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The Henderson-Hasselbalch Equation

SECTION 15 - Applications of Acid-Base Equilibria

In a buffer solution, the pH is governed by the ratio of [HA-] (weak acid) to the common ion, [A-].

The pH depends on the ratio [HA-] / [A-] and for problem-solving, this ratio is integrated into the Henderson-Hasselbalch Equation.

Henderson-Hasselbalch Equation

pH  =  pKa  +  log ( [A-] / [HA-] )

➞  note:  pKa = - log Ka

➞  this is a quick and easy way to replace ICE Tables for buffer calculations.

Henderson-Hasselbalch Formula


ex:  Using the Henderson-Hasselbalch equation, calculate the pH of a buffer solution containing 0.50 M HC2H3O2 and 0.50 M NaC2H3O2.  The Ka for acetic acid is 1.8 x 10-5.

First let's use the given Ka value to find the pKa...

  pKa  =  - log Ka

  pKa  =  - log ( 1.8 x 10-5)

  pKa  =  4.74

Now, we'll use the pKa value in the Henderson-Hasselbalch equation to solve for the pH of the buffer:

  pH  =  pKa  +  log ( [C2H3O2-] / [HC2H3O2] )

  pH  =  4.74  +  log ( 0.50 M / 0.50 M )

  pH  =  4.74  +  log ( 1 )

  pH  =  4.74  ➞  matches ICE Table result from earlier.

➞  see the image below for a better view of our set-up...

Acetic Acid Weak Acid pH Calculations


ex A buffer solution contains 0.25 M NH3 (Kb = 1.8 x 10-5) and 0.40 M NH4Cl.  Calculate the pH.

Alright, our common ion is NH4+

- major species:  NH3H2O (neutral) , NH4+ , Cl- (neutral)

- so we have:  let's use an ICE Table (yes, we could use the H-H Equation here)

NH3 Weak Base ICE Table Calculations


Now, what would be the pH IF 0.10 mol HCl were added to 1.0 L of this buffer (above)?

before any reaction occurs:

- major species:  NH3  ,  NH4+  ,  H+ , Cl- (neutral) , H2O (neutral)

➞ so NH3(aq) will react with H+(aq) as shown below:

Ammonia Ammonium Common Ion Example

See the "after results" of 0.15 mol NH3 and 0.50 mol NH4+?  We can use them in another ICE Table or the Henderson-Hasselbalch equation.

Let's use the H-H equation...

Henderson-Hasselbalch Example


Titrations and Titration Curves

Titration Curves = also called "pH Curves."

Titrations are performed to determine the amount of acid or base in a solution.

A buret and an erlenmeyer flask are used, as shown in the image below...

How Does a Buret Work?

As you can see, the buret contains the titrant (the acid or base) - whichever one we know more about.

In other words, the buret contains the "known" solution.

The acid or base titrant solution has both a known concentration (molarity, M) and a known volume delivered (mL) to the erlenmeyer flask.

The erlenmeyer flask contains the "unknown" analyte solution, where we know the volume (mL) but not the concentration (molarity, M).

If the analyte is a base, the titrant will be an acid -- or vice-versa


Acid-Base Titrations

We will do a zillion examples in the videos that follow, but I want to make two more points about Acid-Base Titrations before we move on:

1.  At the stoichiometric point of the acid-base reaction (the equivalence point of the titration), moles of acid equals moles of base.

In other words, the total # of moles of acid equals the total # of moles of base:

    ➞    Moles of ACID   =   Moles of BASE

2.  The progress of an an acid-base titration can be monitored by plotting the pH (y-axis) vs. the amount of titrant added (x-axis).

    ➞    this plot is called a titration curve (ph curve).


2 Types of Acid-Base Titrations

Strong Acid - Strong Base Titrations

  - similarly, Strong Base - Strong Acid Titrations

ii.  Weak Acid - Strong Base Titrations

  - similarly, Weak Base - Strong Acid Titrations


In the next few videos in SECTION 15 - Applications of Acid-Base Equilibria,

We'll go over a ton of acid-base titration examples and then graph the titration curves...