Acid base reactions

Question

An unknown weak acid with a concentration of .430 M has a pH of 5.600. What is the Ka of the weak acid?

Answer 1

First, let's remember two important equations about Ka and pH:

[H₃O⁺] = 10^-pH

Ka = [H₃O⁺] [A^-] / [HA]

(I'll explain how to use these, so don't worry.) But you should remember them. These equations listed above are necessary to solve this problem (and other problems like this one). Also remember that brackets [ ] mean "concentration" (molarity).

Now let's go step-by-step to solve this problem:

Step 1: Write the dissociation equation for the weak acid

The problem doesn't actually tell us the chemical formula for the weak acid, but that's ok. We can write the generic dissociation equation for a weak acid:

HA <--> H₃O⁺ + A^-

The HA means "the weak acid before it starts dissociating". The H₃O⁺ means the same thing as H+. (You need to remember this: H3O+ and H+ mean the same thing!) The A- means "the base that forms once the H has been removed from the HA by dissociation".

Step 2: Use the equation [H₃O⁺] = 10^-pH to find the [H₃O⁺]

The problem says that the pH is 5.600. (We can write this as just 5.6.) So if the pH is 5.6, we can use the equation to find the H₃O⁺ concentration:

[H₃O⁺] = 10^-5.6

We use a calculator to calculate 10^-5.6 . (Remember to add the negative sign before the pH! It's kind of hard to see here, but I assure you it is there.) Anyway, the calculator says that 10^-5.6 = 2.5 x 10^-6 . (In case you're not totally comfortable with significant figures, this number can also be written as 0.0000025 . This is the [H3O+]. So we know that [H3O+] = 2.5 x 10^-6.

Step 3: Since the problem doesn't give us the identity of the weak acid, we can assume that [A^-] = [H₃O⁺].

We found out in Step 2 that [H3O+] = 2.5 x 10^-6. Since we don't know the chemical formula of the weak acid, we can assume that there is a 1 to 1 ratio between the [H₃O⁺] and [A^-]. In other words, we can assume that [A-} = [H3O+]. So we can assume that [A-] = 2.5 x 10^-6 .

Step 4: Find the concentration of the weak acid that you were given in the problem. [HA] = this concentration.

Remember that the concentration of the weak acid is often written as molarity. The problem says that the concentration of the weak acid is 0.430 M. (Remember that the M is the symbol for molarity.) So we can write that [HA] = 0.430 .

Step 5: Write down the equation for Ka that I gave you in the first few lines of the problem.

As I wrote in the first few lines of this answer:

Ka = [H₃O⁺] [A^-] / [HA]

Step 6: Collect all the numbers for [H₃O⁺], [A^-], and [HA] that we calculated in the previous steps. Get ready to put them into the equation for Ka.

Here are the numbers that we calculated in the previous steps:

[H₃O⁺] = 2.5 x 10^-6

[A^-] = 2.5 x 10^-6

[HA] = 0.430

Step 7: Put these numbers into the equation for Ka:

Ka = (2.5 x 10^-6) (2.5 x 10^-6) / 0.430

Step 8: Start solving for Ka by multiplying the two 2.5 x 10^-6 together.

In other words, we are going to do (2.5 x 10^-6) * (2.5 x 10^-6).

The calculator says that (2.5 x 10^-6) * (2.5 x 10^-6) = 6.25 x 10^-12.

Step 9: Put this number into the equation for Ka instead of the (2.5 x 10^-6) (2.5 x 10^-6):

Ka = 6.25 x 10^-12 / 0.430

Step 10: Use a calculator to calculate 6.25 x 10^-12 / 0.430

Now we just have to divide 6.25 x 10-12 by 0.430.

The calculator says that 6.25 x 10^-12 / 0.430 = 1.453 x 10^-11. So we know that Ka = 1.453 x 10^-11. (Remember that Ka has no units.) If you want to round Ka to 3 significant figures, then Ka = 1.45 x 10^-11

Final answer: Ka = 1.45 x 10^-11