# Consider a solution of a weak acid at a pH equal to its pKa. By how much would the pH change, and in which direction, if we added to this solution enough base to neutralize 10% of the total acid?

##### 1 Answer

#### Answer:

Here's what I got.

#### Explanation:

The pH of a weak acid solution is equal to its **equal concentrations** of weak acid and of its conjugate base.

A solution that contains a weak acid and its conjugate base *in comparable amounts*, not necessarily in equal amounts, is called a buffer solution.

The pH of a buffer is described by the **Henderson - Hasselbalch equation**, which looks like this

#color(blue)("pH" = pK_a + log( (["conjugate base"])/(["weak acid"])))#

As you can see here, equal amounts of weak acid and of conjugate base will make the log term equal to zero, and thus the pH equal to the

Right from the start, wou can predict that adding more base will *increase* the pH of the solution.

Now, a weak acid **cannot** be neutralized by a weak base and a weak base **cannot** be neutralized by a weak acid.

Judging by the information provided in the problem, I will assume that you're adding enough *strong base* to neutralize

A generic weak acid - strong base reaction looks like this

#"HA"_text((aq]) + "BOH"_text((aq]) -> "BA"_text((aq]) + "H"_2"O"_text((l])#

Here

Now, assuming that you have a **one mole** of weak acid and *produces* **one mole** of conjugate base.

Let's say that before adding the strong base, you have

Now you're adding a volume

#x_"acid" = x - 10/100x = 9/10x#

The number of moles of conjugate base will **increase** by the same amount, so you have

#x_"base" = x + 10/100x = 11/10x#

The new concentrations of weak acid and conjugate base will be

#["HA"] = 9/10x * 1/(V + v)#

#["A"^(-)] = 11/10x * 1/(V + v)#

Plug this into the H-H equation to get

#"pH" = pK_a + log( (11/10x * color(red)(cancel(color(black)(1/(V + v)))))/(9/10x * color(red)(cancel(color(black)(1/(V + v))))))#

#"pH" = pK_a + log(11/9) = pK_a + 0.087#

The pH of the solution will thus **increase** by about