## Chem – College: Relationships Between Acid and Base Equilirium Constants (Ka and Kb)

COLLEGE: RELATIONSHIPS BETWEEN ACID AND BASE EQUILIBRIUM CONSTANTS (Ka and Kb):

When you are given multiple Ka or Kb values (like Ka1, Ka2, Ka3), you can also combine them together into an overall Ka or Kb by multiplying them together. The equations below display what I mean.

Ka = Ka1 * Ka2, * Ka3

Kb = Kb1 * Kb2 * Kb3

Examples: Solve for the overall Ka or Kb value below

If Mg(OH)2 has a Kb1 of 0.3 and a Kb2 of 4.5 * 10-3 what is the over all Kb value?

Answer: 0.3 * (4.5 * 10-3) = Kb = 1.35 * 10-3

If H3PO4 has a Ka1 of 2.8 * 10-3 and a Ka2 of 7.1 * 10-6. Then what would be the Ka3 if the overall Ka is 7.75 * 10-17?

Answer: ( 2.8 * 10-3 ) * ( 7.1 * 10-6 ) * Ka3 = 7.75 * 10-17

Ka3 = 3.9 * 10-9

PRACTICE PROBLEMS:

If Al(OH)3 has a Kb1 of 0.04 and a Kb2 of 5.1 * 10-4 what is the over all Kb value?

Answer: 0.04 * (5.1 * 10-4) = Kb = 2.04 * 10-6

If H2SO4 has a Ka1 of 15 and a Ka2 of 2.0 * 10-2. Then what is the over all Ka value?

Answer: 15 * (2.0 * 10-2) = Ka = 0.3

If H3PO3 has Ka2 of 4.7 * 10-5 and a Ka3 of 2.3 * 10-8. Then what would be the Ka1 if the overall Ka is 5.5 * 10-16?

Answer: Ka1 * (4.7 * 10-5) * (2.3 * 10-8) = 5.5 * 10-16 —— Ka1 = 5.09 * 10-4

If Be(OH)2 has a Kb1 of 3.6 * 10-4 and an overall Kb of 8.2 * 10-12 what would be the Kb2?

Answer: (3.6 * 10-4) * Kb2 = 8.2 * 10-12 —— Kb2 = 2.24 * 10-8

It turns out that Ka and Kb are related to one another in a formula. This formula allows you to convert from Ka to Kb and vise versa. The formula is shown below.

Kw = 1.0 * 10-14 = Ka Kb

The great thing about this formula is it also allows you to predict whether something is an acid or a base. The way to figure whether something is an acid or base just by its Ka or Kb value is to compare it to the equilibrium constant for water like in the equation below.

What the Kw formula tells us:

If the Ka turns about to be a larger number than the Kb then the chemical will be an acid.

If the Kb turns about to be a larger number than the Ka then the chemical will be a base.

Another way to say that (at room temperature 25 C):

If Ka is larger than 1.0 * 10-7 then the chemical is an acid.

If Kb is larger than 1.0 * 10-7 then the chemical is an base.

Examples: Temperature of all examples is 25 C.

Give the Kb and tell whether the chemical is an acid or base if it has a Ka of 2.4 * 10-6.

Answer: Acid (Ka is larger than Kb), Kb = 10-14 / 2.4 * 10-6 = 4.17 * 10-9

Give the Ka and tell whether the chemical is an acid or base if it has a Kb of 3.5 * 10-4.

Answer: Base (Kb is larger than Ka), Ka = 10-14 / 3.5 * 10-4 = 2.86 * 10-11

Give the Kb and tell whether the chemical is an acid or base if it has a Ka of 4.3 * 10-9.

Answer: Base (Kb is larger than Ka), Kb = 10-14 / 4.3 * 10-9 = 2.32 * 10-6

Give the Ka and tell whether the chemical is an acid or base if it has a Kb of 8.9 * 10-11.

Answer: Acid (Ka is larger than Kb), Ka = 10-14 / 8.9 * 10-11 = 1.12 * 10-4

PRACTICE PROBLEMS: Temperature of all problems is 25 C.

Give the Kb and tell whether the chemical is an acid or base if it has a Ka of 7.2 * 10-9.

Answer: Base (Kb is larger than Ka), Kb = 10-14 / 7.2 * 10-9 = 1.38 * 10-6

Give the Ka and tell whether the chemical is an acid or base if it has a Kb of 4.2 * 10-12.

Answer: Acid (Ka is larger than Kb), Ka = 10-14 / 4.2 * 10-11 = 2.38 * 10-4

Give the Kb and tell whether the chemical is an acid or base if it has a Ka of 3.4 * 10-3.

Answer: Acid (Ka is larger than Kb), Kb = 10-14 / 3.4 * 10-3 = 2.94 * 10-12

Give the Ka and tell whether the chemical is an acid or base if it has a Kb of 5.6 * 10-7.

Answer: Base (Kb is larger than Ka), Ka = 10-14 / 5.6 * 10-7 = 1.78 * 10-8