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# Acid-Base Titration

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A titration is a process widely used by chemists to determine the unknown concentration of a solution. One method is called acid-base titration. In this article, we will look at the process of acid-base titration, the different types, and how we use it to calculate concentration.

• We will describe the acid-base titration definition and theory
• Next, we will learn the formula for calculating the concentration of the analyte
• We will walk through the titration process and understand how to set up and perform the experiment
• Lastly, we will look at titration curves and see how they illustrate what is happening during the titration

## Acid-base Titration Definition

An acid-base titration is a process of adding a substance with a known concentration (titrant) to a substance with an unknown concentration (analyte) to determine the concentration of that substance. It is considered specifically an acid-base titration because an acid-base reaction is occurring between the titrant and analyte.

## Acid-base Titration Theory

Before we dive into the experiment itself, let's do a recap of acid-base reactions. Acid-base titrations hinge on the fact that the pH of a solution changes when an acid and base are reacted together. When a base is added, the pH increases, the opposite is true for acids. When the pH of a solution is equal to 7, it is at the equivalence point, which is the point where the concentration of the acid is equal to the concentration of the base. The formula for this is:

M1V1 = M2V2

where, M1, is the molarity of solution 1, M2, is the molarity of solution 2, V1, is the volume of solution 1, and V2, is the volume of solution 2.

## Acid-Base Titration Example

Let's look at an example:

15.2 mL of 0.21 M Ba(OH)2 is required to reach the equivalence point with 23.6 mL of HCl, what is the concentration of HCl?

We start by writing out our balanced reaction:

$$Ba(OH)_{2\,(aq)} + 2HCl_{(aq)} \rightarrow BaCl_{2\,(aq)} + 2H_2O_{(l)}$$

Since HCl and Ba(OH)2 have a 2:1 ratio, we need to reflect that in our equation:

$$M_{HCl}V_{HCl}=2M_{Ba(OH)_2}V_{Ba(OH)_2}$$

Now we can plug in our values. We don't need to convert from mL to L since both compounds are using the same units

$$M_{HCl}V_{HCl}=2M_{Ba(OH)_2}V_{Ba(OH)_2}$$

$$M_{HCl}(23.6\,mL)=2(0.21\,M)(15.2\,mL)$$

$$M_{HCl}=0.271\,M$$

Here is another way to solve this problem:

$$15.2\,mL*\frac{1\,L}{1000\,mL}*\frac{0.21\,mol}{L}=0.00319\,mol\,Ba(OH)_2$$

$$0.00319\,mol\,Ba(OH)_2*\frac{2\,mol\,HCl}{1\,mol\,Ba(OH)_2}=0.00638\,mol\,HCl$$

$$\frac{0.00638\,mol}{23.6\,mL*\frac{1\,L}{1000\,mL}}=0.270\,M\,HCl$$

You can use whichever works best for you, but both methods work just fine!

Now that we know the basics, let's look at how we perform the titration.

## Acid-base Titration Procedure

Let's look at how we would perform an acid-base titration in the lab. For our first step, we need to pick our titrant. Since this is an acid-base reaction, if our analyte is an acid, the titrant has to be a base and vice-versa. We take our titrant and pour it into a buret (a long tube with a dropper at the bottom). The buret is clamped above a flask which will be filled with the analyte (make sure to note the volume of both the titrant and analyte). The next thing we need to do is add the indicator to the analyte solution.

An indicator is a weak acid or base that does not take place in the main acid-base reaction. When there is an excess of the titrant, it will react with the indicator, and it will change color. This color change indicates the endpoint of the acid-base reaction.

Many indicators will change color at certain pH ranges. When choosing an indicator, you want to pick one that will change color at a pH close to the endpoint. Here are some common indicators:

 Name Color change (acid to base) pH range Methyl violet Yellow ↔ Blue 0.0-1.6 Methyl orange Red ↔ Yellow 3.2-4.4 Methyl red Red ↔ Yellow 4.8-6.0 Bromothymol blue Yellow ↔ Blue 6.0-7.6 Phenolphthalein Colorless ↔ Pink 8.2-10.0 Thymolphthalein Colorless ↔ Blue 9.4-10.6

Once we have picked our indicator, we will add a few drops of it to our analyte solution. Next, we will turn the buret open, so drops of the titrant can flow out. When a flash of color appears, we close the buret slightly to slow down the flow. When the color stays for longer, we swirl it around until it returns to its original color. Once the indicator has changed color and stayed that way for several seconds, the titration is finished.

The setup for the titration. The pink splash is Phenolphthalein beginning to change color, indicating we are near the endpoint. Pixabay

We note the final volume of the titrant, then repeat the experiment a few times for accuracy. Once we have our average volume of titrant used, we can use that to calculate the concentration of the analyte.

## Acid-base Titration Curves

The way we visualize these titrations is through titration curves.

A titration curve is a graph showing the progress of a titration. It compares the pH of the analyte solution with the volume of titrant added.

A titration curve can help us figure out the volume of the titrant at the equivalence point. The equivalence point is always at pH = 7 since the solution will be neutral when there are equal amounts of acid and base. The shape of the curve is dependent on the strength of the acid/base and whether the analyte is an acid or base. Let's look at an example:

30.0 mL of HCl with an unknown concentration is titrated with 0.1 M of NaOH, what is the concentration of HCl?

The titration curve of HCl (analyte) and NaOH (titrant) shows the equivalence point and why phenolphthalein is used as the indicator. StudySmarter Original

Let's start by looking at the equation for this reaction:

$$NaOH_{(aq)} + HCl_{(aq)} \rightarrow NaCl_{(aq)} + H_2O_{(l)}$$

Based on our formula, there is a 1:1 ratio between NaOH and HCl, so we don't need to tweak our formula.

We know from our titration curve that it takes 20mL of NaOH to reach the equivalence point, so we can plug that data into our formula:

$$M_1V_1=M_2V_2$$

$$M_{HCl}(30.0\,mL)=(0.1\,M)(20.0\,mL)$$

$$M_{HCl}=0.067\,M$$

In our example, I noted the pH range for the color change of phenolphthalein. When choosing an indicator, you want to pick one that's range is both past the equivalence point and before the endpoint (the end of the "spike" in the curve). One of the ways we can determine which to pick is based on the general titration curve shapes. There are 8 of these in total and are shown in the illustrations below:

There are 4 different possible shapes for the curve when an acid is the analyte. StudySmarter Original

There are 4 different possible shapes for the curve when a base is the analyte. StudySmarter Original.

You'll notice that there are technically 4 shapes, as the base analyte curves (in blue) are mirrors of the acid analyte curves (in red). For example, the weak acid/strong base curve for the acid analyte is the reverse of the strong acid/weak base curve. To help pick out an indicator, you need to know the identity of the titrant and analyte as well as their strengths, then you can match up the pair to the curve.

What indicator should be used for an acid-base titration where NH4OH is the analyte and HBr is the titrant?

NH4OH is a base, so we will be picking from the picture on the bottom. It is also considered a weak base, so that knocks out the curves on the left side. Lastly, HBr is a strong acid, so the correct curve is the one on the top right. From that graph, we see that the endpoint is at a pH of approximately 3.5. Methyl orange has a pH range of 3.2-4.4, so it is a good choice for this titration.

### Polyprotic Acid-base Titrations Examples and Curves

The titrations we've looked at previously have all been with monoprotic acids, but these titrations can also be done with polyprotic acids. These are acids that have more than one proton to donate. The titration curves for these look different since there are multiple equivalence points: one for each proton donated. Let's first look at one of these curves:The titration curve of a polyprotic acid (analyte) with a strong base shows the different equivalence points for each step of the reaction. StudySmarter Original

There's a lot going on in this curve, so let's break it down piece by piece. Let's start by looking at the equations for these reactions:

$$H_2SO_{3\,(aq)} +NaOH_{(aq)} \rightarrow HSO_{3\,(aq)}^{-} + H_2O_{(l)}+Na^+$$

$$HSO_{3\,(aq)}^- +NaOH_{(aq)} \rightarrow SO_{3\,(aq)}^{2-} + H_2O_{(l)}+Na^+$$

Sulfurous acid, H2SO3, has 2 protons it can donate, so it has two equivalence points, as shown by the circles on the graph. Their equations are:

$$[HSO_3^-]=[NaOH]\,\,\text{(equivalence point 1)}$$

$$[SO_3^{2-}]=[NaOH]\,\,\text{(equivalence point 2)}$$

The other key points on this graph are the half-equivalence points, triangles on the graph. These are when the concentration of the acid is equal to the concentration of its conjugate base. Their equations are:

$$[H_2SO_3]=[HSO_3^-]\,\,\text{(half-equivalence point 1)}$$

$$[HSO_3^-]=[SO_3^{2-}]\,\,\text{(half-equivalence point 2)}$$

One thing to note is that polyprotic acids are always weak acids. As you can see in the graph, the acid gets weaker as it loses more protons, so the "spike" at the equivalence point gets smaller. But what if our analyte is a base?

The titration curve for a base that becomes a polyprotic acid. This curve is a mirror of the polyprotic acid analyte curve. StudySmarter Original

In this reaction, Na2SO3 is our base. Let's look at the reactions:

$$Na_2SO_{3\,(aq)} + HCl_{(aq)} \rightarrow NaHSO_{3\,(aq)}^- + NaCl_{(aq)}$$

$$NaHSO_{3\,(aq)}^- + HCl_{(aq)} \rightarrow H_2SO_{3\,(aq)} + NaCl_{(aq)}$$

So instead of having a polyprotic acid donate multiple protons, we have a base gaining those protons to form the polyprotic acid. It can do this since HCl is a much stronger acid than H2SO3.

## Acid-Base Titration - Key takeaways

• An acid-base titration is a process of adding a substance with a known concentration (titrant) to a substance with an unknown concentration (analyte) to determine the concentration of that substance.
• We can use the formula $$M_1V_1=M_2V_2$$ to calculate the concentration of the unknown
• An indicator is a weak acid or base that will react with the excess titrant and change color. This color change signifies the endpoint of the reaction
• We use titration curves to visualize a titration
• Polyprotic acids will have multiple equivalence points (equal to the number of protons) when titrated

An acid-base titration is when an acid or base with a known concentration is added to a base or acid with an unknown concentration so that the unknown can be calculated.

A solution of 0.1 M NaOH is slowly added to a solution of HCl until the indicator changes color, which notes the end of the reaction. The volume of NaOH needed can be used to determine the concentration of NaOH.

The analyte solution is poured into a beaker, with a few drops of indicator added to it. A buret full of the titrant is clamped above the beaker. The buret is open so that the titrant is added to the HCl until the indicator changes color. Once it changes color, the buret is closed and the mL of titrant used is recorded.

The four types are: Strong acid-Strong base, Strong acid-Weak base, Weak acid-Strong base, and Weak acid-Weak base.

Acid-base titration is used to determine the concentration of an acid or base.

## Acid-Base Titration Quiz - Teste dein Wissen

Question

43.2 mL of 0.35 M Ba(OH)2 is required to fully react with 54.2 mL of HClO4, what is the concentration of the acid?

0.558 M

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Question

What are the steps in the titration process?

Choose a titrant with a known concentration (if the analyte is an acid choose a base and vice versa). Add the titrant to the buret which is clamped above the flask filled with the analyte (make sure you note the volume). Add an appropriate indicator to the flask. Open the buret and let the titrant flow until the indicator changes color. Then note how many mLs of titrant were used and use that to calculate the concentration of the acid.

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Question

Which of the following indicators is best used for a titration with HCOOH as the analyte and LiOH as the titrant?

Thymolphthalein (9.4-10.6)

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Question

How many equivalence points would a titration of H3PO3 have?

3

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Question

What is an acid-base titration?

An acid-base titration is a process of adding a substance with a known concentration (titrant) to a substance with an unknown concentration (analyte) to determine the concentration of that substance.

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Question

What is an indicator?

An indicator is a weak acid or base that does not take place in the main acid-base reaction. When there is an excess of the titrant, it will react with the indicator, and it will change color. This color change indicates the endpoint of the acid-base reaction.

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Question

What is an equivalence point?

An equivalence point is where we have equal concentrations of acid and base in solution.

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Question

What is a half-equivalence point (for polyprotic acids)?

A half-equivalence point is where the concentration of acid is equal to the concentration of its conjugate base

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Question

True or False: Indicators change color at the titration's equivalence point

False

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Question

What two factors determine the shape of a titration curve?

1. Strength of the acid and base

2. Whether the analyte is an acid or base

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