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Relationship between Ka and Kb

Relationship between Ka of a weak acid and Kb for its conjugate base. Equations for converting between Ka and Kb, and converting between pKa and pKb. 

Key points

For conjugate-acid base pairs, the acid dissociation constant Ka and base ionization constant Kb are related by the following equations:
  • KaKb=Kw
    where Kw is the autoionization constant
  • pKa+pKb=14  at 25C

Introduction: Weak acid and bases ionize reversibly

Weak acids, generically abbreviated as HA, donate H+ (or proton) to water to form the conjugate base A and H3O+:
  acid          base            acid              base
Similarly, a base (abbreviated as B) will accept a proton in water to form the conjugate acid, HB+, and OH:
  base         acid          acid          base
For a weak acid or base, the equilibrium constant for the ionization reaction quantifies the relative amounts of each species. In this article, we will discuss the relationship between the equilibrium constants Ka and Kb for a conjugate acid-base pair.
An aqueous solution of hydrofluoric acid, a weak acid, contains undissociated HF molecules which are in equilibrium with protons and fluoride ions.
Note: For this article, all solutions will be assumed to be aqueous solutions.

Finding Ka for HA reacting as an acid

Let's look more closely at the dissociation reaction for a monoprotic weak acid HA:
The products of this reversible reaction are A, the conjugate base of HA, and H3O+. We can write the following expression for the equilibrium constant Ka:

Finding Kb for A reacting as a base

Since A is a base, we can also write the reversible reaction for A acting as a base by accepting a proton from water :
The products of this reaction are HA and OH. We can write out the equilibrium constant Kb for the reaction where A acts as a base:
Even though this almost looks like the reverse of HA acting as an acid, they are actually very different reactions. When HA acts as an acid, one of the products is H3O+. When the conjugate base A acts as a base, one of the products is OH.

Relationship between Ka and Kb for conjugate acid-base pair

If we multiply Ka for HA with the Kb of its conjugate base A, that gives:
where Kw is the water dissociation constant. This relationship is very useful for relating Ka and Kb for a conjugate acid-base pair!! We can also use the value of Kw at 25C to derive other handy equations:
KaKb=Kw=1.0×1014 at 25C(Eq. 1)
If we take the negative log10 of both sides of the Eq. 1, we get:
pKa+pKb=14  at 25C(Eq. 2)
We can use these equations to determine Kb (or pKb) of a weak base given Ka of the conjugate acid. We can also calculate the Ka (or pKa) of a weak acid given Kb of the conjugate base.
An important thing to remember is that these equations only work for conjugate acid-base pairs!! For a quick review on how to identify conjugate acid-base pairs, check out the video on conjugate acid-base pairs.
Concept check: Which of the following values can we calculate if we know the Kb of NH3 at 25C?
Choose 1 answer:

Example: Finding Kb of a weak base

The pKa of hydrofluoric acid (HF) is 3.36 at 25C.
What is Kb for fluoride, F(aq)?
Let's work through this problem step-by-step.

Step 1: Make sure we have a conjugate acid-base pair

We can check the conjugate acid-base pair relationship by writing out the dissociation reaction for HF:
We can see that HF donates its proton to water to form H3O+ and F. Therefore, F is the conjugate base of HF. That means we can use the pKa of HF to find the pKb of F. Hooray!

Step 2: Use Eq. 2 to find pKb from pKa

Rearranging Eq. 2 to solve for pKb, we have:
Plugging in our known pKa for HF, we get:
Therefore, the pKb for F is 10.64.

Step 3: Calculate Kb from pKb

Finally, we can convert pKb to Kb using the following equation:
Solving this equation for Kb, we get:
Substituting our known value of pKb and solving, we get:
Therefore, the Kb of F is 2.3×1011.


For conjugate-acid base pairs, the acid dissociation constant Ka and base ionization constant Kb are related by the following equations:
  • Kw=KaKb
  • pKa+pKb=14  at 25C

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