- [Instructor] The Henderson-Hasselbalch equation
is an equation that's often used
to calculate the pH of buffer solutions.
Buffers consists of a weak acid and its conjugate base.
So for a generic weak acid,
we could call that HA,
and therefore, its conjugate base would be A-.
To calculate the pH of the buffer solution,
we would find the pKa of the weak acid,
and to that we would add the log of the concentration
of the conjugate base divided by the concentration
of the weak acid.
Let's use the Henderson-Hasselbalch equation
to calculate the pH of an aqueous buffer solution
that consists of acetic acid and its conjugate base,
the acetate anion.
And let's use this particulate diagram
to help us calculate the pH of the buffer solution.
Remember that the goal of a particulate diagram
is not to represent every particle in the solution,
but to give us an idea about what's going on
in the entire solution.
And also, when looking at the particulate diagrams
of buffer solutions,
water molecules and cations are often left out for clarity.
Let's count the number of particles of acetic acid
in our particulate diagram.
So in our diagram, there are five particles of acetic acid,
and for the acetate anion, there are also five.
Because there are five particles
of both acetic acid and the acetate anion,
the concentration of acetic acid
is equal to the concentration of the acetate anion.
Next, let's think about the Henderson-Hasselbalch equation.
Our goal is to calculate the pH of this buffer solution
represented in the particulate diagram.
And so first, we need to know the pKa of the weak acid,
which is acetic acid.
At 25 degrees Celsius, the Ka value for acetic acid
is equal to 1.8 times 10 to the negative fifth.
The Ka value is less than one because acetic acid
is a weak acid.
To find the pKa of acetic acid,
we take the negative log of the Ka value.
So the negative log of 1.8 times 10 to the negative fifth
is equal to 4.74.
So we can go back to the Henderson-Hasselbalch equation
and write that the pH is equal to the pKa,
which we just calculated to be 4.74
plus the log of the concentration of the conjugate base.
And the conjugate base is the acetate anions,
so let's write that in here, CH3COO-,
and that's divided by the concentration of the weak acid,
which is acetic acid, CH3COOH.
We've already figured out
that the concentration of acetic acid
is equal to the concentration of the acetate anion.
Therefore, the concentration of the acetate anion
divided by the concentration of acetic acid
is just equal to one.
And the log of one is equal to zero.
So let's go ahead and write that in here,
the log of one is equal to zero.
Therefore, the pH of the buffer solution
is equal to 4.74 plus zero
or just 4.74.
So whenever the concentration of the weak acid
is equal to the concentration of the conjugate base,
the pH of the buffer solution
is equal to the pKa of the weak acid.
Let's look at another particulate diagram.
We still have an acetic acid-acetate buffer solution.
However, this is a different buffer solution
than the previous problem.
So let's count our particles.
For acetic acid, there are six particles
and for the acetate anion, there are only four.
Since we have more acetic acid particles
than acetate particles,
the concentration of acetic acid
is greater than the concentration of the acetate anion.
We can use the Henderson-Hasselbalch equation
to think about the pH of this buffer solution.
So the pH is equal to the pKa,
which we calculated in the previous problem
for acetic acid,
it's 4.74 at 25 degrees Celsius,
plus the log of the concentration of the acetate anion,
divided by the concentration of acetic acid.
In this case, the concentration of acetic acid
is greater than the concentration of the acetate anion.
Therefore, we have a smaller concentration
divided by a larger concentration.
So we have a number less than one.
And the log of a number less than one is negative.
Therefore, all of this would be negative or less than zero.
So we would be subtracting a number from 4.74.
Therefore, we can say the pH of the solution
would be less than 4.74.
Let's do one more particulate diagram
of an acetic acid-acetate buffer solution.
Once again, we count our particles.
So for acetic acid, this time, there are four particles
and for the acetate anion,
this time, there are six particles.
Since we have only four particles of acetic acid
and six particles of the acetate anion,
the concentration of acetic acid
is less than the concentration of the acetate anion
or we could say the concentration of the acetate anion
is greater than the concentration of acetic acid.
Thinking about the Henderson-Hasselbalch equation,
once again, the pKa is equal to 4.74,
and we need to think about the ratio
of the concentration of the acetate anion
to the concentration of acetic acid.
For this example, the concentration of the acetate anion
is greater than the concentration of acetic acid.
Therefore, the ratio would be greater than one,
and the log of a number greater than one
is positive or greater than zero.
Therefore, we would be adding a number to 4.74.
So for this buffer solution,
the pH would be greater than 4.74.
Finally, let's summarize what we've learned
from our three different particulate diagrams.
In the first example,
the concentration of the weak acid
was equal to the concentration of the conjugate base.
And therefore, the pH of the buffer solution
was equal to the pKa of the weak acid.
In the second example,
the concentration of the weak acid
was greater than the concentration of the conjugate base.
And therefore, the pH of the buffer solution
is less than the pKa of the weak acid.
And in the third example,
the concentration of the weak acid
was less than the concentration of the conjugate base.
Therefore, the pH of the buffer solution
was greater than the pKa of the weak acid.
So if we know the pH of a buffer solution,
we can think about the Henderson-Hasselbalch equation
to think about the relative concentrations
of the weak acid and the conjugate base.
For example, if we have a particular buffer solution
and we know the pH of the buffer solution
is less than the pKa of the weak acid,
we know that in that buffer at that moment in time,
the concentration of the weak acid
is greater than the concentration of the conjugate base.