Buffer capacity | Acids and bases | AP Chemistry | Khan Academy

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 1 and buffer solution 2, and see which one has the higher buffer capacity. Buffer solution 1 has a concentration of acetic acid of 0.250 molar and a concentration of acetate anion also 0.250 molar. Buffer solution 2 consists of acetic acid and the acetate anion; however, in this case, both concentrations are 0.0250 molar.

So, buffer solution 1 has a higher concentration of both acetic 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 acetic 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 acetic acid.

For buffer solution number one, the concentration of the acetate anion is equal to the concentration of acetic 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 acetic 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 acetic acid at 25 degrees Celsius is equal to 4.74. So, the pH of both buffer solutions is equal to 4.74 plus 0, 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 going to add 0.0200 moles of hydroxide anions. 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, which is acetic acid.

So, acetic acid is going to react with the hydroxide anions, and to make the math easier, we're going to assume that the total volume of the buffer solutions is equal to 1 liter both before and after the addition of the base. If the total volume of the solution is 1 liter and the concentration of acetic acid is equal to 0.250 molar in buffer 1, that means there's 0.250 moles of acetic acid in the buffer.

So, 0.250 moles of acetic acid will react with the 0.0200 moles of hydroxide anions that we're adding to buffer solution 1. Let's calculate the pH of buffer solution 1 after the addition of the hydroxide anions. The hydroxide anions react with acetic acid to form water and the acetate anion. In buffer solution 1, the initial moles of both acetic 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 acetic acid and the acetate anion, we're going to use an ICF table where I is the initial amount of moles, C is the change in moles, and F is the final amount of moles. For this reaction, hydroxide anions are the limiting reactant, so we're going to use up all of the 0.020 moles of hydroxide anions, and we're left with nothing.

Since the mole ratio of hydroxide anions to acetic acid is a one-to-one mole ratio, we're also going to use up 0.0200 moles of acetic acid, which leaves us with 0.230 moles of acetic acid. For the acetate anion, there's also a coefficient of 1 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. The pH is equal to the pKa value, which for acetic acid is 4.74, plus the log of the ratio of the concentrations. 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. We can get our moles directly from our ICF table. The moles of the acetate anion are equal to 0.270, and the moles of acetic acid are equal to 0.230. When we solve for the pH, we find the pH of the solution is equal to 4.8.

So buffer 1 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 1 did a pretty good job of resisting a large change in pH.

Next, let's calculate the pH of buffer 2 after the addition of the hydroxide anions. The initial moles of acetic acid in buffer two is equal to 0.0250 moles, which is the same number of moles as the acetate anion, so 0.0250. The hydroxide anions that we add are equal to 0.0200 moles.

Once again, hydroxide anions are the limiting reactants, so all the hydroxide anions are used up, and we're left with zero moles. Since the mole ratio of hydroxide anions to acetic acid is one-to-one, we use up the same amount of acetic acid, 0.0200 moles, and we're left with 0.0050 moles of acetic 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.

The pH is equal to the pKa value of acetic acid of 4.74 plus the log of the concentration of the conjugate base divided by the concentration of the weak acid. Since we can substitute in moles for that, we can grab those from our ICF table and plug in the moles of acetate and the moles of acetic acid, and then solve for the pH. When we solve for the pH, we find that the pH of buffer solution 2 is equal to 5.69.

So buffer solution 2 started at a 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 1, the initial pH was 4.74, and the pH rose to 4.81 upon the addition of the base. For buffer solution 2, we started at 4.74, and the pH rose to 5.69. Therefore, buffer solution 1 had a higher capacity to neutralize the added base.

So we say that buffer solution 1 has the higher buffer capacity, and since buffer solution 2 had the more dramatic change in pH upon the addition of the same amount of base, buffer 2 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 acetic 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 of carbonic acid, the concentration of the conjugate base is greater than the concentration of the weak acid. 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 that 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.