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# Relationship between Ka and Kb

The relationship between Ka and Kb, and pKa and pKb. Examples of finding Ka of a weak acid given Kb of the conjugate base.

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• What is the relationship between( PKa+PKb=14)and (PH +POH=14)
• There a slight relationship (see bottom), due to the fact that their measurements are very similar. For PH, the concentration of H3O+ is measured, for PKa, products over reactants is used.

If you think of it mathematically:
Ka x Kb = ( [H3O+]{Base] / [Acid] ) x ( [OH-][Acid] / [Base] ) = [H3O+][OH-] = 1.0x10^(-14)
and:
pKa + pKb = -log( [H3O+]{Base] / [Acid] ) + -log( [OH-][Acid] / [Base] )
= -log( [H3O+]{Base] / [Acid] ) x ( [OH-][Acid] / [Base] )
= -log( [H3O+][OH-] ) = 14

So: pH x pOH = pKa x pKb
This is why the conversions between pH and pOH are so similar to conversions between pKa and pKb.
• Can we compare pKa to pKb? So for example, if pKa for NH4+ is 10, and pKb for NH3 is 4, in this situation, can we say that NH3 is a stronger/better base, then NH4+ is an acid?
• Thar's exactly what you can say.
NH₃ is a stronger base than NH₄⁺ is an acid.
• What is the relationship between pKa/pKb and pH/pOH?
• pH and pOH add up to equal 14
pKa and pKb are the -logs of Ka and Kb; Ka and Kb, when multiplied, are equal to Kw (1.0x10^-14). Kw is also equal to the hydronium and hydroxide concentrations when multiplied.
• What is the physical sense of adding the two equilibrium reactions ...is it just mathematical?
• It's justified because NH4+ and NH3 are a conjugate acid-base pair. The transfer of a proton converts one to the other.

Remember, the two reactions that are being added together are each reversible. Each reaction is interconverting NH4+ and NH3. If you have NH3 in water, both reactions will take place (although the equilibrium constant if different for each).
• I entered 1x10^-14 / 3.7x10^-4 to my graphing calculator and it gives me the answer 2.7027x10^-19. Does anyone know why I am getting the wrong answer?
• Yes. You are probably using the "x" sign to make 1x10^-14.
Don't do that. Your calculator should have a key that says EE or maybe EEX. You use that to create scientific notation.
When you do it the way you are currently doing it, your calculator thinks you are doing multiplication and division of 4 numbers:
1
10^-14
3.7
and
10^-4

It uses standard order of operations, doing multiplication and division from left to right, so you get
1 x 10^-14 = 1x10^-14
1x10^-14/3.7 = 2.7 x 10^-15
2.7 x 10^-15 x 10^-4 = 2.7x10^-19

If you want to insist on doing it this way, you need to use parentheses
(1x10^-14) / (3.7x10^-4)
Then you will get the right answer

But you really need to learn how to use your calculator properly. You need to be able to enter 3.7E-4 as a single number, not as the product of 3.7 and 10^-4. It's much faster, and much more accurate.
• This is more of a math than conceptual question, but what is a quick way to convert the pKa or pKb back Ka or Kb? Like for example if a question asks what is the Kb of a base with a pKb of 5.4?
• this is also a conceptual question because it looks like you might not be fully comfortable with the idea of Ka/Kb yet. you can work with these numbers the same way you would convert an acid/base concentration to pH/pOH. so if the pKb is 5.4, you can take 10^-5.4 to get the Kb.
• Is the equation Ka x Kb = Kw (similarly, pKa + pKb = 14) only applicable for reactions where the H2O is the solvent?
• Yes but all acids and bases are dissolved in H2O so this is always the case.
• What does the numerical value of Ka and Kb signify? I get its the equilibrium constant, but what does it mean for something to have a constant of 5.6 X 10^-10? Is it the rate that the forward/backward reactions occur?
(1 vote)
• The K values give us an idea of the relative amounts of products and reactants at equilibrium.
If K is large, there is a large amount of H⁺ or OH⁻ at equilibrium and very little undissociated acid or base. We have a strong acid or base.
If K is very small, there is very little H+ or OH- at equilibrium, and mostly undissociated acid or base. We have a weak acid or base.
• Is there a maximum and a minimum value of pKa and pKb? If there are, are they 14 and 0 respectively, where 14 would be a very weak acid/base and 0 a very strong acid/base?
(1 vote)
• There aren't really any mathematical reasons that pKa (or pKb, since they are measured the same way, just measuring different properties) would be limited to any particular range, but there are some chemical reasons. To get to greater extremes of acid or base, you have to use more extreme materials, and you would be working against what the atoms generally want to do. So, there are some practical limits.

Lots of familiar acids have negative pKa: hydrochloric acid, HCl, has a pKa of about -6. Sulphuric acid, H2SO4, is around -3 (for the first proton, the second is harder to remove).
Some of the strongest acids have much lower pKa: Fluoroantimonic acid is mind-bogglingly acidic, with a pKa of -25!

On the other hand, pKa values can go very high for basic compounds, or for other molecules that don't really act as acid or base. For example, methane, CH4, is pretty happy where it is, and doesn't especially want to give up or to take a proton, and has one of the highest pKa values I've seen, at around 45.

Mind, these are extreme extremes, and most of what you see will be in that middle range of around -7 to 15 or so. So, keep this range in mind for normal stuff, and the extremes in mind as a "sanity check" if you get an answer that seems way out there.