Introduction The first of a series of similar experiments, this investigation focuses upon acid-base chemistry and in particular, the scientific technique known as a titration. In general terms, titrations utilize a known property of one solution to describe a similar property of an unknown solution. Specifically, these include acid-base titrations, potentiometric titrations (redox), complexometric titrations, and even titrations utilized to determine specific concentrations of bacteria or viruses. For example, the alkalinity and acidity of water in streams and rivers is an important topic to several environmental chemists, and in order to observe such characteristics, they use the same technique you will learn in this experiment—an acid-base titration. Titration Set-up The generalized setup of a titration is shown below (Figure 1). As you can see, the base solution is placed in the buret, so that an extremely precise amount of solution can be added to your acid. In detail, the buret's precision is attributed to its graduations up and down the tube, making it one of the more expensive instruments you will be using this semester. Please be careful, your wallet will thank you! You will also notice a knob on the buret. This device is called a stopcock, and its sole purpose is to deliver your titrant to your solution in a drop-wise manner. It too is fairly fragile!
Acid-Base Titrations When an acid solution is initially titrated with a strong base such as NaOH, the initial pH of the solution is low. As base is added to the acidic solution, the pH will gradually rise until the volume added is near the equivalence point, the point during the titration when equal molar amounts of acid and base have been mixed. Immediately before the equivalence point, the pH increases very rapidly until leveling off again with the addition of excess base (Figure 2). Overall, the volume of NaOH used to obtain the equivalence point allows you to determine the concentration of hydronium in your solution, and therefore the unknown concentration of your acid (or as in this experiment, titration of a known concentration of acid with an unknown concentration of base allows you to determine the concentration of hydroxide in your unknown). Figure 2 Essential to a successful titration is visualizing the ‘end’ of a particular titration, specifically referred to as the end point, and is the volume at which no more titrant should be added. In layman’s terms, this is the point at which your solution has undergone some chemical change, whether it is from an acidic solution to basic or when the solution is fully reduced/oxidized. To accomplish this feat, we often employ indicators. Indicators, often added in minute amounts to the solution of interest, are chemical compounds that undergo dramatic changes of color when a particular property of a solution is changed. Like titrations, indicators must also be specific for the reaction we are analyzing, acid-base titrations must use pH indicators, potentiometric titrations must use redox indicators, and so forth. pH and pH Meters The hydrogen ion concentration, expressed in terms of pH, is one of the most important properties of aqueous solutions as it can control the solubility of various species, the formation of complexes, and even the kinetics of an individual reaction. In order to obtain precise data of the particular hydronium concentrations of your various solutions, and to clearly observe the change in pH at the equivalence point, you will be using a device known as a pH meter. In general, a pH meter measures the differences in electromotive force between two electrodes. Specifically, this instrument contains an electrode sensitive to the concentration of the hydrogen ion as well as one used solely for a reference. If a thin membrane of a special glass is used to separate two solutions of different pH, then a potential difference is established between the two sides of the membrane. In fact, this is the effect that will be measured by your pH meters. Since there is a linear relationship between the measured potential difference of your solution and the pH, and the notion that all other variables remain fairly constant, pH meters utilize the Nernst equation to report the corresponding pH. Specifically, the Nernst equation is manipulated—shown below, where E is the measured electromotive force (EMF) and C is an instrument or electrode constant for the particular instrument being used—to report the pH of your solution.
For accurate measurements, it is necessary to calibrate the instrument using a buffer solution of approximately the same pH as the sample to be used. This calibration takes care of temperature effects and minor variations in the potential due to changes in the membrane, and is described in further detail here. Experiment Concepts Now with a detailed, and most likely boring, discussion of the methods and instruments to be utilized in this lab completed, we can dive into the actual chemistry behind this experiment. Since we are dealing with an acid-base titration, we have to first standardize our titrant, a solution of sodium hydroxide (NaOH), with a known concentration of hydrochloric acid (HCl). Then, with the standardized solution of NaOH, two polyprotic acids of unknown concentration will be titrated; the strong phosphoric acid (H3PO4) and the much weaker citric acid (H3C6H5O7) found in a sample of 7-Up®. As most of you are already experts in strong acid-strong base equilibria, we will devote a little extra time towards weak-acid equilibria. Weak Acid Equilibria A weak acid (HA) is one that will not fully dissociate in water. In other words, if the weak acid represented is allowed to ionize, as shown in the equation below, then a significant amount of HA will remain undissolved.
Further, at equilibrium, the dissociation for weak acids is generally referred to by its acid-dissociation constant (KA) and is mathematically represented as follows:
In this investigation you will be asked to experimentally determine the acid-dissociation constants of both phosphoric acid and citric acid, which at first appearance seems to be quite a difficult task. However, if we observe the generalized equilibrium expression for weak-acids, and realize that a substantial concentration of HA remains unionized, the task becomes far more bearable. From prior knowledge, we know that at equilibrium the concentration of the free hydronium ions (H3O+) is equal to the concentration of the conjugate base(A-). Therefore, the concentration of the weak acid at equilibrium is simply the concentration of H3O+, or A-, subtracted from the starting concentration of our weak acid. Mathematically, the relationship is expressed below:
From this logic, combined with the fact that pH is equal to the negative log of the hydrogen ion concentration, we can arrive at an expression for KA incorporating only the initial concentration of the weak acid, determined by titration, and the experimentally determined pH.
The acid-dissociation constant of a weak acid can also be obtained by another method. This method involves the ‘half equivalence point’, where just enough NaOH has been added to the weak acid to convert half of the acid to its salt. At this point, the concentration of the weak acid, [HA], is equal to the concentration of its conjugate base, [A-]. Utilizing this fact, our generalized equilibrium expression can now be defined as shown below due to the notion that [A-] and [HA] can be canceled out of the expression.
In fact, this form of the equation is often written as the Henderson-Hasselbalch equation, one you will become far too familiar with later this semester. Click Here to see the full derivation.
Overall, by performing all three of these titrations and plotting the pH versus volume of NaOH added, you will slowly begin to see how the pH of the solution changes as an acid, or base, is added. In fact, if you are precise enough, you will start to get an idea of just how the shape of a titration curve can be influenced by both the concentration and nature of the acid or base. Further, by titrating both strong and weak acids you will see different titration curves and how they change with the strength of the acid. Polyprotic Acids Both phosphoric acid and citric acid are triprotic acids, one form of polyprotic acid. This means that each of these acids has three ionizable hydrogens and thus three separate pKA values; one for each dissociation. What is important to understand about a polyprotic acid dissociation is that at any point along the curve there is some percentage of each acid form present in the solution. This means that unlike a monoprotic dissociation that is rather all or nothing, the pH of a polyprotic acid solution is dependent on several forms of the acid. Below is a collection of the equations of the fractional dissociation of phosphoric acid were we to try to accurately describe the forms of the acid present at each pH:
If you would like to see the plot of these equations which describes the "comings and goings" of each form of the acid (H3PO4 (f0), H2PO4-(f1), HPO42-(f2), and PO43-(f3)) click here and select the living graphs menu item. You can place the cursor on any point on the graph shown and it will give you the fractional composition of the acid. What you should notice is that at almost every pH there is at least some fraction of each form present. This holds true for all polyprotic acids.
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Titration of 7-Up©
