense at all.
