Animated Solution for Chemistry - Ionic Equilibrium: The pH of ammonium phosphate solution, if $p{K}_a$ of phosphoric acid and $p{K}_b$ of ammonium hydroxide are 5.23 and 4.75 respectively, is ......... .

Imagine you are in a chemistry lab, holding a beaker filled with an aqueous solution of ammonium phosphate.

What exactly is happening inside this beaker?

As soon as the salt dissolves, it completely dissociates into its constituent ions: ammonium ions and phosphate ions.

But the story doesn't end there. These ions are not mere spectators; they actively react with water in a process known as hydrolysis.

To understand the nature of this solution, we must trace these ions back to their origins.

The phosphate ion comes from phosphoric acid, which is a classic example of a weak acid.

Similarly, the ammonium ion originates from ammonium hydroxide, a well-known weak base.

Therefore, ammonium phosphate is classified as a salt derived from a weak acid and a weak base.

When dealing with a salt of a weak acid and a weak base, the pH of the solution is governed by a beautiful and elegant formula.

Unlike other salts, the pH here does not depend on the concentration of the salt itself!

The master equation is:

This equation tells us that the final pH is a delicate tug-of-war between the strength of the parent acid and the parent base.

If the acid is weaker (higher $p{K}_a$), the solution leans basic. If the base is weaker (higher $p{K}_b$), the solution leans acidic.

Now, let's bring in the numbers provided in our problem.

We are given the $p{K}_a$ of phosphoric acid as $5.23$ and the $p{K}_b$ of ammonium hydroxide as $4.75$.

Let's carefully substitute these values into our master equation:

First, we evaluate the difference inside the parentheses.

Next, we divide this difference by two:

Finally, we add this to seven:

The question asks us to round off the answer to the nearest integer.

Since $7.24$ is closer to $7$, our final, definitive answer is 7.

This slight deviation from a perfect 7 makes sense because the $p{K}_a$ is slightly higher than the $p{K}_b$, meaning the parent base is marginally stronger than the parent acid, nudging the pH just above neutral!