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Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: MitchTwitchita on February 02, 2008, 09:38:34 PM

Title: Acid-Base Equilibrium
Post by: MitchTwitchita on February 02, 2008, 09:38:34 PM
A 0.44 M solution of a weak base B has a pH of 11.08.  The equation for ionization is B(aq) + H2O ---> BH+ + OH- 
What are the BH+, OH-, and B concentrations at equilibrium?  Calculate Kb for the base.

O.k. so, would 0.44 be the concentration for B?

BH+ = 10^-11.08 = 8.32 x 10^-12

OH- = 1 x 10^-14/8.32 x 10^-12 = 1.20 x 10^-3

Kb = [BH+][OH-]/B
= (8.32 x 10^-12)^2/0.12 - 8.32 x 10^-12
=5.77 x 10^-22 ?

Somehow I think I'm doing this problem wrong.  Can anybody please show me what I'm doing wrong?
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 03:20:49 AM
BH+ = 10^-11.08 = 8.32 x 10^-12

This is [H+] not [BH+]. Now what can you tell about [BH+]?
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 01:46:34 PM
I think you would have to add the B in order to get the concentration of BH+ but the number 8.32 x 10^-12 is so nominal it doesn't even contribute. 
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 02:12:24 PM
I think you would have to add the B in order to get the concentration of BH+ but the number 8.32 x 10^-12 is so nominal it doesn't even contribute. 

 ???

Your calculation of [OH-] is correct. For 1 mol OH- how many moles BH+ are formed?
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 02:15:48 PM
1
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 02:42:25 PM
correct  :)
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 02:52:26 PM
I'm afraid I don't understand where you're leading me.  Surely, BH+ doesn't have the same concentration as OH-?
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 03:06:57 PM
Why not? I confess, I neglected the self-ionization of water and assumed that the pH was not changed by adding a different acid/base.

Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 03:12:47 PM
The autoionization of water is assumed to be negligible.  If the concentrations of BH+ and OH- were the same, wouldn't that make the solution neutral? 
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 03:19:31 PM
neutral means [OH-]=[H+]=10-7 mol/l
we have [OH-]=[BH+]=1.2 * 10-3 mol/l
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 03:31:39 PM
Kw = (Ka)(Kb)

1 x 10^-14 = (BH+)(1.20 x 10^-3)
BH+ = 1 x 10^-14/1.20 x 10^-3
=8.33 x 10^-12

wouldn't this be the way that BH+ would be calculated?

Title: Re: Acid-Base Equilibrium
Post by: Borek on February 03, 2008, 03:56:13 PM
BH+ is not the same thing as H+.
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 03:56:22 PM
Ok, I'll start from the beginning.

You have the equilibrium
B + H2O (https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww.forkosh.dreamhost.com%2Fmimetex.cgi%3F%5Crightleftharpoons&hash=157e2a14e3d1ec4923b187ed514226fe1ec08b02) BH+ + OH-

(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww.forkosh.dreamhost.com%2Fmimetex.cgi%3FK_b%3D%5Cfrac%7B%5BBH%5E%2B%5D%2A%5BOH%5E-%5D%7D%7B%5BB%5D%7D&hash=7cf029a8f3b3bf2936b7a98da2d517e077ab52c8)

The value of Ka is not of interest here. Just for you to understand, try to set up the equation for Ka. Which equilibrium is described by Ka? (remember conjugated acid/base pairs)

Ok. Let's go on. We know that every OH- comes from the dissociation of the base (neglecting self-ionization of water). From the reaction equation we see that for every OH- ion we also get one BH+ ion. So [OH-] must be the same as [BH+]. The pH is given, so we can calculate [OH-] resp. [BH+]
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 04:01:25 PM
Oh man, I got it now!  my malfunction was confusing BH+ with H+.  The Ka would be [BH+][OH-]/H2O.  Thanks a lot, you've been a very big *delete me*
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 04:03:18 PM
Why did the last post say *delete me* for help?  Anyhoo, the rest of the answers were right though?  Thanks again!
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 04:18:40 PM
Oh man, I got it now!  my malfunction was confusing BH+ with H+. 

I am pleased.

The Ka would be [BH+][OH-]/H2O.

No. Kb is for the base B. The conjugated acid of B is BH+. How does it react with water? What's the formula for Ka?
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 04:29:20 PM
BH+ would donate the proton and Ka would equal [OH-]/[H30] ?
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 04:37:13 PM
BH+ would donate the proton

Yes

and Ka would equal [B ][OH-]/[H30] ?

No. Please post the equilibrium you want to describe and then set up the acid dissociation constant.

P.S.
B is interpreted as a bold tag ;)
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 04:45:31 PM
H2O ---> H+ + OH-

Ka = [H+][OH-]/[H2O], is this what you mean?
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 04:52:28 PM
This is K (not Ka!) for the self-ionization of water. I'll tell you what I meant:

You have the equilibrium
B + H2O (https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww.forkosh.dreamhost.com%2Fmimetex.cgi%3F%5Crightleftharpoons&hash=157e2a14e3d1ec4923b187ed514226fe1ec08b02) BH+ + OH-

(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww.forkosh.dreamhost.com%2Fmimetex.cgi%3FK_b%3D%5Cfrac%7B%5BBH%5E%2B%5D%2A%5BOH%5E-%5D%7D%7B%5BB%5D%7D&hash=7cf029a8f3b3bf2936b7a98da2d517e077ab52c8)

The value of Ka is not of interest here. Just for you to understand, try to set up the equation for Ka. Which equilibrium is described by Ka? (remember conjugated acid/base pairs)

BH+ + H2O (https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww.forkosh.dreamhost.com%2Fmimetex.cgi%3F%5Crightleftharpoons&hash=157e2a14e3d1ec4923b187ed514226fe1ec08b02) B + H3O+

(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fwww.forkosh.dreamhost.com%2Fmimetex.cgi%3FK_a%3D%5Cfrac%7B%5BB%5D%2A%5BH%5E%2B%5D%7D%7B%5BBH%5E%2B%5D%7D&hash=edb7dc2b35eda8eaae5e261528eda70604373d4c)

Ka*Kb = 10-14 for conjugated acid/base pairs.
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 05:02:00 PM
O.K., so my Kb should be [BH+][OH-]/
=(1.2 x 10^-3)^2/0.44 - 1.2 x 10^-3
=3.28 x 10^-6
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 05:03:59 PM
OK.

It is not 100 % clear whether 0.44 mol/l means [B ] or [B ]0, but because of [B ]~[B ]0 you don't have to care.
Title: Re: Acid-Base Equilibrium
Post by: MitchTwitchita on February 03, 2008, 05:12:42 PM
Thanks Kryolith!
Title: Re: Acid-Base Equilibrium
Post by: Kryolith on February 03, 2008, 05:15:33 PM
You're welcome.