Why is the steepness of a titration curve helpful

In the case of a weak acid, for example, the initial pH is likely to be higher, so the titration curve starts higher. Further, the weaker the acid, the stronger will be its conjugate base, so the higher will be the pH at the equivalence point. These two factors raise the bottom part of the titration curve. The upper extent of the curve is of course limited by the concentration and strength of the titrant. These principles are clearly evident in the above plots for the titrations of acids and bases having various strengths.

Notice the blue curves that represent the titration of pure water a very weak acid with strong acid or base. Adding even half a drop of titrant can take us across the equivalence point!

When one of the reactants is weak, the pH changes rapidly at first until buffering sets in. The equivalence point pH of 7 in these examples reflects the near-equality of pK a and pK b of the reactants.

Chem Ed. The problem here is that aqueous solutions are buffered against pH change at very low and very high pH ranges. An extreme example occurs in the titration of pure water with a strong acid or base. The above plots clearly show that the most easily-detectable equivalence points occur when an acid with is titrated with a strong base such as sodium hydroxide or a base is titrated with a strong acid. In practice, many of the titrations carried out in research, industry, and clinical practice involve mixtures of more than one acid.

Examples include natural waters, physiological fluids, fruit juices, wine making, brewing, and industrial effluents. For titrating these kinds of samples, the use of anything other than a strong titrant presents the possibility that the titrant may be weaker than one or more of the "stronger" components in the sample, in which case it would be incapable of titrating these components to completion. In terms of proton-free energies, the proton source the acidic titrant would be unable to deliver an equivalent quantity of protons to the stronger component of the mixture.

There will be as many equivalence points as there are replaceable hydrogens in an acid. In general, there are two requirements for a clearly discernible jump in the pH to occur in a polyprotic titration:. The effect of the first point is seen by comparing the titration curves of two diprotic acids, sulfurous and succinic. The appearance of only one equivalence point in the latter is a consequence of the closeness of the first and second acid dissociation constants.

The pK a 's of sulfurous acid below, left are sufficiently far apart that its titration curve can be regarded as the superposition of those for two independent monoprotic acids having the corresponding K a 's. This reflects the fact that the two acidic —OH groups are connected to the same central atom, so that the local negative charge that remains when HSO 3 — is formed acts to suppress the second dissociation step. Inspection of the species distribution curves for succinic acid above, right reveals that the fraction of the ampholyte HA can never exceed 75 percent.

Thus the rise in the pH that would normally be expected as HA is produced will be prevented by consumption of OH — in the second step which will be well underway at that point; only when all steps are completed and hydroxide ion is no longer being consumed will the pH rise. Two other examples of polyprotic acids whose titration curves do not reveal all of the equivalence points are sulfuric and phosphoric acids.

Whether or not the equivalence point is revealed by a distinct "break" in the titration curve, it will correspond to a unique hydrogen ion concentration which can be calculated in advance.

There are many ways of determining the equivalence point of an acid-base titration. The traditional method of detecting the equivalence point has been to employ an indicator dye, which is a second acid-base system in which the protonated and deprotonated forms differ in color, and whose pK a is close to the pH expected at the equivalence point.

If the acid being titrated is not a strong one, it is important to keep the indicator concentration as low as possible in order to prevent its own consumption of OH — from distorting the titration curve. The observed color change of an indicator does not take place sharply, but occurs over a range of about 1. Indicators are therefore only useful in the titration of acids and bases that are sufficiently strong to show a definite break in the titration curve.

Some plants contain coloring agents that can act as natural pH indicators. These include cabbage shown , beets, and hydrangea flowers. For a strong acid - strong base titration, almost any indicator can be used, although phenolphthalein is most commonly employed. For titrations involving weak acids or bases, as in the acid titration of sodium carbonate solution shown here, the indicator should have a pK close to that of the substance being titrated.

When titrating a polyprotic acid or base, multiple indicators are required if more than one equivalence point is to be seen. The pK a s of phenolphthalein and methyl orange are 9. A more modern way of finding an equivalence point is to follow the titration by means of a pH meter. Because it involves measuring the electrical potential difference between two electrodes, this method is known as potentiometry.

Until around , pH meters were too expensive for regular use in student laboratories, but this has changed; potentiometry is now the standard tool for determining equivalence points. Plotting the pH after each volume increment of titrant has been added can yield a titration curve as detailed as desired, but there are better ways of locating the equivalence point. A second-derivative curve locates the inflection point by finding where the rate at which the pH changes is zero.

The differential plot , showing rate-of-change of pH against titrant volume, locates the inflection point which is also the equivalence point. In a standard plot of pH-vs-volume of titrant added, the inflection point is located visually as half-way along the steepest part of the curve.

The idealized plots shown above are unlikely to be seen in practice. Recall that the ionization constant for a weak acid is as follows:. Taking the negative logarithm of both sides,. When a strong base is added to a solution of a polyprotic acid, the neutralization reaction occurs in stages. The most acidic group is titrated first, followed by the next most acidic, and so forth. Oxalic acid, the simplest dicarboxylic acid, is found in rhubarb and many other plants.

Oxalate salts are toxic for two reasons. As a result, calcium oxalate dissolves in the dilute acid of the stomach, allowing oxalate to be absorbed and transported into cells, where it can react with calcium to form tiny calcium oxalate crystals that damage tissues.

Second, oxalate forms stable complexes with metal ions, which can alter the distribution of metal ions in biological fluids. Again we proceed by determining the millimoles of acid and base initially present:. This leaves 6. The reactions can be written as follows:. If we had added exactly enough hydroxide to completely titrate the first proton plus half of the second, we would be at the midpoint of the second step in the titration, and the pH would be 3.

A dog is given mg 5. In practice, most acid—base titrations are not monitored by recording the pH as a function of the amount of the strong acid or base solution used as the titrant.

Instead, an acid—base indicator is often used that, if carefully selected, undergoes a dramatic color change at the pH corresponding to the equivalence point of the titration. Indicators are weak acids or bases that exhibit intense colors that vary with pH.

The conjugate acid and conjugate base of a good indicator have very different colors so that they can be distinguished easily. Some indicators are colorless in the conjugate acid form but intensely colored when deprotonated phenolphthalein, for example , which makes them particularly useful. We can describe the chemistry of indicators by the following general equation:. Many different substances can be used as indicators, depending on the particular reaction to be monitored. For example, red cabbage juice contains a mixture of colored substances that change from deep red at low pH to light blue at intermediate pH to yellow at high pH.

Acidic soils will produce blue flowers, whereas alkaline soils will produce pinkish flowers. Irrespective of the origins, a good indicator must have the following properties:. Synthetic indicators have been developed that meet these criteria and cover virtually the entire pH range. In addition, some indicators such as thymol blue are polyprotic acids or bases, which change color twice at widely separated pH values.

It is important to be aware that an indicator does not change color abruptly at a particular pH value; instead, it actually undergoes a pH titration just like any other acid or base. Thus most indicators change color over a pH range of about two pH units. We have stated that a good indicator should have a pKin value that is close to the expected pH at the equivalence point. For a strong acid—strong base titration, the choice of the indicator is not especially critical due to the very large change in pH that occurs around the equivalence point.

This figure shows plots of pH versus volume of base added for the titration of In contrast, the titration of acetic acid will give very different results depending on whether methyl red or phenolphthalein is used as the indicator.

Although the pH range over which phenolphthalein changes color is slightly greater than the pH at the equivalence point of the strong acid titration, the error will be negligible due to the slope of this portion of the titration curve.

In contrast, methyl red begins to change from red to yellow around pH 5, which is near the midpoint of the acetic acid titration, not the equivalence point. The graph shows the results obtained using two indicators methyl red and phenolphthalein for the titration of 0.

Due to the steepness of the titration curve of a strong acid around the equivalence point, either indicator will rapidly change color at the equivalence point for the titration of the strong acid. In contrast, the pKin for methyl red 5. In general, for titrations of strong acids with strong bases and vice versa , any indicator with a pKin between about 4. For the titration of a weak acid, however, the pH at the equivalence point is greater than 7.

Conversely, for the titration of a weak base, where the pH at the equivalence point is less than 7. The existence of many different indicators with different colors and pKin values also provides a convenient way to estimate the pH of a solution without using an expensive electronic pH meter and a fragile pH electrode.

That reaction is slowest at either end of the titration curve , because the concentration of either component is low there , and that low concentration makes the reaction even slower. This is the reason why the curve is steep in the middle, and gradually sloped at the beginning and end.

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