Ok sorta confused about TBR's weak acid equation

[argama]

Ok so in TBR's Acid and Bases Section, Equation (4.15)

pH = 1/2(pKa) - 1/2(log[HA])

I'm not sure what error I'm making but every time I use it I always seem to get the opposite sign for the "-1/2(log[HA])" part.

Simple example: 0.1 M of HA what is pH?
TBR says shortcut, which is pH = 1/2pKa + 0.5 which is fine but I wanted to see if I mathematically understood equation 4.15

so I did pH = 1/2pKa - 1/2 (log0.1) and log0.1 = log (1 x 10^-1) = 1 - log1 = 1

So I plug it back in and I get pH = 1/2pKa -1/2

Soo where am I screwing up my math? Because I'm obviously not getting pH = 1/2pKa + 1/2.....

Thanks, sorry if it's an obv question..

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[milski]

Ok so in TBR's Acid and Bases Section, Equation (4.15)

pH = 1/2(pKa) - 1/2(log[HA])

I'm not sure what error I'm making but every time I use it I always seem to get the opposite sign for the "-1/2(log[HA])" part.

Simple example: 0.1 M of HA what is pH?
TBR says shortcut, which is pH = 1/2pKa + 0.5 which is fine but I wanted to see if I mathematically understood equation 4.15

so I did pH = 1/2pKa - 1/2 (log0.1) and log0.1 = log (1 x 10^-1) = 1 - log1 = 1

So I plug it back in and I get pH = 1/2pKa -1/2

Soo where am I screwing up my math? Because I'm obviously not getting pH = 1/2pKa + 1/2.....

Thanks, sorry if it's an obv question..

This is your problem. log 0.1 = log(10^-1)=-1 (or in your way: log(1x10^-1)=log(1)+log(10^-1)=0+(-1)=-1

In general log(x)<0 for x<1

 

[BryanNextStep]

There are a bunch of different shortcuts you can use with logs but the MCAT doesn't really require a ton of precision, so I'd suggest that you just fudge it:

-log ( A x 10 ^ -B )

B - log A

It looks like you tried to use that "shortcut" but the mistake you made was that you dropped the minus sign. So you had:

log (A x 10 ^ -B)

In general for things that are a power of ten, you just pull down the exponent as the log:

log 0.001 = -3
log 0.01 = -2
log 0.1 = -1
log 1 = 0
log 10 = 1
log 100 = 2

etc.

 

[BerkReviewTeach]

A great technique for getting the pH of a strong acid (or pOH of a strong base) is addressed here.