Ka and Kb Question

[SyrianHero]

Why does Ka*Kb always have to equal 1*10^-14? I don't understand why this is.

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[RaspberrySlushy]

It actually only holds at 25 degrees C and it's b/c 1x10^-14 is the Kw at that temp. It will be slightly different at different temperatures.

Ka x Kb = Kw

As for the value of Kw, it comes from the equilibrium expression for auto-ionization in water.

Kc = [H+][OH-]/[H2O]
Divide both sides by the concentration of water so you have:
Kc x [H2O] = [H+][OH-]
Kc x [H2O] = Kw

So really Kw is just the equil constant for water at a given temperature x the concentration of pure water which is 55M at 25 C.

I'm sure that's way more info than you need on the MCAT but that's the reasoning behind it.

 

[SyrianHero]

It actually only holds at 25 degrees C and it's b/c 1x10^-14 is the Kw at that temp. It will be slightly different at different temperatures.

Ka x Kb = Kw

As for the value of Kw, it comes from the equilibrium expression for auto-ionization in water.

Kc = [H+][OH-]/[H2O]
Divide both sides by the concentration of water so you have:
Kc x [H2O] = [H+][OH-]
Kc x [H2O] = Kw

So really Kw is just the equil constant for water at a given temperature x the concentration of pure water which is 55M at 25 C.

I'm sure that's way more info than you need on the MCAT but that's the reasoning behind it.

Thanks, this is very helpful! But I thought you don't include the concentration of water in the equilibrium constant equation?

 

[RH8448]

The H2O would be written as (aq) which means it is completely dissolved. The H+ and OH- and H2O are all dissolved together in equilibrium. If it is said (l) or liquid then you wouldn't include it in the equilibrium expression. So, if you has organics involved, that would be a liquid layer that cannot dissolve into the aqueous making the liquid irrelevant in the equilibrium expression.

 

[chemtopper]

Why does Ka*Kb always have to equal 1*10^-14? I don't understand why this is.

Pl take care value of kw is temperature dependent...so it is not same at all temperatures