The pH-scale

The acidity or basicity of a solution can be described in terms of its H30 or OH ion concentrations. 

These concentrations are usually small. For example, H30 ion concentration is 110 M in the neutral solution. Thus, the concentration of H30 is generally expressed as the negative logarithm. This is known as pH. From now on, for simplicity H will be used instead of H30.  

The pH value of a solution gives an idea about the condition of a solution as follows  

Interestingly, the pH value of soil will alter the color of certain flowers. 

A less accurate way to measure pH is to use indicators. An indiccitor is a compound, such as phenolphthalein or methyl orange, that changes color reversibly at different pH values. For example, phenolphthalein is a colorless substance in any solution with a pH value smaller than 8.3. It turns red-violet in solutions with a pH value greater than 8.3. 

The details of equilibrium constants and their calculation are treated in a later chapter. For the moment, it is only necessary that you know the following rule  

The product of the hydrogen ion and hydroxide ion concentrations in any aqueous solution will always be 1.00 x 10 at 25 °C. 

This expression is known as the ion product of water, and it applies to all aqueous solutions, not just to pure water. The consequences of this are far-reaching, because it implies that if the concentration of H+ is large, that of OH will be small, and vice versa. This means that H+ ions are present in all aqueous solutions, not just acidic ones. This leads to the following important definitions, which you must memorize  

The possible values of [H+] and [OH ] in an aqueous solution can span many orders of magnitude, ranging from about 10 to 10. It is therefore convenient to represent them on a more compressed logarithmic scale. By convention, we use the pH scale to denote hydrogen ion concentrations  

The pH scale was invented to reduce the necessity for using exponential numbers to report acidity. The pH is defined as 

Special note for electronic calculator users To determine the negative of the logarithm of a quantity, on some calculators, enter the quantity, press the LOG key, then press the change-sign key, -f/—. On other calculators. 

EXAMPLE 17.12. What is the difference in calculating the pH of a solution of a weak acid and that of a strong acid  

For a strong acid, the H3O+ concentration can be determined directly from the concentration of the acid. Eor a weak acid, the H3O+ concentration must be determined first from an equilibrium constant calculation (Sec. 17.3) then the pH is calculated. 

From the way pH is defined and the value of, we can deduce that solutions with pH = 7 are neutral, those with pH less than 7 are acidic, and those with pH greater than 7 are basic. 

Step 3 Substitute the known [H3O ] or [OH ] into the equation and calculate. 

What is the [H30 ] of an ammonia cleaning solution with [OH- ] = 4.0 X 10- M Is the solution acidic, basic, or neutral  

35 In an acidic solution, how does the concentration of HaO compare to the concentration of OH  

36 If a base is added to pure water, why does the [HaO ] decrease  

37 Indicate whether each of the following solutions is an acidic, basic, or neutral  

FIGURE 10.4 On the pH scale, values below 7.0 are acidic, a value of 7.0 is neutral, and values above 7.0 are basic. 

FIGURE 10.5 The pH of a solution can be determined using (a) a pH meter, (b) pH paper, and (c) indicators that turn different colors corresponding to different pH values. 

Which item in the list in Sample Problem 10.7 has the highest [OH ]  

The pH scale is a logarithmic scale that corresponds to the [H30 ] of aqueous solutions. Mathematically, pH is the negative logarithm (base 10) of the [H30 ]. 

Essentially, the negative powers of 10 in the molar concentrations are converted to positive numbers. For example, a lemon juice solution with the [H30 ] = 1.0 X 10 M has a pH of 2.00. This can be calculated using the pH equation  

To express small numbers conveniently, chemists often use the p scale/ which is based on common logarithms (base 10 logs). In this system, if N represents some number, then 

That is, the p means to take the log of the number that follows and multiply the result by -1. For example, to express the number 1.0 x 10 on the p scale. 

To obtain the pH value of a solution, we must compute the negative log of the [H ]. On a typical calculator, this involves the following steps  

To represent pH to the appropriate number of significant figures, you need to know the following mle for logarithms  

The molar concentration of H aq) in an aqueous solution is usually very small. For convenience, we therefore usually express [H ] in terms of pH, which is the negative logarithm in base 10 of [H ]  

What happens to the pH of a solution as we make the solution more acidic, so that [H ] increases Because of the negative sign in the logarithm term of Equation 16.17, the pH decreases as [H ] increases. For example, when we add sufficient acid to make [H+] = 1.0 X 10 M the pH is 

Is it possible for a solution to have a negative pH If so, would that pH signify a 

Ana lyze We are asked to determine the pH of aqueous solutions for which we have already calculated [iT]. 

Plan We can calculate pH using its defining equation, Equation 16.17. Solve 

The pH of a neutral solution is 7.00 at 25 °C. Notice that the pH is reported with two decimal places. We do so because only the numbers to the right of the decimal point are the significant 

At 25 °C the pH of a basic solution is greater than 7.00. The relationships among [H ], 

Because [H+] in an aqueous solution is typically quite small, the pH scale provides a convenient way to represent solution acidity. The pH is a log scale based on 10, where 

At this point we need to discuss significant figures for logarithms. The rule is that the number of decimal places in the log is equal to the number of significant figures in the original number. Thus 

The definition of pH in terms of [H ]. neglects any correction for nonideality of the solutions. 

Similar log scales are used for representing other quantities. For example, 

Since pH is a log scale based on 10, the pH changes by 1 for every power of 10 change in [H+]. For example, a solution of pH 3 has an H+ concentration 10 times that of a solution of pH 4 and 100 times that of a solution of pH 5. Also note that because pH is defined as -log[H+], the pH decreases as [H+] increases. The pH scale and the pH values for several common substances are shown in Fig. 7.3. 

The pH of a solution is usually measured using a pH meter, an electronic device with a probe that can be inserted into a solution of unknown pH. The probe contains an acidic aqueous solution enclosed by a special glass membrane that allows migration of H ions. If the unknown solution has a different pH from the solution in the probe, an electric potential results, which is registered on the meter (see Fig. 14.7). 

For dilute solutions, the molar concentrations of hydrogen ions are small. For example, the hydrogen ion concentration of a 0.1 M solution of HCI in water is 0.1 M. As a shorthand notation, the hydrogen ion concentrations of dilute solutions are generally indicated by their pH value which is defined by 

At the beginning of this section we defined a solution as being neutral if [H+(aq)] = [OH (aq)]. Pure water is neutral therefore, from Eqs. (5.12) and (5.13) 

the pH of pure water is -log(10 ) = 7. It follows that acidic solutions have pH 7 and basic solutions have pH 7. 

Exercise 5.2. The pH of natural rainwater is about 5.6. Assuming that all of this acidity is due to the absorption of CO2 by the rain. 

Solution. Since the pH of rainwater is 5.6, the concentration of H30 (aq) in natural rainwater is given by 

The concentration of the acid itself is of little significance other than analytical, with the exception of strong acids in dilute aqueous solutions. The concentration of H+ itself is not satisfactory either, because it is solvated diversely and the ability of transferring a proton to another base depends on the nature of the medium. The real physical quantity describing the acidity of a medium is the activity of the proton au. The experimental determination of the activity of the proton requires the measurement of the potential of a hydrogen electrode or a glass electrode in equilibrium with the solution to be tested. The equation is of the following type [Eq. (1.7)], wherein Cis a constant. 

It was S0rensen s idea7 to use this relationship, which can be considered as a basis to the modern definition of the pH scale of acidity for aqueous solutions. The pH of a dilute solution of acid is related to the concentration of the solvated proton from Eq. (1.8). Depending on the dilution, the proton can be further solvated by two or more solvent molecules. 

When the acid solution is highly diluted in water, the pH measurement is convenient, but it becomes critical when the acid concentration increases and, even more so, if nonaqueous media are employed. Since areference cell is used with aliquid junction, the potential at the liquid junction also has to be known. The hydrogen ion activity cannot be measured independently, and for this reason the equality of Eq. (1.9) cannot be definitely established for any solution. 

Chemists can find out if a solution is acidic or alkaline by adding an indicator to the solution. An indicator is a substance that usually has one colour in very acidic solutions and another colour in very alkaline solutions. Table 22 on page 21 of the IB Chemistry data booklet lists a number of common indicators, with their two colours and the pH range over which they change colour. 

Any indicator can be used for the titration of a strong base with a strong acid. However, if a strong acid is titrated with a weak acid then a suitable indicator is methyl orange (pK 3.7), or any other indicator whose pK value is below 7. If a weak acid is titrated with a strong base then a suitable indicator is phenolphthalein (pK value 9.6) or any other indicator whose pK value is above 7. A weak acid and a weak base cannot be titrated in the presence of an indicator. 

The theory of indicators, pK values (as a measure of acid strength) and the choice of indicators for acid-base titrations is discussed in Chapter 18. 

Pure or anhydrous acids do not behave as acids and do not exhibit the characteristic properties of acids described previously. These properties are only shown after the acids have been reacted and dissolved in water to form dilute aqueous solutions. 

The importance of water in acid solutions can be demonstrated by dissolving hydrogen chloride gas, HCl, in both water and an organic liquid such as methylbenzene, C5H5CH3. Solutions are formed in both cases, but only the aqueous solution exhibits typical acidic properties (Table 8.3). 

Because the concentration of ions in solution generally is quite small one has for the sake of convenience chose to express a solutions acidness based on the decimal logarithm to the concentration of BT ions completely analogous to the principles that the acid constant Ka was expressed as an acid exponent pKa. this is known as the pH scale and the pH values are defined as  

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As pH is a logarithmic scale based on the decimal system means that the pH value of a solution is changed one unit for each time the [H ] is changed 10 times. E.g. does a solution with a pH-value of 4 have a concentration of H ions 10 times as high as a solution with a pH value of 5. 

The acidity of an aqueous solution depends on the concentration of hydronium ions, [H30 ]. This concentration can range over many orders of magnitude, which can make reporting the numbers cumbersome. To describe the acidity of a solution, rather than report the molar concentration of hydronium ions, we typically use the more convenient pH scale. ThepJT of a solution is defined as the negative base-10 logarithm of the hydronium ion concentration (in mol/L). 

The pH of a solution is a dimensionless quantity, so the units of concentration must be removed from [ftO ] before taking the logarithm. Because [H30 = [OH ] = 1.0 x 10 M in pure water at 25°C, the pH of pure water at 25°C is 

TABLE 16.3 Benchmark pH Values for a Concentrations at 25°C Range of Hydronium Ion  

Equation 16.2 converts numbas that can span an enormous range 1 o to 10 to numbers 

A word about significant figures When we take the log of a number with two significant figures, we report the result to two places past the decimal point Thus. pH 7.00 has two significant figures, not three. 

The pH of a solution is a dimensionless quantity, so the units of concentration must be removed 

A measured pH can be used to determine experimentally the concentration of hydronium ion in solution. Solving Equation 16.2 for gives 

The concentration of H or OH in aqueous solution can vary over extremely wide ranges, from 1 M or greater to 10 M or less. To construct a plot of concentration against some variable would be very difficult if the concentration changed from, say, 10 M to 10 M. This range is common in a titration. It is more convenient to compress the acidity scale by placing it on a logarithm basis. The pH of a solution was defined by Sprenson as 

Calculate the pH of a solution prepared by mixing 2.0 mL of a strong acid solu- Keep track of millimoles tion of pH 3.00 and 3.0 mL of a strong base of pH 10.00. 

When [ ] = [OH ], then a solution is said to be neutral. If [H ] [OH ], then the solution is acidic. And if [H ] [OH ], the solution is alkaline. The hydrogen ion and hydroxyl ion concentrations in pure water at 25°C are each IQ- M, and the pH of water is 7. A pH of 7 is therefore neutral. Values of pH that are greater than this are alkaline, and pH values less than this are acidic. The reverse is true of pOH values. A pOH of 7 is also neutral. Note that the product of [H ] and [OH ] is always at 25°C, and the sum of pH and pOH is always 14. If the temperature is other than 25°C, then is different from 1.00 X and a neutral solution will have other than 10 M H and OH (see below). 

If the concentration of an acid or base is much less than 10 M, then its contribution to the acidity or basicity will be negligible compared with the contribution from water. The pH of a 10 M sodium hydroxide solution would therefore not differ significantly from 7. If the concentration of the acid or base is around 10 M, then its contribution is not negligible and neither is that from water hence the sum of the two contributions must be taken. 

Since the hydrogen ions contributed from the ionization of water are not negligible compared to the HCl added, 

EXERCISE 16.2 Caicuiate [H ] in a solution in which [OH ] = 2.0 x 10 M. Is this solution acidic, neutral, or basic  

This is not possible. The product of [H+] and [OH-] must always be 1.0 x 10- in water at 25 °C, so a solution could not have [H+] = [OH ] = 0.010 M. If H and OH- are added to water in these amounts, they will react with each other to form H2O, 

This is a general result. When H+ and OH- are added to water in amounts such that the product of their concentrations is greater than 1.0 x 10 they will react to form water until enough H and OH- are consumed so that [H+][OH-] = 1.0 X 10-1  

To understand pH and pOH. To learn to find pOH and pH for various solutions. To learn to use a calculator in these calculations. 

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As a result of a variable liquid-junction potential, the measured pH may be expected to differ seriously from the determined from cells without a liquid junction in solutions of high acidity or high alkalinity. Merely to affirm the proper functioning of the glass electrode at the extreme ends of the pH scale, two secondary standards are included in Table 8.14. In addition, values for a 0.1 m solution of HCl are given to extend the pH scale up to 275°C [see R. S. Greeley, Anal. Chem. 32 1717 (I960)] ... 

The pH of an acidic solution, therefore, must be less than 7.00. A basic solution, on the other hand, will have a pH greater than 7.00. Figure 6.3 shows the pH scale along with pH values for some representative solutions. 

Acidity is defined in terms of the pH scale, where pH is the negative logarithm of the hydrogen ion [H ] concentration. 

Fig. 10-11. The pH scale is a measure of hydrogen ion concentration. The pH of common substances is shown with various values along the scale. The Adirondack Lakes are located in the state of New York and are considered to be receptors of acidic deposition. Source U.S. Environmental Protection Agency, Acid Rain—Research Summary," EPA-600/8-79-028, Cincinnati, 1979.

At the pH = Jt there is a balance of charge and there is no migration in an electric field. This is referred to as the isoelectric point and is determined by the relative dissociation constants of the acidic and basic side groups and does not necessarily correspond to neutrality on the pH scale. The isoelectric point for casein is about pH = 4.6 and at this point colloidal stability is at a minimum. This fact is utilised in the acid coagulation techniques for separating casein from skimmed milk. 

Many organic reactions involve acid concentrations considerably higher than can be accurately measured on the pH scale, which applies to relatively dilute aqueous solutions. It is not difficult to prepare solutions in which the formal proton concentration is 10 M or more, but these formal concentrations are not a suitable measure of the activity of protons in such solutions. For this reason, it has been necessaiy to develop acidity functions to measure the proton-donating strength of concentrated acidic solutions. The activity of the hydrogen ion (solvated proton) can be related to the extent of protonation of a series of bases by the equilibrium expression for the protonation reaction. 

Table 2.2 gives the pH scale. Note again the reciprocal relationship between [H ] and [OH ]. Also, because the pH scale is based on negative logarithms, low pH values represent the highest H concentrations (and the lowest OH concentrations, as K, specifies). Note also that... 

The pH scale is widely used in biological applications because hydrogen ion concentrations in biological fluids are very low, about 10 M or 0.0000001 M, a value more easily represented as pH 7. The pH of blood plasma, for example, is 7.4 or 0.00000004 M H. Certain disease conditions may lower the plasma pH level to 6.8 or less, a situation that may result in death. At pH 6.8, the H concentration is 0.00000016 M, four times greater than at pH 7.4. 

At pH 7, [H ] = [OH ] that is, there is no excess acidity or basicity. The point of neutrality is at pH 7, and solutions having a pH of 7 are said to be at neutral pH. The pH values of various fluids of biological origin or relevance are given in Table 2.3. Because the pH scale is a logarithmic scale, two solutions whose pH values differ by one pH unit have a 10-fold difference in [H ]. For example, grapefruit juice at pH 3.2 contains more than 12 times as much H as orange juice at pH 4.3. 

FIGURE 2.13 The titration curves of several weak electrolytes acetic acid, Imidazole, and ammonlnm. Note that the shape of these different curves Is Identical. Only their position along the pH scale Is displaced. In accordance with their respective affinities for ions, as reflected In their differing values. 

Hydrogen was recognized as the essential element in acids by H. Davy after his work on the hydrohalic acids, and theories of acids and bases have played an important role ever since. The electrolytic dissociation theory of S. A. Arrhenius and W. Ostwald in the 1880s, the introduction of the pH scale for hydrogen-ion concentrations by S. P. L. Sprensen in 1909, the theory of acid-base titrations and indicators, and J. N. Brdnsted s fruitful concept of acids and conjugate bases as proton donors and acceptors (1923) are other land marks (see p. 48). The di.scovery of ortho- and para-hydrogen in 1924, closely followed by the discovery of heavy hydrogen (deuterium) and... 

Fig. 2.8 Potential-pH diagram calculated for Fe-H20 system at 250 C. The pH scale refers to the solution measured at 25°C and then raised to 250°C (after Ashworth )...

Several complications are involved in the calculation of potential-pH equilibrium diagrams for temperatures other than 25°C including the fact that the pH scale itself varies with temperature thus, diagrams in which the pH scale refers to the temperature for which the equilibria are calculated are probably preferable for most purposes . The most notable consequence of increasing temperature on the equilibria appears to be a widening of the pH range within which the hydroxide Ni(OH)2 is thermodynamically stable. 

Click Coached Problems for a self-study module on the pH scale. 

The two hydrogen electrodes may be replaced by a single glass electrode which is transferred from one cell to the other. The pH difference thus determined is a pure number. The pH scale is defined by specifying the nature of the standard solution and assigning a pH value to it. 

Consider the two diagrams in Fig. 6-3. Both are said to feature upward bends. In terms used earlier, Fig. 6-3a represents a transition with increasing [H+] from zeroth to first order in [H+], and Fig. 6-3b from negative first to zeroth. (Of course, the use of the pH scale reverses their appearance.) As noted previously (Rule 8, Section 6.2), this observation signifies a mechanism with two independent pathways. 

The pH scale was introduced by the Danish chemist Soren Sorensen in 1909 in the course of his work on quality control in the brewing of beer and is now used throughout science, medicine, agriculture, and engineering. 

Using Environmental Examples to Teach About Acids. Acid-base reactions are usually presented to secondary students as examples of aqueous equilibrium (2). In their study of acids and bases, students are expected to master the characteristic properties and reactions. They are taught to test the acidity of solutions, identify familiar acids and label them as strong or weak. The ionic dissociation of water, the pH scale and some common reactions of acids are also included in high school chemistry. All of these topics may be illustrated with examples related to acid deposition (5). A lesson plan is presented in Table I. 

Because hydronium concentrations usually involve negative powers of ten, chemists use a negative log scale in expressing these concentrations. Equation defines the pH scale of acid concentration pH = - log [H3 O ] The pH of a solution is obtained by taking the logarithm of the hydronium ion concentration and then changing the sign. For example, the pH of pure water is pH = - log [H3 O ] = - log (1.0 X 10 ) — -(-7.00) — 7.00 The reverse conversion from pH to [H3 O ] uses powers of 10. For example, lemon juice has a pH of about 2.0 ... 

ISO Guide 33 (1998) deals with other uses of RMs. It elaborates on various uses of RMs, excluding calibration, which is the subject of ISO Guide 32. In most cases, RMs are used as a quality control measure, i.e. to assess the performance of a measurement method. Most matrix RMs are produced with this purpose in mind. Other purposes of RMs are the maintenance of conventional scales, such as the octane number and the pH scale. ISO Guide 33 provides guidance on the proper use of RMs, and therefore it is together with ISO Guide 32 the most important document for users of CRMs. 

Another important use of RMs is the maintenance of conventional scales. The octane number of gasoline is an example of such a scale. The scale is defined through chemicals. This definition can be realized through RMs. Another example is the pH scale, which is defined by buffers with pH = 4, pH = 7, and pH = 10. These buffers are defined as mixtures of salts, dissolved in water. These define the pH scale can be used by laboratories for the purpose of calibrating their pH meters. 

The pH scale is used to rank the hydronium ion concentration of a given substance. Which of the following sequences shows these solutions from least acidic to most acidic ... 

While the pH scale has made it convenient to describe the order of hydrogen ion concentrations and to give a measure of the acid strength or alkalinity of a solution, it suffers from a defect which is less obvious. A 4 10-5 N HC1 solution is clearly twice as acidic as a 2 10-5 N solution, but the pH values of these solutions, 4.40 and 4.70, provide no idea of the relative strengths of these solutions. 

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