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.

1 Answer
Aug 4, 2016

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:
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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