# Properties of Buffers

Our stomachs contain gastric acid to break down food. This acid can even dissolve steel! How is it that such a potent acid is in our stomachs? Well, our body has a "safety" in place, so our stomach isn't acidic enough to dissolve itself! Stomach cells produce bicarbonate which buffers the acid to prevent it from getting too strong (which we will discuss below).

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The buffer keeps the stomach pH stable (which we will also discuss later). This pH is between 1.5-3.5. It keeps stomach acid from getting too acidic, but it also prevents it from getting so basic that it can no longer dissolve food. In this article, we'll be diving into buffers and see about their preparation, their properties, and their applications.

• First, we will cover buffer properties.
• Then we'll use the Henderson-Hasselbalch equation to calculate the pH of a buffer solution.
• Thereafter, we'll learn about what is happening in a buffer solution.
• Next, we'll walk through buffer preparation.
• Lastly, we'll cover what makes a good buffer and buffer applications.

## pH Measurements and the Properties of Buffers

I talked a lot about buffers and pH, but what are they?

A buffer (or buffer solution) is a solution whose pH will not change drastically when an acid/base is added. The buffer capacity is the amount of acid/base a buffer can absorb before the pH changes significantly.

The pH measures how acidic/basic a solution is. The pH scale ranges begin at 0 (most acidic) and go to 14 (most basic).

Now that we know the basic definitions, let's cover the properties of buffers.

### Properties of Buffers

Buffers have an identifying set of characteristics, these are:

1. A definite pH

2. pH won't change over time

3. Dilution won't change pH

4. A slight pH change if a small amount of acid/base is added

5. A range where they are the most effective

As mentioned previously, buffers have a buffer capacity, which is the amount of acid/base that can be added until a significant pH change occurs. Typically, we consider this to be a change of 1 unit. (ex. from 3 to 4). A buffer's concentration determines its capacity. As concentration increases, more acid/base can be absorbed until a large change happens.

Figure 1: Buffer Capacity - the greater the concentration, the greater the buffer capacity. Study Smarter Orginal

As illustrated above, the greater the concentration of the buffer, the greater the capacity. The "spike" in the graph shows where the pH begins to significantly change (buffer isn't as effective). After the spike, it becomes an effective basic buffer.

The buffer range is the range of pH values where a buffer is most effective. The best solutions have a 50:50 ratio of acid to base. Generally, a buffer isn't effective when one component is >10% of the other. For example, a buffer is prepared that has 0.1 M acetic acid (CH3COOH) and 0.008 M acetate (CH3COONa). If more base is added, the buffer will be "overwhelmed" and the pH will change significantly.

Figure 2: Once there is a 10:1 ratio of base to acid, the pH begins to change significantly as more base is added. StudySmarter Original.

As more base is added, the acetic acid converts to acetate. Once there is a 10:1 ratio of acetate to acetic acid (shown by the black dot), the pH starts changing significantly. From the data, we see that the acetic acid buffer loses effectiveness around pH = 6.

### pH Measurements and the Henderson-Hasselbalch Equation

We measure a buffer's pH using the Henderson-Hasselbalch equation.

The Henderson-Hasselbalch equation measures a buffer's pH. The formula is: $$pH=pK_a+log_{10}(\frac{[A^-]}{[HA]})$$

pKa: negative logarithm of the acid dissociation constant (Ka)

[A-]: concentration of the conjugate base

[HA]: concentration of the acid

The acid dissociation constant measures an acid's strength. A larger constant means a stronger acid. For a general reaction: $$HA+B\leftrightarrow A^-+HB$$

The acid dissociation constant formula is:$$K_a=\frac{[A^-][HB]}{[HA][B]}$$

We measure the pH to see if our buffer is "working". If we add an acid/base, we want to ensure a minimal pH change, or else we would switch buffers.Let's say we have a buffer solution of CH3COOH (weak acid) and CH3COONa (conjugate base). Our acid equilibrium looks like:$$CH_3COOH\leftrightarrow CH_3COO^-+H^+$$

When a strong acid is added, its H+ ions combine with the CH3COO- ions and re-form the weak acid. This "neutralizes" the acid, preventing a large pH change.

What is the pH of the solution if 0.26 mol of CH3COOH and 0.23 mol of CH3COONa are combined, with a total volume of 4 L? What is the new pH and change in pH if 0.14 mol of HCl is added, making the total volume 5 L? Ka = 1.75 X 10-5.

First we calculate the pH. To get the concentration of our acid/base, we divide the number of moles by the total volume for each:

$$[CH_3COOH]=[HA]=(0.26\,mol\,4)=0.065\,M$$

$$[CH_3COONa]=[A^-]=(0.23\,mol/4)=0.0575\,M$$

Now we convert from Ka to pKa:

$$pK_a=-log[K_a]$$

$$pK_a=-log[1.75X10^-5]=4.76$$

We plug these values into our main equation:

$$pH=pK_a+log_{10}(\frac{[A^-]}{[HA]})$$

$$pH=4.76+log_{10}(\frac{[0.0575\,mol]}{[0.065\,mol]})$$

$$pH=4.71$$

For the second part of the problem, we must calculate the new concentrations of acid/base. The base concentration is the molar amount divided by the new volume. The acid concentration is equal to moles of weak acid plus moles of strong acid divided by volume.

$$[HA]=[HCl]+[CH_3COOH]=(0.26\,mol+0.14\,mol)/5L=0.08\,M$$

$$[A^-]=[CH_3COONa]=(0.23\,mol/5\,L)=0.046\,M$$

We plug these concentrations into the equation:

$$pH=pK_a+log_{10}(\frac{[A^-]}{[HA]})$$

$$pH=4.76+log_{10}(\frac{[0.046\,mol]}{[0.08\,mol]})$$

$$pH=4.52$$

Our change in pH is:

$$4.71-4.52=0.19$$

Despite a strong acid being added, the pH didn't change much.

## Structure and Properties of Water pH Buffers

There are two types of buffers: weak acids + their conjugate base, or weak bases + their conjugate acid. Buffers are aqueous solutions (dissolved in water).

The previous example was a weak acid and its conjugate base. (acetic acid/acetate). We covered what happens when this type has a strong acid added to it, but what about a strong base?

$$CH_3COOH\leftrightarrow CH_3COO^-+H^+$$

$$CH_3COOH+OH^-\leftrightarrow CH_3COO^-+H_2O$$

The base adds OH- ions which react with the weak acid to produce water, so the pH is unchanged.

Now for weak base/conjugate acid pairs. The main difference between the types is there is a weak base equilibrium, instead of a weak acid one. Let's look at the NH4OH/NH4Cl pair as an example. The equilibrium equation is:

$$NH_4OH\leftrightarrow NH_4^+ + OH^-$$

If an acid is added, the H+ ions combine with the weak base to form water

$$NH_4OH+H^+\leftrightarrow NH_4^+ +H_2O$$

When a base is added, the OH- ions will react with the NH4+ ions to form the weak base.

$$NH_4^+ + OH^-\leftrightarrow NH_4OH^+$$

## Determination of Appropriate Indicators & Preparation and Properties of Buffers

Now that we've covered how a buffer works, we'll cover how to make and choose a buffer.

### Determining an Appropriate Buffer

When choosing a buffer, you want to ensure that it can buffer the system you want. The buffer range should cover the pH you wish to stabilize. Some common buffers are:

 Buffer pKa pH range Phosphoric acid 2.1 1.1-3.1 Formic acid 3.8 2.8-3.8 Acetic acid 4.8 3.8-5.8 Carbonic acid 6.4 5.4-7.4 Phosphate 7.2 6.2-7.2 Bicarbonate 10.3 9.3-11.3

For example, if you want to keep a system neutral (pH=7), you would choose the phosphate buffer (phosphate + phosphoric acid).

### Preparing a Buffer Solution

Once you have chosen your buffer, you can prepare the solution. Let's walk through the steps:

Step 1: Use the Henderson-Hasselbalch equation to calculate the acid/base concentration.

Plug in your desired pH and the buffer pKa into the equation, solving for the ratio of base to acid.

Calculate the ratio of formate to formic acid needed if the buffer is to keep the pH at 3.2. pKa=3.8.

We plug our values into the Henderson-Hasselbalch equation and solve for the ratio of acid to base.

$$pH=pK_a+log_{10}\frac{[A^-]}{[HA]}$$

$$3.2=3.8+log_{10}\frac{[formate]}{[formic\,acid]}$$

$$-0.6=log_{10}\frac{[formate]}{[formic\,acid]}$$

$$10^{-0.6}=\frac{[formate]}{[formic\,acid]}$$

$$\frac{[formate]}{[formic\,acid]}=0.251$$

Step 2: Mix the required amounts of the weak acid/base with its conjugate base/acid.

The conjugate base can be added directly to the acid or a strong base can be added to the weak acid, partially converting it to the conjugate base (the same can be done with a strong acid+weak base)

Continuing from the previous problem, if the buffer needs to be 0.20 M and 100.0 mL, how many grams of formate (CHO2) and formic acid (CH2O2) must be combined?

Firstly, we calculate the total molar amount.

$$100.0\,mL*\frac{1\,L}{1000\,mL}=0.1\,L$$

$$\frac{0.20\,mol}{L}*0.1\,L=0.020\,mol$$

This means the sum of the moles of acid/base is equal to 0.020. The ratio of base to acid is 0.251, so we use that to solve for each molar amount.

$$[formate]+[formic\,acid]=0.020\,mol$$

$$\frac{[formate]}{[formic\,acid]}=0.251$$

$$[formate]=0.251[formic\,acid]$$

We substitute this expression into the first equation and solve for the moles of base

$$[formate]+[formic\,acid]=0.020\,mol$$

$$0.251[formic\,acid] +[formic\,acid]=0.020\,mol$$

$$1.251[formic\,acid]=0.020\,mol$$

$$[formic\,acid]=0.0160\,mol$$

$$[formate]+[formic\,acid]=0.020\,mol$$

$$[formate]+0.0160=0.020\,mol$$

$$[formate]=0.004\,mol$$

Our last step is to convert from moles to grams. We do this by calculating the molar mass of each species and multiplying it by our molar amounts.

Let's start with formic acid (CH2O2), first let's calculate its molar mass:

$$H:\frac{1.01\,g}{mol}$$

$$C:\frac{12.01\,g}{mol}$$

$$O:\frac{16.00\,g}{mol}$$

$$12.01+2(16.00)+2(1.01)=\frac{46.03\,g}{mol}$$

Since formate (CHO2) is just formic acid minus one hydrogen, we subtract the mass of one hydrogen from formic acid's molar mass to get formate's.

$$46.03-1.01=\frac{45.02\,g}{mol}$$

Lastly, we multiply the molar amounts by their molar masses to convert to grams.

$$0.0160\,mol*\frac{46.03\,g\,CH_2O_2}{mol}=0.736\,g\,CH_2O_2$$

$$0.004\,mol*\frac{45.02\,g\,CHO_2}{mol}=0.18\,g\,CHO_2$$

Step 3 (optional): Adjust the pH.

When experimenting, there may be some error that makes the pH slightly off. Using a pH meter, you can monitor the pH as you add small amounts of strong acid/base to get the desired pH.

## Characteristics of a Good Buffer

What makes a buffer "good"?

• [HA] = [A-]. The logarithm in the Henderson-Hasselbalch equation will be equal to zero, so the pH = pKa. This means the system can equally absorb acids/bases.
• If the desired pH is basic, then a weak base + its acid is the most effective. It's the opposite for acids.
• The desired pH is within the buffer's range
Buffers want to keep the pH stable, so a "good" buffer is any buffer that can keep a system stable at the desired pH.

## Applications of a Buffer Solution

Buffers have several applications. Enzymes must be kept in a specific pH range or else they will degrade\lose usefulness, so the body uses buffers to stabilize the pH. Buffers are also important in manufacturing and industry. They are used during fermentation and during the production of products like inks, dyes, and paper. They are also important for food preservation.

## Properties of Buffers - Key takeaways

• A buffer (or buffer solution) is a solution whose pH will not change drastically when an acid/base is added. The buffer capacity is the amount of acid/base a buffer can absorb before the pH changes significantly.
• The pH measures how acidic/basic a solution is. The pH scale ranges begin at 0 (most acidic) and go to 14 (most basic)
• The buffer range is the range of pH values where a buffer is most effective.
• Buffers neutralize acids/bases by reacting with them to either form water or the weak acid/base depending on the system.
• The Henderson-Hasselbalch equation measures a buffer's pH. The formula is: $$pH=pK_a+log_{10}(\frac{[A^-]}{[HA]})$$
• To prepare a buffer, we use the Henderson-Hasselbalch equation to calculate the required ratio of base to acid. The ratio is used to calculate the amount of weak acid/base and its conjugate that needs to be mixed.
• Buffers have many applications, such as keeping enzymes stable, manufacturing, and chemical analysis.

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What are the characteristics of buffers?

1. They have a definite pH
2. The pH will not change if left alone for long periods of time
3. The pH won't change if the solution is diluted
4. The pH will only change slightly if a small amount of acid or base is added
5. They have a range for which they are the most effective at neutralization

What is the most important property of a buffer solution?

They prevent the pH from changing significantly.

What are buffer solutions?

buffer (or buffer solution) is a solution whose pH will not change drastically when an acid or base is added.

What are examples of buffers?

Some examples are: acetic acid/acetate, formic acid/formate, and bicarbonate/carbonic acid.

Why are buffers used?

They have many applications, such as preventing enzymes from breaking down, preserving food, and calibrating pH meters. They are used because of their ability to minimize changes to the pH.

## Test your knowledge with multiple choice flashcards

If a buffer solution is 0.34 mol H3PO4 and 0.38 mol H2PO4 with a volume of 2.3 L, what is the pH when 0.25 M HCl is added and the new volume is 2.5 L? The pKa of phosphoric acid (H3PO4) is 2.1.

Which of the following buffers would be the best for a basic solution?

Calculate the ratio to bicarbonate to carbonic acid if the buffer system will be used to keep the pH at 10.1. The pKa of bicarbonate is 10.3.

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