Acid and Base Concentrations

An Arrhenius acid is a substance that produces hydrogen ions when it dissolves in water, while a base produces hydroxide ions. Hydrogen ions immediately react with water to form hydronium ions, but for simplicity, we'll keep thinking of them as hydrogen ions. Depending on the amount of hydrogen ions or hydroxide ions in the solution, it is considered acidic or basic.

We measure the amount of acidity or basicity using pH, which is calculated as the negative log of the concentration of hydrogen ions. So, pH values under 7 are acidic, and pH values above 7 are basic. pH 7 is neutral.

Acids and bases are also compared based on their strength, which is different from their pH. An acid's strength is related to how easily the hydrogen ion dissociates from the anion, called the conjugate base. The same idea follows for a base in reference to the hydroxide ion and its conjugate acid. We can assign a value to that strength using the acid dissociation constant, or K_a.

K_a is defined using the concentrations of the non-dissociated acid and the dissociated hydrogen ions and conjugate base. You may often see this relationship represented as pK_a, which is simply the negative log of the K_a. The smaller the pK_a, the stronger the acid.

Some acids, like hydrochloric acid, are monoprotic, meaning that they can dissociate only one hydrogen ion. Polyprotic acids, like phosphoric acid, can dissociate several hydrogen ions. Each dissociation has its own pK_a.

So, how can we determine pK_a? One way is to perform an acid-base titration. Titration is performed by slowly adding a solution of known concentration to a solution of unknown concentration while observing the reaction between them. In this case, the acid reacts with the base in a neutralization reaction to form a salt and water.

So, if we want to measure the concentration of hydrogen ions in an acid, we can simply titrate with a strong base with a known hydroxide ion concentration until the acid is neutralized. To perform a titration accurately, the base needs to be standardized — meaning that you know the exact hydroxide ion concentration. This is not always straightforward.

For example, NaOH, which you will use in your experiment, is very hygroscopic, meaning that it absorbs water from the atmosphere. This happens to NaOH both as a solid and in solution. So, the true concentration of a NaOH solution may be lower than you would expect.

To determine the exact concentration of NaOH, we must first perform an acid-base titration. To do this, you must use the base to titrate an acid with a known concentration. Potassium hydrogen phthalate, KHP, is a non-hygroscopic acid, so we can accurately calculate its concentration from its mass.

We can see when the titration is complete — meaning that the acid is neutralized — by using a pH indicator like phenolphthalein. Phenolphthalein is neutral and colorless between about pH 0 and pH 8.

As the pH increases, two hydrogen ions dissociate. This anionic form is pink. So, when we begin the titration, the KHP solution is acidic and the phenolphthalein is colorless. As we add NaOH and the hydrogen ions are neutralized, the pH increases.

In this reaction, the solution is neutral when equal amounts of acid and base have been mixed together. After that, the addition of a little more NaOH makes the pH basic and the solution turns pink. This is referred to as the endpoint. If we know the moles of KHP and the volume of NaOH used to neutralize it, we can calculate the exact concentration of the base.

Once we have a standardized base, we can determine the pK_a of an acid by titrating a known concentration of the acid with our standardized base while monitoring the pH. The plot of pH versus the volume of base added is called a titration curve. The curve usually follows an S or sigmoidal shape, where the inflection point of the steepest part of the curve denotes an equivalence point.

Here, the moles of hydroxide ions and dissociated hydrogen ions are equal. Like pK_a, we'll see one equivalence point for each dissociated hydrogen ion. So, a monoprotic acid has only one equivalence point, and a triprotic acid has three.

When we perform the titration, we will know that we have passed the equivalence point when the pH indicator just barely turns from colorless to pink. This is called the titration endpoint. Like when we standardize the base, this is when the solution has a small excess of hydroxide ions and thus is slightly basic.

Another inflection point in the graph occurs halfway to the equivalence point. Here, the concentrations of the dissociated and non-dissociated acids are equal. Thus, the pH at this point is equal to the pK_a. So, if we perform a titration and determine the equivalence point volume, then we can calculate pK_a as the pH at half of this volume.

In this lab, you'll first standardize your base and then perform a titration using that standardized base to determine two pK_a’s of a polyprotic acid.