- [Instructor] Buffer capacity refers to the amount of acid
or base a buffer can neutralize before the pH changes
by a large amount.
An increased buffer capacity
means an increased amount of acid or base neutralized
before the pH changes dramatically.
Let's compare two buffers;
buffer solution one and buffer solution two,
and see which one has the higher buffer capacity.
Buffer solution one has a concentration
of acidic acid of 0.250 molar
and a concentration of acetate anion also 0.250 molar.
Buffer solution two also consists of acidic acid
and the acetate anion.
However, in this case,
both concentrations are 0.0250 molar.
So buffer solution one has a higher concentration
of both acidic acid and the acetate anion.
Let's calculate the initial pH of both buffer solutions
using the Henderson-Hasselbalch equation.
In the Henderson-Hasselbalch equation,
the pH of the solution is equal to the pka of the weak acid,
which for both buffers is a acidic acid
plus the log of the concentration of the conjugate base
divided by the concentration of the weak acid.
In this case, the conjugate base is the acetate anion,
so the concentration of the acetate anion
divided by the concentration of acidic acid.
For buffer solution number one,
the concentration of the acetate anion
is equal to the concentration of acidic acid.
Therefore, the ratio of their concentrations
is equal to one.
And it's the same idea for buffer solution number two,
the concentration of the acetate anion
is equal to the concentration of acidic acid.
Therefore, the ratio of their concentrations
is also equal to one for buffer two.
Since the ratio of the concentrations is equal to one,
the log of one is equal to zero,
and the pka value of acidic acid at 25 degrees Celsius
is equal to 4.74.
So the pH of both buffer solutions is equal to 4.74
plus zero, or just 4.74.
So we're starting with two buffer solutions,
each at a pH of 4.74, and to those buffer solutions,
we're gonna add 0.0200 moles of hydroxide anions.
And by calculating the pH change
after adding the hydroxide anions,
we'll be able to see
which buffer has the higher buffer capacity.
The added hydroxide anions will be neutralized
by the weak acid that's present in the buffer system.
So that's acidic acid.
So acidic acid is going to react with the hydroxide anions.
And to make the math easier,
we're gonna assume that the total volume
of the buffer solutions is equal to one that liter
both before and after the addition of the base.
So if the total volume of the solution is one liter
and the concentration of acidic acid
is equal to 0.250 molar in buffer one,
that means there's 0.250 moles of acidic acid in the buffer.
So 0.250 moles of a acidic acid will react
with the 0.0200 moles of hydroxide anions
that we're adding to buffer solution one.
Let's calculate the pH of buffer solution one
after the addition of the hydroxide anions.
The hydroxide anions react with a acidic acid
to form water and the acetate anion.
In buffer solution one, the initial moles
of both acidic acid and the acetate anion are both 0.250.
And to that buffer solution we're adding
0.0200 moles of hydroxide anions.
To help us find the final moles of acidic acid
and the acetate anion, we're gonna use an ICF table,
where I is the initial amount of moles,
C is the change in moles and F as the final amount of moles.
For this reaction, hydroxide anions
are the limiting reactant.
So we're gonna use up
all of the 0.0200 moles of hydroxide anions,
and we're left with nothing.
Since the mole ratio of hydroxide anions to acidic acid
is a one-to-one mole ratio,
we're also gonna use up 0.0200 moles
of acidic acid,
which leaves us with 0.230 moles of acidic acid.
And for the acetate anion, there's also a coefficient of one
in the balanced equation.
So for losing 0.0200 moles for the reactants,
we're gaining 0.0200 moles for the acetate anion,
which gives us a final amount of moles
of the acetate anion of 0.270.
Now that we have our final moles,
we're ready to calculate the pH of the buffer solution.
So the pH is equal to the pka value,
which for a acidic acid is 4.74,
plus the log of the ratio of the concentrations.
And we could put in the concentrations,
but since concentration or molarity
is equal to moles divided by liters,
a ratio of the concentrations
would just have the volume cancel out because it's the same
for both our conjugate base and our weak acid.
So a ratio of the moles is the same thing
as a ratio of the concentrations
in the Henderson-Hasselbalch equation.
And we can get our moles directly from our ICF table.
So the moles of the acetate anion are equal to 0.270,
and the moles of a acidic acid is equal to 0.230.
And when we solve for the pH,
we find the pH of the solution is equal to 4.81.
So buffer one started at a pH of 4.74,
and after the addition of the hydroxide anions,
the pH rose a little bit to 4.81,
however, that's a relatively small change in the pH.
So buffer one did a pretty good job
of resisting a large change in pH.
Next, let's calculate the pH of buffer two
after the addition of the hydroxide anions.
So the initial moles of a acidic acid in buffer two
is equal to 0.0250 moles,
which is the same number of moles as the acetate anion,
so 0.0250,
and the hydroxide anions that we add
is equal to 0.0200 moles.
Once again, hydroxide anions are the limiting reactant,
so all of the hydroxide anions are used up
and we're left with zero moles.
Since the mole ratio of hydroxide anions to acidic acid
is one to one, we use up the same amount of acidic acid,
0.0200 moles,
and we're left with 0.0050 moles of a acidic acid
after the neutralization.
And since there's a one as a coefficient
in front of the acetate anion,
the acetate anion is going to gain 0.0200 moles
for a final moles of 0.0450.
Next, we can calculate the pH of the solution
using the Henderson-Hasselbalch equation.
So the pH is equal to the pka value of acidic acid of 4.74,
plus the log of the concentration of the conjugate base
divided by the concentration of the weak acid.
And since we can substitute moles for that,
we can grab those from our ICF table and plug in
the moles of acetate anion and the moles of acidic acid,
and then solve for the pH.
When we solve for the pH,
we find that the pH of buffer solution two is equal to 5.69.
So buffer solution two started at pH of 4.74,
and after the addition of the hydroxide anions,
the pH rose to 5.69.
That's a relatively large increase
in the pH of the solution.
So going back to buffer solution one,
the initial pH was 4.74,
and the pH rose to 4.81 upon the addition of the base.
For buffer solution two, we started at 4.74
and the pH rose to 5.69.
Therefore buffer solution one had a higher capacity
to neutralize the added base.
And so we say that buffer solution one
has the higher buffer capacity.
And since buffer solution two
had the more dramatic change in pH
upon the addition of the same amount of base,
buffer two has a decreased capacity to neutralize the base
compared to buffer one.
So we say that buffer two has a decreased buffer capacity.
Remember that the only difference between these two buffers
was that buffer one had a higher concentration
of acidic acid and the acetate anion.
Therefore the higher the concentration of the weak acid
and the conjugate base, the higher the buffer capacity.
We just looked at two buffer solutions
in which the concentrations of weak acid
and conjugate base were equal.
However, a buffer solution doesn't have to start
with equal concentrations of the weak acid
and its conjugate base.
For example, when the concentration of weak acid
is greater than the concentration of conjugate base,
the buffer has a higher capacity
for added base than added acid.
And when the concentration of conjugate base
is greater than the concentration of weak acid,
the buffer has a higher capacity for added acid
than added base.
As an example, let's think about blood,
which has a pH of 7.4.
The major buffer system used to control the pH of blood
is the carbonic acid bicarbonate buffer system.
In blood, the concentration of bicarbonate
is greater than the concentration of carbonic acid.
And since bicarbonate is the conjugate base
to carbonic acid, the concentration of the conjugate base
is greater than the concentration of the weak acid.
And therefore the buffer system has a higher capacity
for added acid than added base.
The reason why the buffer system
needs to have a higher capacity for added acid
is because the products of metabolism
that enter the bloodstream are mostly acidic
and therefore the bicarbonate anion
can react with those acidic products and neutralize them.
Therefore, the buffer system is able to resist large changes
to the pH of blood.