Question

How do you use the Henderson-Hasselbalch to calculate the pH of a buffer solution that is .50 M in `NH_3` and . 20 M in `NH_4Cl`?

For ammonia, `pK_b=4.75`.

Answer 1

That buffer solution has a pH of `9.65`

Explanation:

Before I introduce Henderson-Hasselbalch's equation, we should identify the acid and base. Ammonia `(NH_3)` is always a base and the ammonium ion `(NH_4^(+))` is the conjugate acid of ammonia. A conjugate acid has one more proton `(H^+)`than the base you started with.

Now, we can use this equation:

As you can see, we are given a pKb instead of a pKa. But, no worries we can use the following equation that relates both constants to each other:

`color(white)(aaaaaaaaaaaaaaaaaaa)`pKa + pKb = 14

We can solve for the pKa by subtracting the given pKb from 14:

`14 - 4.75 = 9.25`

Thus, your pKa is 9.25

Next, we can obtain the [base] and [acid] from the question.

[`NH_3`]= .50 M [`NH_4`] =.20 M

We're not really concerned with the chloride anion that attached to the ammonium ion because it's a spectator ion and it has no effect on the buffer system.

Now, we have all of the information to determine the pH. Let's plug our values into the equation:

`pH = 9.25 + log( [0.50]/[0.20])`

`pH = 9.65`