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

Answer:

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#