TBR pH question

[Meredith92]

This may be really easy and i may be completely brain dead from my practice test this morning, but for some reason i dont clearly understand how they got to this answer

This is from gen chem chapter four example 4.15
What is the pH of a solution where the hydroxide concentration is 10^6 times greater than the hydronium concentration?
A 4
B 6
C 10
D 13

"because the concentrations differ by a factor of 10^6 the pH and pOH differ by of 10^6 which is 6. If the pH is 10 then the pOH is 4, which are different by 6.... the answer is C"

I am trying to see how this works out mathematically
pH + pOH = 14
-log [H3O+] -log [OH-]= 13
-log[x]-log[x(10^6)]=13
But I'm kind of stuck at this point... what am I missin'? Thanks for your help

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[milski]

You are missing log(a*b) = log(a)+log(b).

Apply it for log(10^6*x).

pH+pOH=14
-log([H+])-log([OH-])=14
-log(x)-log(10^6*x)=14
-log(x)-log(10^6)-log(x)=14
-2log(x)=log(10^6)+14
-2log(x)=6+14
log(x)=-10
pH=10

 

[Meredith92]

Thanks as always

The only thing is the answer key did not go through that calculation (which makes sense now). They just simply stated "because the concentrations differ by a factor of 10^6 the pH and pOH differ by of 10^6 which is 6." How is this an obvious statement?

 

[milski]

Obvious is in the eye of the beholder.

I'd tell you to google the author and send him a nasty email but that probably is not the best idea.

 

[Meredith92]

haha you rock, milski. I'm gonna miss you when my mcat is over!!

 

[milski]

See you around for Step 1 then.

 

[dudewheresmymd]

See you around for Step 1 then.

SDN reunion in 2-3 years yall.