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# Acid-Base Reactions and Buffers

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When you take a shower and lather up your hair with shampoo, you are being protected by something called a buffer. The detergents in shampoo are so naturally alkaline/basic that you could burn your scalp, and nobody wants that! Compounds like citric acid or sodium citrate are used to keep the shampoo slightly acidic to neutralize the natural alkalinity. Buffers are also used in products like baby lotion, which keeps the skin slightly acidic to prevent bacteria growth.

• We will first define what these terms are and see what acid-base reactions look like.
• Then we will learn about the different types of buffer solutions and see how they work.
• Lastly, we will learn how to calculate the pH of buffer solutions using the Henderson-Hasselbalch equation and walk through some examples using it.

## Definition of Acid-base Reactions and Buffers

For starters, let's take a look at the definition of an acid-base reaction, and a buffer solution.

In an acid-base reaction, an acid donates a proton (H+ ion) to a base, which accepts it. These reactions involve a change in pH, which is a measure of how acidic/basic a solution is: the range of the pH scale is 0 (most acidic) to 14 (most basic).

A buffer is a solution that resists changes in pH. The solution is a mix of a weak acid and its conjugate base (the base that results from that acid losing a proton) or a weak base and its conjugate acid (the acid that results from that base gaining a proton).

Now that we've covered the basic definitions, let's look at what acid-base reactions look like!

The definition we are using for acid-base reaction is based on the Brønsted-Lowry definition of acids and bases. There is a second classification called Lewis acids and bases. In these acid-base reactions, electrons are donated instead of protons.

## Acid-base Reaction Equations

Acid-base reactions follow a basic structure: $$HA + B \rightarrow A^- + HB$$

Here, HA is our acid, which donates a proton to the base, B. The symbol, A-, is the conjugate base and HB is the conjugate acid.

While all acid-base reactions follow this same structure, the reaction is slightly different based on the strength of the acid and/or base. Strong acids/bases dissociate completely. Here is an example:

$$HCl \rightleftharpoons H^+ + Cl^-$$

Hydrochloric acid (HCl) is a strong acid, so it will completely dissociate into its ions: H+ and Cl-. After the dissociation, the concentration of the ions is equal to the initial concentration of the strong acid/base.

Weak acids/bases work differently because they do not dissociate completely. Here's another example: $$CH_3COOH \rightleftharpoons CH_3COO^- + H^+$$

Acetic acid is a weak acid, so it only partially dissociates into an H+ ion and the conjugate base. Since the dissociation isn't complete, you will still have the weak acid, and in a much higher concentration than its ions.

Here is a diagram to explain:

Fig. 1 - Strong acids dissociate completely, while weak acids only partly dissociate.

When a strong acid (or base), dissociates it will be completely converted into its ions. For a weak acid/base, however, there is only a partial conversion.

The difference in how these reactions work is why buffers are made from weak acids and bases and not strong ones.

## Types of Buffer Solution

Before we get into why buffer solutions use weak acids/bases, let's talk about the different types of bases. There are two types of buffers:

1. Acidic buffer solutions
2. Alkaline buffer solutions

Acidic buffer solutions are used in systems that have a pH below 7 (i.e. acidic systems). These are made up of a weak acid and its conjugate base. Alkaline buffer solutions are used in systems with a pH above 7 (basic solutions). These are made up of a weak base and its conjugate acid.

Here is a table of some common buffers:

 Name of buffer Chemical formula of buffer Type of buffer pKa Hydrofluoric acid/Sodium fluorate HF/NaF Acidic 3.8 Phosphate/Phosphoric acid H2PO4-/H3PO4 Alkaline 12.4 Ammonia/Ammonium NH4+/NH3 Alkaline 9.3 Acetic acid/Acetate CH3COOH/CH3COO- Acidic 4.8 Nitrous acid/Sodium nitrite HNO2/NaNO2 Acidic 3.2 Bicarbonate/Carbonic acid HCO3-/H2CO3 Alkaline 10.3

Now that we know the different types, we can learn how buffer solutions keep the pH stable.

## Neutralization Reaction of Acids and Bases for Buffers

The goal of a buffer is to neutralize any added acid or base as much as possible, therefore these buffers participate in neutralization reactions.

A neutralization reaction is a reaction between an acid and a base that produces water and a salt. The acid and base "cancel" each other, so that the products have a neutral pH (7).

The reactions that happen are dependent on what is being added to the buffer system. Let's start by looking at acidic buffers. The system we will be using is acetic acid/acetate (HC2H3O2/C2H3O2-).

When a strong base is added, the OH- will be neutralized by the weak acid:

$$HC_2H_3O_2 + OH^-\rightarrow H_2O + C_2H_3O_2^-$$

The buffer "absorbs" the OH- ions, so the pH won't change much.

When a strong acid is added, the H+ ions will combine with the conjugate base to reform the weak acid: $$H^+ + C_2H_3O_2^-\rightarrow HC_2H_3O_2$$

Here is a graphic showing what's going on in solution:

Fig. 2 - The effects of adding a strong acid or base on a buffer system.

The formation of the weak acid/conjugate base will only change the pH slightly, due to their weakness. However, if this was a strong acid or base, that would be a different story. Buffers are made from weak acids/bases because of this.

Alkaline buffers work in the same way since they also contain a weak acid and weak base.

## pH of Buffer Solution

We know that buffers are designed to keep the pH stable, but the pH will still be altered slightly when a strong acid or base is added. The way we measure the pH of a buffer solution is by using the Henderson-Hasselbalch equation.

The Henderson-Hasselbalch equation measures the pH of buffer systems. The formula is: $$pH=pK_a+log(\frac{[A^-]}{[HA]})$$

where [A-] is the concentration of base, [HA] is the concentration of acid, and pKa is the negative logarithm of Ka the acid dissociation constant

The acid dissociation constant (Ka) measures the strength of an acid. The larger the Ka, the stronger the acid. For a general reaction

$$HA \rightleftharpoons A^- + H^+$$

The formula for Ka is:

$$K_a=\frac{[A^-][H^+]}{[HA]}$$

Let's work on a quick example problem.

What is the pH of a buffer solution of 0.2 M acetic acid (CH3COOH) / 0.15 M acetate (CH3COO-) if the pKa of acetic acid is 4.8?

All we need to do is plug these values into our equation. Here acetate is the base, so it will be in the numerator.

$$p\,H = pK_a+log( \frac{[A^-]} {[HA]} )$$ $$p\,H = 4.8+log(\frac{[0.15\,M]}{[0.2\,M]})$$ $$p\,H = 4.8-0.125$$ $$p\,H = 4.675$$

When the concentrations of the acid and base are equal, then the logarithm will be equal to zero. This means that the pKa= pH

The concentration of acid and base listed in the equation is the total concentration, not just for the buffer. So if HCl was added to a buffer sample, the concentration of the acid would be a sum of the concentrations of the weak base and the HCl. In the next section, we will walk through these types of examples.

## Examples of Acid-base Reactions and Buffers

Now that we know how to calculate the pH of buffer solutions, we can learn how to calculate the pH when a strong acid/base is added. Let's walk through some examples together.

A 1.0 L buffer solution of 0.20 mol hydrofluoric acid (HF) and 0.20 mol sodium fluoride (NaF) is used to keep the pH of an acidic system stable. What is pH when 0.15 mol of HCl is added which brings the total volume to 1.2 L? The pKa of HF is 3.8.

As mentioned previously, we calculate the pH using the total concentration of the acid and base. Firstly, we can calculate the concentration of base, which is just the molar amount divided by the (new) total volume.

$$\frac{0.20\,mol}{1.2\,L}=0.167\,M\,A^-$$

I labeled the acid and base as HA and A- instead of by their names since that is the terms the Henderson-Hasselbalch equation is in.

Next, we calculate the volume of the acid. We do this by adding the molar amounts of HF and HCl together, then dividing that by the volume.

$$\frac{0.20\,mol+0.15\,mol}{1.2\,L}=0.29\,M\,HA$$

Now we just plug these values into our equation to get the pH of the system when the HCl is added.

$$pH=pK_a+log(\frac{[A^-]}{[HA]})$$ $$pH=3.8+log(\frac{[0.167\,M]}{[0.29\,M]})$$ $$pH=3.8-0.24$$ $$pH=3.56$$

Now let's try an example where a base is added.

A 1.6 L buffer solution of 0.35 mol ammonia (NH3)/ammonium (NH4Cl) is used to keep the pH of a basic system stable. What is the pH when 0.22 mol of NaOH is added, bringing the total volume to 2.0 L? The pKa of ammonium is 9.3.

Like before, we need to calculate the concentration of both the acid and base. The concentration of acid is just the molar amount of ammonium divided by the total volume, while the concentration of base is the sum of the molar amounts of ammonia and NaOH divided by volume.

$$\frac{0.35\,mol}{2.0\,L}=0.175\,M\,HA$$ $$\frac{(0.35\,mol+0.22\,mol)}{2.0\,L}=0.285\,M\,A^-$$

Now we plug this info into the equation and solve for pH.

$$pH=pK_a+log(\frac{[A^-]}{[HA]})$$ $$pH=9.3+log\frac{[0.285\,M]}{[0.175\,M]}$$ $$pH=9.3+0.21$$ $$pH=9.51$$

Let's do one more problem. This time we'll be calculating the change in pH.

A 2.3 L buffer solution of 0.25 mol nitrous acid (HNO2)/ 0.23 mol sodium nitrite (NaNO2) is used to keep the pH of an acid system stable. What is the change in pH if 0.17 mol of LiOH is added to the system, bringing the total volume up to 2.8 L? The pKa of nitrous acid is 3.16.

Since we want the change in pH, we need to calculate the pH before and after the base is added. We first need to get the concentrations of the acid and base before LiOH is added: $$\frac{0.25\,mol}{2.3\,L}=0.109\,M\,HA$$

$$\frac{0.23\,mol}{2.3\,L}=0.100\,M\,A^-$$ Now we calculate pH

$$pH=pK_a+log(\frac{[A^-]}{[HA]})$$ $$pH=3.16+log\frac{[0.100\,M]}{[0.109\,M]}$$ $$pH=3.16-0.037$$ $$pH=3.123$$

Now we need to solve for the pH of the system once LiOH is added. Like before, the concentration of base is equal to the sum of the molar amounts LiOH plus NaNO2 divided by the new total volume. $$\frac{0.25\,mol}{2.8\,L}=0.089\,M\,HA$$ $$\frac{(0.17\,mol+0.23\,mol)}{2.8\,L}=0.14\,M\,A^-$$

Now we calculate the new pH: $$pH=pK_a+log(\frac{[A^-]}{[HA]})$$ $$pH=3.16+log\frac{[0.14\,M]}{[0.089\,M]}$$ $$pH=3.16+0.20$$ $$pH=3.36$$

Lastly, we need to calculate the change in pH by subtracting the original pH from the new pH. $$3.36-3.123=0.237$$

Now, I hope that you feel more confident in your understanding of acid-base reactions and buffers!

## Acid-Base Reactions and Buffers - Key takeaways

• In an acid-base reaction, an acid donates a proton (H+ ion) to a base, which accepts it. These reactions involve a change in pH, which is a measure of how acidic/basic a solution is, from 0 (most acidic) to 14 (most basic).
• A buffer is a solution that resists changes in pH.
• The solution is a mix of a weak acid and its conjugate base (the base that results from that acid losing a proton) or a weak base and its conjugate acid (the acid that results from that base gaining a proton).
• There are two types of buffers:
• The Henderson-Hasselbalch equation measures the pH of buffer systems. The formula is: $$pH=pK_a+log(\frac{[A^-]}{[HA]})$$, where [A-] is the concentration of base, [HA] is the concentration of acid, and pKa is the negative logarithm of Ka the acid dissociation constant.

A strong base can be added to the weak acid to partially convert it into its conjugate base, so the solution contains both the weak acid and conjugate base.

Buffers are a combination of a weak acid + its conjugate base or of a weak base + its conjugate acid. Acids and bases can be either strong or weak. Acids donate protons, while bases accept them.

Some examples are the reaction of HCl (acid) and NaOH (base), and HBr (acid) and LiOH (base).

Only weak acids and bases can make buffers. Some examples are bicarbonate + carbonic acid and acetic acid + acetate. The buffers are made of a weak base + its conjugate acid or a weak acid and its conjugate base.

A buffer is a solution that resists changes in pH. The solution is a mix of a weak acid and its conjugate base (the base that results from that acid losing a proton) or a weak base and its conjugate acid (the acid that results from that base gaining a proton). The two types of buffers are acidic (used in acidic solutions) and alkaline (used in alkaline/basic solutions).

## Acid-Base Reactions and Buffers Quiz - Teste dein Wissen

Question

What is an acid-base reaction?

In an acid-base reaction, an acid donates a proton (H+ ion) to a base, who accepts it. These reactions involve a change in pH, which is a measure of how acidic/basic a solution is, from 0 (most acidic) to 14 (most basic).

Show question

Question

What is a buffer?

A buffer is a solution that resists changes in pH. The solution is a mix of a weak acid and its conjugate base (the base that results from that acid losing a proton) or a weak base and its conjugate acid (the acid that results from that base gaining a proton).

Show question

Question

Which of the following is the correct general equation for an acid-base reaction?

$$HA + B \rightarrow A^- + HB$$

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Question

Fill in the blanks: A ___ acid/base dissociates completely, while a ___ acid/base only partially dissociates.

Strong, weak

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Question

What are the two types of buffers?

Acidic and Alkaline

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Question

Which of the following is an alkaline buffer?

Bicarbonate/carbonic acid $$pK_a=10.3$$

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Question

What is a neutralization reaction?

A neutralization reaction is a reaction between an acid and a base that produces water and a salt. The acid and base "cancel" each other, so that the products have a neutral pH (7).

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Question

Which of the following reactions represents a strong base being added to a buffer solution?

$$HF + OH^- \rightarrow H_2O + F^-$$

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Question

True or False: A buffer prevents any change to the pH

False

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Question

What is the Henderson-Hasselbalch equation?

The Henderson-Hasselbalch equation measures the pH of buffer systems. The formula is: $$pH=pK_a+log(\frac{[A^-]}{[HA]})$$

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Question

Which of the following are reasons why buffers cannot be made of strong acids/bases. (Select all that apply)

They dissociate completely

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Question

What is the pH of a 0.28 M ammonia (NH3)/ 0.33 M ammonium (NH4+) buffer solution? The pKa of ammonium is 9.3

pH=9.23

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Question

A 1.2 L solution of 0.20 mol acetic acid (CH3COOH)/0.30 mol acetate (CH3COO-) is used to keep the pH of an acidic system stable. A 0.25 mol solution of LiOH was added, bringing the total volume to 1.7 L. What is the new pH of the system? The pKa of acetic acid is 4.8.

pH=5.23

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Question

A 2.1 L buffer solution of 0.16 mol phosphate (PO43-)/0.21 mol phosphoric acid (HPO42-) is used to keep the pH of a basic system stable. A 0.22 mol solution of HBr was added, bringing the total volume to 2.6 L. What is the new pH of the system? The pKa of phosphoric acid is 12.4

pH=11.96

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Question

A 2.4 L buffer solution of 0.21 mol hydrofluoric acid (HF)/0.25 mol sodium fluorate (NaF) is used to keep the pH of an acidic system stable. What is the change in pH if 0.17 mol solution of NaOH is added to the solution, bringing the total volume to 2.7 L? The pKa of HF is 3.8.

0.39

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