Atoms and Molecules

Computer-assisted learning

The following student centred learning package (pH/Titrations) makes use of biological chemical simulations. It contains programs explaining pH, titrations, titration curves, and amino acid structures and titrations. You are recommended to read these accompanying notes as you work through the package.

pH/Titrations

This set of programs contains material about the ionisation of acids and bases, pH, acid/base titrations, amphoteric molecules, and titrations involving amino acids. In addition, the simulations of equilibria and titrations will help you to understand dynamic processes.

There are five main sections in this program package. Each is self-contained. Section A defines pH in terms of exponential notation. It is the negative logarithm to the base ten of the hydrogen ion concentration in the solution in moles per litre. In section B, the equilibrium constant is defined. A simulation of an experiment, in which an acid dissociates, demonstrates that, whatever their initial concentrations, the reactant and product molecules eventually reach an equilibrium state at which they react at the same rates.

Section C introduces buffers, indicators, and the titrations of acids and bases using animated graphics. Amphoteric molecules, capable of acting both as acids and bases, are discussed next (Section D), with particular reference to amino acids. Finally, in section E, titrations of the acid forms of many amino acids against base are simulated graphically.

How to get started

The file (phtit.exe) should be downloaded to a local folder (Right click it then 'Save Target as..'), unpacked by running it (double-click it) to give several files (Ph.000, Ph.001, Ph.002, Ph.003, Ph.exe, Ph.txt). Ph.txt is a text file that essentially repeats this page. Run (double-click it) Ph.exe which is the executable program.  After the title page has been displayed, the main menu will appear. This makes use of the up and down cursor keys, or letters, plus the <Enter> key in order to make a choice. The menus may additionally be exited by use of the escape key <Esc>. This menu allows sound effects to be switched on or off and the background colour to be changed between black and blue. In addition it allows the use of a 'tutorial mode'. In this mode the program will continue without returning to the main menu. Sections may be deliberately exited prematurely by use of the Ctrl C key-press (i.e. press the <C> key whilst holding down the <Ctrl> key).

The program will allow you time to absorb what is on the screen and then invite you to move on. You should then press either the space bar or any alphanumeric key to continue as indicated by the program.

A. pH (logarithmic scale)

The pH scale is a measure of the acidity or the alkalinity of a solution. If a solution has a high concentration of hydrogen ions, it is acidic. In a neutral solution, the concentrations of hydrogen ions and hydroxyl ions are equal. In an alkaline solution, the concentration of hydrogen ions is low.

The concentration of hydrogen ions in a solution is often represented by H⁺ inside square brackets, i.e. [H⁺]. Aqueous solutions may contain hydrogen ions over a wide range of concentrations, usually between 0.1 and 0.000 000 000 000 1 M (moles per litre). These figures are usually expressed in exponential notation. This is far more economical and avoids writing all the zeros behind the decimal point, something which tends to encourage mistakes. The range of concentrations mentioned above are 10^-1 and 10^-13 M respectively in this exponential format. (Note. This program uses the commonly-accepted exponential notation format e.g. 1.43E-2 means 0.0143 and - 2.56E3 means - 2560. The number represented equals the mantissa (number to the left of the letter E ) times 10 to the power of the exponent (number to the right of the letter E ). The exponent must be an integer.)
The pH of a solution is defined as minus the logarithm of the H⁺ concentration,
i.e.             pH = - log₁₀[H⁺]
Thus if [H⁺] = 10^-5 M, the pH of the solution is 5. If [H⁺] = 10^-2 M, the pH is two, and so on.
The pH scale is therefore logarithmic to the base ten. That is, the hydrogen ions in a solution of pH 2 ([H⁺] = 0.01 M = 10^-2 M) are ten times more concentrated than those at pH 3 ([H⁺] = 0.001 M = 10^-3 M ) and a hundred times more concentrated than at pH 4 ([H⁺] = 10^-4 M). Note that [H⁺] x [OH^-] for a solution equals 10^-14. In other words, the concentrations of the two ions are inversely related. When [H⁺] = 10^-7 M (i.e. pH = 7) the concentration of OH^- ions must also be 10^-7; that is, the concentrations of hydrogen ions and hydroxyl ions are equal and the solution is neutral.

The program derives the pH equation, then gives numerical examples and finally poses several numerical questions about pH. You may move on from the numerical examples to numerical questions by pressing the Escape <Esc> key. Put in your answers, preferably in normal decimal notation, and press the 'Return' key after each one. After the computer has assessed and acted on your input it waits for a key press before continuing. In each case the last question or answer stays on the screen for reference or comparison.

Concentrations are expressed in decimal notation in order to aid a clearer understanding. Where appropriate, the exponential notation is also given. It is recommended that you use your own calculator in order to work out the results for the problems. However, there is a calculator available within the program. Pressing the <C> key in place of part of an answer accesses this. Any expression, involving the +, -, * (multiply), / (divide), ^ (to the power), (, ) (brackets) or the functions 'LOG', 'LN' or 'EXP' up to 40 characters long, may be entered (the normal rules of operator precedence apply). The result is obtained by pressing the <=> (equals) or <Enter> key. The expression may be edited by use of the left and right cursor keys, the <End> and <Home> keys and the delete key. Error messages will be displayed, if necessary, indicating approximately the position of the error. Only numbers in the range 10^-16 ~ 10⁺¹⁹ or zero may be entered.

B. Equilibrium

Reversible reactions, such as the dissociation of an acid, consist of forward and back reactions proceeding simultaneously. Imagine that an acid is represented by the formula AH, in which 'A' represents most of the molecule and H represents the hydrogen atom that can be ionised. On ionisation, the AH molecule dissociates to give rise to an A^- anion and a H⁺ cation:

AH A^- + H⁺

The number of acid molecules which dissociate in a certain time is known as its rate of dissociation, k₁. Simultaneously, the back-reaction occurs:

A^- + H⁺ AH

The number of acid molecules which associate in the same time interval is known as its rate of association, k₂. The result of these two reactions after a suitable time period is always an equilibrium. The relative concentrations at equilibrium of AH on the one hand, and A^- and H⁺ on the other hand, are characteristic of the acid which is dissociating. At equilibrium, the concentrations of A^- and H⁺ may be far higher than that of AH. Nevertheless at equilibrium, the rate at which AH molecules dissociate equals the rate at which the A^- and H⁺ molecules associate to produce AH.
The equilibrium constant, K_eq is the ratio of the concentrations of products to reactants at equilibrium.
For example, for an acid, AH

K_eq = [A^-] x [ H⁺]
           [AH]

If K_eq is high, the acid is strongly dissociated ([H⁺] ³ [AH] , e.g. hydrochloric acid) and if K_eq is low, the acid is weakly dissociated (([ H⁺]<< [AH] ,e.g. acetic acid). By convention for acids, the equilibrium constant K_eq is the same as the dissociation constant and is known as K_a.
Whatever the concentrations of AH and A^- and H⁺ ions at the beginning of an experiment, the concentrations will change with time until the equilibrium concentrations are reached. This is shown in the simulation on the screen. The program simulates the changes that occur with time in a solution of a compound that dissociates in this way. Two pools of molecules are shown, one representing AH (magenta) and the other representing A^- (light blue). For simplicity, the H⁺ ions are not shown. They are assumed to be constant throughout the simulation at 1 M. You can choose the rates of the forward (k₁) and back (k₂) reactions by entering numbers between 1 and 99, representing the rates. Notices that whatever figures you enter, equilibrium between the molecules in the two 'containers' is always reached in the end. At equilibrium, molecules are being converted from AH to A^- at the same rate as from A^- to AH, and so there is no change in the overall concentrations of AH and A^- .
Each acid or acidic group has its own pK_a. This is equivalent to the pH at which half the acid molecules AH are dissociated into A^- and H⁺. The pK_a = - log₁₀(K_a) Thus an acid, AH, of concentration 1 M, can dissociate to yield at equilibrium a concentration of hydrogen ions anywhere between (say) 1 M (acid completely dissociated) and 0.000 000 000 000 1 M (acid weakly dissociated), depending on its pK_a.

The simulation is followed by several numerical questions, which may be omitted, if desired, by use of the <Esc> key. If any difficulty is encountered in these calculations, hints are available by pressing the <H> key. In the initial problems, the hints are simply prompts to use an equation that is already on the screen. Later hints follow a reasoned path to the solution of the problem. The problems may be worked out using your own calculator or using the calculator available in this section (see Section A for details).

C. Titrations

In this section of the program package, various titrations are modelled on the computer. You have a choice between eight titrations. Before you begin each titration you have to choose an appropriate indicator. Indicators are molecules that change colour when they ionise. Two indicators are used here, phenolphthalein and methyl red. Phenolphthalein changes from colourless (acid) to red (alkali) with pK_a of 9.1 (see notes on section B). In other words, it changes colour at a pH around 9.1. Methyl red changes from red (acid) to yellow (alkali) with a pK_a of 5.4 (i.e. at a pH around 5.4). The indicator should be chosen such that the change in colour occurs just after the titration of the group that is of interest. Try titrations of both strong and weak acids and note the differences between the titration curves. To carry out each titration press the <spacebar>. Each time that you press the <spacebar>, a drop of liquid falls from the burette into the solution beneath.

Buffers are solutions of weak acids or bases acting within one pH unit of their pK_a. Within this range, the addition of small quantities of strong acids or bases causes hardly any change in pH, that is, these solutions 'buffer' the pH. You can see this from the titration curves of acetic or carbonic acid displayed in the program. Can you explain why the addition of H⁺ or OH^- ions hardly affects the pH within this narrow range near the pK_a?

D. Amphoteric molecules

Amphoteric molecules are those which can act as both acids and bases, in other words, they can both donate and accept hydrogen ions. In this program, amino acids are used as examples of amphoteric molecules.

The program first describes the structure of an amino acid. It consists of a central carbon atom with four groups bonded to it. These are a carboxylate group, an amine group, a hydrogen atom and an R-group, which is different in each of the twenty common naturally-occurring amino acids.
In an amino acid both the carboxylic acid group and the amino group can ionise. Imagine an amino acid in a solution that starts at pH 0 (i.e. 1 M H⁺) and slowly becomes more alkaline. At pH 0 the carboxylic acid group is -COOH (not ionised) and the amino group has ionised by accepting a hydrogen ion, becoming -NH₃⁺ Therefore, the amino acid is positively charged. As the pH increases, the carboxylic acid group ionises to become -COO^-. From pH 2.3 to pH 9 the amino acid molecule is both negatively charged (-COO^-) and positively charged (-NH₃⁺). At pH's above pH 9 the -NH₃⁺ group loses its H⁺ ion to form -NH₂. This is why amino acid molecules are positively charged at acidic pH's and they are negatively charged at alkaline pH's. At a particular intermediate pH that is specific to each amino acid the molecule has no net charge. This pH is known as the isoelectric point. The simulation in the next section clarifies this.

E. Amino acid titrations

In this section you have the opportunity to titrate any of the 20 common amino acids against acid or alkali. The table of amino acids shows their pK_a`s and classifies them as hydrophilic (water loving), hydrophobic (water hating), acidic or basic. These properties depend on the atoms in their R-groups. There may be other ionisable groups in the R-groups besides the carboxylic and amine groups attached directly to the central carbon atom. You can select an amino acid to titrate, by pressing the key appropriate to it on the list.

For each amino acid you will see a complex screen display with three components. Take time to study it before you start. Note the isoelectric point and the pK_a`s (shown as horizontal white dotted lines). If there are more than two pK<sub>a</sub>`s, look at the structure of the amino acid molecule to find out where the other ionisable groups are likely to be. Press the <H> key now for a description of the amino acid that is about to be titrated. Press any key to return to the full screen and start the simulation. This description window may be returned to at any time during the titration.
As the simulation begins, notice that the charge on the amino acid molecules at that pH is shown on the right-hand side of the screen. This graph changes as the simulation proceeds. Notice also that the ionised groups are shown on the diagram of the molecular structure of the amino acid. They also change as the simulation proceeds. The simulation can be stopped or restarted by using any alphanumeric key (a 'beep' will sound to indicate that the program has responded to the request). The graph displays a number of horizontal inflection points at the pK_a`s. When the graph moves through an inflection point the machine makes a sound. It makes a different noise signature when the line moves through the isoelectric point. Can you explain why each of these inflection points exists? Cysteine has three inflection points. Why?

Less information may be shown on the screen, in order to clarify particular points, by changing the 'option' (by the use of the <O> key) on the section menu. The titration curve may be shown by itself or with the amino acid structure but without the charge indicator.
To leave this section of the program package, use the exit <X> key option from the section menu or the Ctrl C key combination (press the <Ctrl> and <C> keys simultaneous).

F. Review questions

Make sure that you attempt all seven multiple-choice questions in this section. You may need your calculator to answer some of them. The answers are given on another page but do not read these unless you have difficulty.

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This page was last updated by Martin Chaplin
on 11 February, 2005