Titration

We will now discuss the topic of titrations, with a focus on acid-base titrations. Titration is an extremely common technique in laboratory chemistry, and your lab work for this week will center on a titration. While not all titrations involve acid-base reactions, this will be a good context for you to learn about them; if you take future chemistry classes, you may encounter other kinds of titration.

To fully understand titrations, there are three points that are important to get down:

Purpose: the goal of a titration is to determine the concentration of an unknown solution by reacting it under certain conditions with a known solution. Despite the name, we must have some minimal information about our unknown solution; for example, we must know that it contains an acid. We may or may not know exactly what is in it, or what its concentration is. For the known solution, we must know its what it contains, its concentration, and how it reacts with the unknown.
Concept: a titration relies on the concept of the equivalence point. An equivalence point is a point at which exactly enough of the known solution has been mixed with the unknown solution to fully use it up (and no more). At that point, a mathematical relationship between the volumes and concentrations of the two solutions can be developed (details below).
Method: in order to perform a titration, certain tools are needed. You need to be able to add one solution to the other in a gradual, controlled way. You also need to be able to tell when the equivalence point has been reached, so that you know when to stop adding the solution and do your calculations. This is usually accomplished using an indicator, which is a substance that changes color when the reaction is complete, although other methods (like tracking the pH as solutions are mixed) can also be used.

Neutralization Reactions

A titration involves mixing two solutions that react together in a way that is safe, convenient, rapid, and well-understood. Neutralization reactions of acids and bases (which we learned about in Lesson 5) usually meet these requirements: they are extremely fast and easy to perform, and while care must be taken any time you work with acids and bases, neutralizations almost always create products that are safer than the reactants. In addition, there are straightforward rules for writing equations of neutralizations, and the mathematics of their behavior can be easily understood using the concept of equivalents/normality we just learned.

As you have learned, neutralizations occur between acids (which contain H⁺) and bases (which contain OH^-). The combination of these ions makes water (written as HOH at right), while the "leftover" cation and anion combine to make a salt (ionic compound).

A simple example is shown below. You can see how the potassium and chloride ions are recombined in the reaction, and a water molecule is created.

HCl + KOH → H₂O + KCl

The example below is a bit more complex because it combines a monoprotic acid and diprotic base. This creates two water molecules and also forces you to pay attention to the formula of the salt and how the equation balances.

2 HNO₃ + Ba(OH)₂ → 2 H₂O + Ba(NO₃)₂

One final example, even more complex in terms of its balancing and formulas, is shown below. You should be able to write an equation for the neutralization of any acid and base you are given. Review Lesson 5 if needed to make sure you have a good handle on this topic.

2 H₃PO₄ + 3 Ca(OH)₂ → 6 H₂O + Ca₃(PO₄)₂

Performing a Titration

We do an acid-base titration to learn the concentration of an unknown solution. For example, I might have a flask of HCl whose concentration is unknown. Or I might not even know what acid I have, just that it is an acid in solution. In either case, we will determine the acid's concentration by reacting it with a base (of known concentration) in a neutralization reaction. A KOH solution of known concentration would be a good choice, and the reaction will proceed according to the top equation above.

We need to perform this reaction in a particular way. We will measure the volume of our unknown solution (the acid in this case) and then add enough known solution (base) to exactly react with all the acid. Put another way, we want neither of our reactants to be limiting or in excess; rather, we are looking for the equivalence point (also known as the endpoint) where they are perfectly balanced.

How do we find this point? Well, first off, we will need to add our known solution slowly and steadily. The best tool for doing this is a burette, which is a long glass tube with markings much like a graduated cylinder. However, instead of pouring from a burette, it is equipped with a stopcock that allows you to easily dispense small amounts of solution. Or, even better, you can set the stopcock so that the known solution drips in at a slow, steady rate. This means that when the endpoint is detected, you can quickly shut the burette and measure the volume of solution that has been added.

Most neutralization reactions are totally invisible. There is no visual indication of the reaction taking place, and no way to detect when the unknown solution has been all used up. Fortunately, we can use an indicator, such as phenolphthalein, to tell us when we have reached our reaction endpoint.

Phenolphthalein is a compound that is colorless in acids but pink in the presence of bases. We mix it with our acid before beginning to add base, and at first it is invisible.

However, as time goes on, we will begin to see flashes of pink appear as drops of base hit the titration flask. The phenolphthalein is turning briefly pink, until the base reacts with the acid and is consumed. This is a good indication that the endpoint is coming up and you should slow down the addition of base.

Once the acid is entirely used up, the base stops being consumed as it is dropped into the flask. With nowhere for it to go, the pink color of the phenolphthalein no longer disappears. This is how the phenolphthalein acts as an indicator; when the solution turns a pale pink, you know you have reached your titration's equivalence point, and you can measure the volume of known solution you have added (using the burette markings).

It's important to be careful not to overshoot the endpoint. A dark pink color indicates that excess base has been added, meaning the measurement of the volume of base will be somewhat inaccurate, throwing off the subsequent calculations we will learn about below.

Titration Calculations

At the end of the titration we will have three important pieces of data. First is the concentration of known solution, in this case the base concentration. This we will usually know because we prepared the solution ourselves or it was given to us with the concentration on the label. While we may be given a concentration in molar, it will be essential that we convert this value to be in normal (N) before our calculations.

We also know the volumes of both solutions involved. In this case, we would have measured the acid volume prior to adding any base, and we would use the initial and final volumes of our burette.

The calculations are easiest when you use normality for the concentration, because normality is based on equivalents and one equivalent of any acid exactly neutralizes one equivalent of any base. Therefore, at the endpoint, the number of equivalents of acid must be the same as the number of equivalents of base.

Recall that an equivalent is the amount of acid (or base) that delivers one mole of H⁺ (or OH^-) ions. If the number of equivalents of acid is the same as the number of equivalents of base, then the number of H⁺ ions must be the same as the number of OH^- ions, and the two will just exactly neutralize each other.

How does this relate to the volumes we measured? Well, normality is equal to the number of equivalents in a solution over that solution's volume, and we can rearrange that equation to show that the number of equivalents of either acid or base are equal to the normality times the volume.

Substituting this product in for equivalents of acid and base, we get the equation N_AV_A = N_BV_B as shown at right.

Since you know both volumes and one of the concentrations, it’s an easy matter to solve for and compute the concentration you don’t know.

In these equations, notice that one volume is divided by the other. This means that it is not necessary to convert the volumes from milliliters to liters before performing the calculations. It is necessary, however, to have the two volumes expressed in the same units. Those units, no matter what they are, will then cancel.

Suppose, for example, that the titration of 23.60 mL of HNO₃ with 0.204 N NaOH requires 11.20 mL of the base.

To find the concentration of the acid, we solve the titration equation for N_A, plug in the values for the two volumes and the normality of the base, and perform the arithmetic.

Even though the concentration of base is expressed in equivalents per liter, it was not necessary to change the volumes from milliliters to liters. The units of the volumes, mL, canceled.

Your lab workbook has several titration practice problems you can complete to test your skills. Ultimately, the equation is not that complicated ... just make sure you are correctly plugging in your concentration and volume values, and work carefully through the algebra.

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