Lab.13.pH measurement Key words: pH, pOH, acids, bases, buffers, electrodes, buffer capacity. Theoretical background Introduction In chemistry, pH is a measure of the acidity or basicity of an aqueous solution. Pure water is said to be neutral, with a pH close to 7.0 at 25 C (77 F). Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic or alkaline. pH measurements are important in medicine, biology, chemistry, food science, environmental science, oceanography, civil engineering and many other applications. In a solution pH approximates but is not equal to p[H], the negative logarithm (base 10) of the molar concentration of dissolved hydronium ions (H3O+); a low pH indicates a high concentration of hydronium ions, while a high pH indicates a low concentration. Crudely, this negative of the logarithm matches the number of places behind the decimal point, so for example 0.1 molar hydrochloric acid should be near pH 1 and 0.0001 molar HCl should be near pH 4 (the base 10 logarithms of 0.1 and 0.0001 being −1, and −4, respectively). Pure (de-ionised) water is neutral, and can be considered either a very weak acid or a very weak base (center of the 0 to 14 pH scale), giving it a pH of 7 (at 25 C (77°F)), or 0.0000001 M H+. For an aqueous solution to have a higher pH, a base must be dissolved in it, which binds away many of these rare hydrogen ions. Hydrogen ions in water can be written simply as H+ or as hydronium (H3O+) or higher species (e.g. H9O4+) to account for solvation, but all describe the same entity. Most of the Earth's freshwater surface bodies are slightly acidic due to the abundance and absorption of carbon dioxide; in fact, for millennia in the past most fresh water bodies have long existed at a slightly acidic pH level. However, pH is not precisely p[H], but takes into account an activity factor. This represents the tendency of hydrogen ions to interact with other components of the solution, which affects among other things the electrical potential read using a pH meter. As a result, pH can be Lab.13.pH measurement affected by the ionic strength of a solution – for example, the pH of a 0.05 M potassium hydrogen phthalate solution can vary by as much as 0.5 pH units as a function of added potassium chloride, even though the added salt is neither acidic nor basic. Hydrogen ion activity coefficients cannot be measured directly by any thermodynamically sound method, so they are based on theoretical calculations. Therefore the pH scale is defined in practice as traceable to a set of standard solutions whose pH is established by international agreement. Primary pH standard values are determined by the Harned cell, a hydrogen gas electrode, using the Bates–Guggenheim Convention. History The concept of p[H] was first introduced by Danish chemist Søren Peder Lauritz Sørensen at the Carlsberg Laboratory in 1909 and revised to the modern pH in 1924 after it became apparent that electromotive force (emf) in cells depended on activity rather than concentration of hydrogen ions. In the first papers, the notation had the H as a subscript to the lower case p, like so: pH. It is unknown what the exact definition of 'p' in pH is. A common definition often used in schools is "percentage". However some references suggest the p stands for “Power”, others refer to the German word “Potenz” (meaning power in German), still others refer to “potential”. Jens Norby published a paper in 2000 arguing that p is a constant and stands for “negative logarithm”; H then stands for Hydrogen. According to the Carlsberg Foundation pH stands for "power of hydrogen". Other suggestions that have surfaced over the years are that the p stands for puissance (also meaning power but then the Carlsberg Laboratory was French speaking) or that pH stands for the Latin terms pondus Hydrogenii or potentia hydrogenii. It is also suggested that Sørensen used the letters p and q (commonly paired letters in mathematics) simply to label the test solution (p) and the reference solution (q). Mathematical definition pH is defined as a negative decimal logarithm of the hydrogen ion activity in a solution. (1) Lab.13.pH measurement where aH is the activity of hydrogen ions in units of mol/L (molar concentration). Activity has a sense of concentration, however activity is always less than the concentration and is defined as a concentration (mol/L) of an ion multiplied by activity coefficient. The activity coefficient is a number between 0 and 1 and it depends on many parameters of a solution, such as nature of ion, ion force, temperature etc. For a strong electrolyte activity of an ion approaches it concentration in diluted solutions. Activity can be measured experimentally by means of an ion-selective electrode which responds, according to the Nernst equation, to hydrogen ion activity. pH is commonly measured by means of a glass electrode connected to a milli-voltmeter with very high input impedance which measures the potential difference, or electromotive force, E, between an electrode sensitive to the hydrogen ion activity and a reference electrode, such as a calomel electrode or a silver chloride electrode. Quite often glass electrode is combined with the reference electrode and a temperature sensor in one body. The glass electrode relatively good (95 - 99.9%) follows the Nernst equation: (2,3) where E is a measured potential , E0 is the standard electrode potential, that is, the electrode potential for the standard state in which the activity is one. R is the gas constant, T is the temperature in Kelvins, F is the Faraday constant and n is the number of electrons transferred (ion charge), one in this instance. The electrode potential, E, is proportional to the logarithm of the hydrogen ion activity (or concentration at first approximation). This definition, by itself, is wholly impractical, because the hydrogen ion activity is the product of the concentration and an activity coefficient. To get proper results, the electrode must be calibrated using standard solutions of known activity. Note that, the pH of a solution is temperature-dependent. Measurement of extremely low pH values, such as some very acidic mine waters, requires special procedures. Calibration of the electrode in such cases can be done with standard Lab.13.pH measurement solutions of concentrated sulfuric acid, whose pH values can be calculated with using Pitzer parameters to calculate activity coefficients. pH is an example of an acidity function. Hydrogen ion concentrations can be measured in non-aqueous solvents, but this leads, in effect, to a different acidity function, because the standard state for a non-aqueous solvent is different from the standard state for water. Superacids are a class of non-aqueous acids for which the Hammett acidity function, H0, has been developed. pOH pOH is sometimes used as a measure of the concentration of hydroxide ions, OH−, or alkalinity. pOH is not measured independently, but is derived from pH. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by [OH−] = KW /[H+] (4) where KW is the self-ionisation constant of water. Taking cologarithms pOH = pKW − pH. (5) So, at room temperature pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of soil alkalinity. Application Pure (neutral) water has a pH around 7 at 25 °C (77 °F); this value varies with temperature. When an acid is dissolved in water the pH will be less than 7 (if at 25 °C (77 °F)) and when a base, or alkali is dissolved in water the pH will be greater than 7 (if at 25 °C (77 °F)). A solution of a strong acid, such as hydrochloric acid, at concentration 1 mol dm−3 has a pH of 0. A solution of a strong alkali, such as sodium hydroxide, at concentration 1 mol dm−3 has a pH of 14. Thus, measured pH values will mostly lie in the range 0 to 14. Since pH is a logarithmic scale a difference of one pH unit is equivalent to a tenfold difference in hydrogen ion concentration. Lab.13.pH measurement Because the glass electrode (and other ion selective electrodes) responds to activity, the electrode should be calibrated in a medium similar to the one being investigated. For instance, if one wishes to measure the pH of a seawater sample, the electrode should be calibrated in a solution resembling seawater in its chemical composition. An approximate measure of pH may be obtained by using a pH indicator. A pH indicator is a substance that changes color around a particular pH value. It is a weak acid or weak base and the color change occurs around 1 pH unit either side of its acid dissociation constant, or pKa, value. For example, the naturally occurring indicator litmus is red in acidic solutions (pH<7 at 25 °C (77 °F)) and blue in alkaline (pH>7 at 25 °C (77 °F)) solutions. Universal indicator consists of a mixture of indicators such that there is a continuous color change from about pH 2 to pH 10. Universal indicator paper is simple paper that has been impregnated with universal indicator. A solution whose pH is 7 (at 25 °C (77 °F)) is said to be neutral, that is, it is neither acidic nor basic. Water is subject to a self-ionization process. H2O H+ + OH− The dissociation constant, KW, has a value of about 10−14, so in neutral solution of a salt both the hydrogen ion concentration and hydroxide ion concentration are about 10−7 mol dm−3. The pH of pure water decreases with increasing temperatures. For example, the pH of pure water at 50 °C is 6.55. Note, however, that water that has been exposed to air is mildly acidic. This is because water absorbs carbon dioxide from the air, which is then slowly converted into carbonic acid, which dissociates to liberate hydrogen ions: CO2 + H2O H2CO3 HCO3− + H+ Calculation of pH for weak and strong acids In the case of a strong acid, there is complete dissociation, so the pH is simply equal to minus the logarithm of the acid concentration. Lab.13.pH measurement For example, a 0.01 molar solution of hydrochloric acid has a pH = −log(0.01), that is, pH = 2. The pH of a solution of a weak acid may be calculated by means of an ICE table. For acids with a pKa value greater than about 2, pH = ½ ( pKa − log c0) (6) where c0 is the concentration of the acid. This is equivalent to Burrows' weak acid pH equation (7) A more general method is as follows. Consider the case of dissolving a weak acid, HA, in water. First write down the equilibrium expression. HA A− + H+ The equilibrium constant for this reaction is specified by (8) The analytical concentration of the two reagents, CA for [A−] and CH for [H+] must be equal to the sum of concentrations of those species that contain the reagents. CH is the concentration of added mineral acid. CA = [A−] + Ka[A−][H+] (9) CH = [H+] + Ka[A−][H+] (10) From the equation (8) (11) Substitution of this expression into the equation (9) gives Lab.13.pH measurement (12) This simplifies to a quadratic equation in the hydrogen ion concentration (13) Solution of this equation gives [H+] and hence pH. This method can also be used for polyprotic acids. For example, for the diprotic acid oxalic acid, writing A2− for the oxalate ion, CA = [A2−] + β1[A2−][H+] + β2[A2−][H+]2 (14) CH = [H+] + β1[A2−][H+] + 2β2[A2−][H+]2 (15) where β1 and β2 are cumulative protonation constants. Following the same procedure of substituting from the first equation into the second, a cubic equation in [H+] results. In general, the degree of the equation is one more than the number of ionisable protons. The solution of these equations can be obtained relatively easily with the aid of a spreadsheet such as EXCEL or Origin. The pH always has an amount of fractional figures equal to the amount of significant figures of the concentration. pH in nature pH-dependent plant pigments that can be used as pH indicators occur in many plants, including hibiscus, marigold, red cabbage (anthocyanin), and red wine. Living systems Lab.13.pH measurement The pH of different cellular compartments, body fluids, and organs is usually tightly regulated in a process called acid-base homeostasis. Tab. pH in living systems Compartment pH pH Gastric acid Lysosomes Granules of chromaffin cells Human skin Urine Neutral H2O at 37 °C Cytosol Cerebrospinal fluid (CSF) Blood 1 4.5 5.5 5.5 6.0 6.81 7.2 7.3 7.34–7.45 Mitochondrial matrix Pancreas secretions 7.5 8.1 The pH of blood is usually slightly basic with a value of pH 7.365. This value is often referred to as physiological pH in biology and medicine. Plaque can create a local acidic environment that can result in tooth decay by demineralisation. Enzymes and other proteins have an optimum pH range and can become inactivated or denatured outside this range. The most common disorder in acid-base homeostasis is acidosis, which means an acid overload in the body, generally defined by pH falling below 7.35 Lab.13.pH measurement In the blood, pH can be estimated from known base excess (be) and bicarbonate concentration (HCO3) by the following equation: (16) pH meter A pH meter is an electronic instrument measuring the pH (acidity or alkalinity) of a liquid (though special probes are sometimes used to measure the pH of semi-solid substances). A typical pH meter consists of a special measuring probe (a glass electrode) connected to an electronic meter that measures and displays the pH reading. The probe The pH probe measures pH as the activity of hydrogen ions surrounding a thin-walled glass bulb at its tip. The probe produces a small voltage (about 0.06 volt per pH unit) that is measured and displayed as pH units by the meter. For more information about pH probes, see glass electrode. pH meter Calibration and use For very precise work the pH meter should be calibrated before each measurement. For normal use calibration should be performed at the beginning of each day. The reason for this is that the glass electrode does not give a reproducible e.m.f. over longer periods of time. Calibration should be performed with at least two standard buffer solutions that span the range of pH values to be measured. For general purposes buffers at pH 4 and pH 10 are acceptable. The pH meter has one control (calibrate) to set the meter reading equal to the value of the first standard buffer and a second control (slope) which is used to adjust the meter reading to the value of the second buffer. A third control allows the temperature to be set. Standard buffer sachets, which can be obtained from a variety of suppliers, usually state how the buffer value changes with temperature. The calibration process correlates the voltage produced by the probe (approximately 0.06 volts per pH unit) with the pH scale. After each single measurement, the probe is rinsed with distilled water or deionized water to remove any traces of the solution being measured, blotted Lab.13.pH measurement with a clean tissue to absorb any remaining water which could dilute the sample and thus alter the reading, and then quickly immersed in another solution. Storage conditions of the glass probes When not in use, the glass probe tip must be kept wet at all times to avoid the pH sensing membrane dehydration and the subsequent dysfunction of the electrode. A glass electrode alone (i.e., without combined reference electrode) is typically stored immersed in an acidic solution of around pH 3.0. In an emergency, acidified tap water can be used, but distilled or deionised water must never be used for longer-term probe storage as the relatively ionless water "sucks" ions out of the probe membrane through diffusion, which degrades it. Combined electrodes (glass membrane + reference electrode) are better stored immersed in the bridge electrolyte (often KCl 3 M) to avoid the diffusion of the electrolyte (KCl) out of the liquid junction. Types of pH meters pH meters range from simple and inexpensive pen-like devices to complex and expensive laboratory instruments with computer interfaces and several inputs for indicatorerature measurements be entered to adjust for the slight variation in pH caused by temperature. Specialty meters and probes are available for use in special applications, harsh environments, etc. Glass electrode A glass electrode is a type of ion-selective electrode made of a doped glass membrane that is sensitive to a specific ion. It is an important part of the instrumentation for chemical analysis and physico-chemical studies. In modern practice, widely used membranous ion-selective electrodes (ISE, including glasses) are part of a galvanic cell. The electric potential of the electrode system in solution is sensitive to changes in the content of a certain type of ions, which is reflected in the dependence of the electromotive force (EMF) of galvanic element concentrations of these ions. Lab.13.pH measurement History 909 — F. Haber and Z. Klemensiewicz [polish scientist] publicized on January 28, 1909 results of their research on the glass electrode in The Society of Chemistry in Karlsruhe (first publication — The Journal of Physical Chemistry by W. Ostwald and J. H. van 't Hoff) — 1909). Legend: 1. a sensing part of electrode, a bulb made from specific glass 2. internal electrode, usually silver chloride electrode or calomel electrode 3. internal solution, usually 0.1M HCl for pH electrodes or 0.1M MeCl for pMe electrodes 4. sometimes electrode contain small amount of AgCl precipitate inside the glass electrode 5. reference electrode, usually the same type as 2 6. internal solution, usually 0.1M HCl for pH electrodes or 0.1M MeCl for pMe electrodes Lab.13.pH measurement 7. junction with studied solution, usually made from ceramics or capillary with asbestos or quartz fiber. 8. body of electrode, made from non-conductive glass or plastics. Applications Glass electrodes are commonly used for pH measurements. There are also specialized ion sensitive glass electrodes used for determination of concentration of lithium, sodium, ammonium, and other ions. Glass electrodes have been utilized in a wide range of applications — from pure research, control of industrial processes, to analyze foods, cosmetics and comparison of indicators of the environment and environmental regulations: a microelectrode measurements of membrane electrical potential of a biological cell, analysis of soil acidity, etc. Saturated calomel electrode The Saturated calomel electrode (SCE) is a reference electrode based on the reaction between elemental mercury and mercury(I) chloride. The aqueous phase in contact with the mercury and the mercury(I) chloride (Hg2Cl2, "calomel") is a saturated solution of potassium chloride in water. The electrode is normally linked via a porous frit to the solution in which the other electrode is immersed. This porous frit is a salt bridge. In cell notation the electrode is written as: Theory of operation The electrode is based on the redox reaction The Nernst equation for this reaction is Lab.13.pH measurement where E0 is the standard electrode potential for the reaction and aHg is the activity for the mercury cation (the activity for a liquid of 1 Molar is 1). This activity can be found from the solubility product of the reaction By replacing the activity in the Nernst equation with the value in the solubility equation, we get The only variable in this equation is the activity (or concentration) of the chloride anion. But since the inner solution is saturated with potassium chloride, this activity is fixed by the solubility of potassium chloride. When saturated the redox potential of the calomel electrode is +0.2444 V vs. SHE at 25 °C, but slightly higher when the chloride solution is less than saturated. For example, a 3.5M KCl electrolyte solution increases the reference potential to +0.250 V vs. SHE at 25 °C, and a 0.1 M solution to +0.3356 V at the same temperature. Application The SCE is used in pH measurement, cyclic voltammetry and general aqueous electrochemistry. This electrode and the silver/silver chloride reference electrode work in the same way. In both electrodes, the activity of the metal ion is fixed by the solubility of the metal salt. The calomel electrode contains mercury, which poses much greater health hazards than the silver metal used in the Ag/AgCl electrode. Standard hydrogen electrode The standard hydrogen electrode (abbreviated SHE), also called normal hydrogen electrode (NHE), is a redox electrode which forms the basis of the thermodynamic scale of oxidationreduction potentials. Its absolute electrode potential is estimated to be 4.44 ± 0.02 V at 25 °C, but to form a basis for comparison with all other electrode reactions, hydrogen's standard Lab.13.pH measurement electrode potential (E0) is declared to be zero at all temperatures. Potentials of any other electrodes are compared with that of the standard hydrogen electrode at the same temperature. Hydrogen electrode is based on the redox half cell: 2H+(aq) + 2e- → H2(g) This redox reaction occurs at platinized platinum electrode. The electrode is dipped in an acidic solution and pure hydrogen gas is bubbled through it. The concentration of both the reduced form and oxidised form is maintained at unity. That implies that the pressure of hydrogen gas is 1 bar and the activity of hydrogen ions in the solution is 1 molar. The activity of hydrogen ions is their effective concentration, which is equal to the formal concentration times the activity coefficient. Activity coefficients are close to 1.00 for very dilute water solutions, but are usually lower for more concentrated solutions. The Nernst equation should be written as: or where: aH+ is the activity of the hydrogen ions, aH+=fH+ CH+ /C0 pH2 is the partial pressure of the hydrogen gas, in pascals, Pa R is the universal gas constant T is the temperature, in kelvins F is the Faraday constant (the charge per a mole of electrons), equal to 9.6485309*104 C mol-1 p0 is the standard pressure 105 in Pa Lab.13.pH measurement Standard hydrogen electrode scheme: 1. platinized platinum electrode 2. hydrogen gas 3. acid solution with an activity of H+=1 mol/l 4. hydroseal for prevention of oxygen inteference 5. reservoir via which the second half-element of the galvanic cell should be attached On line pH calculator http://www.webqc.org/phsolver.php For solutions with ionic strengths of 0,1 M or less, the electrolyte effect is independent of the kind of ions and dependent only on the ionic strength. Lab.13.pH measurement EXPERIMENTAL PART Equipment pH meter; solutions of different acids and bases solutions of acetic acid, ammonia solution different salts solution Procedure 1.Measurement of pH of strong acids Step 1. Prepare 5 solutions of H2SO4 (concentration from 1.0 to 0.0001 M, according to data in Table 1) in the beakers of capacity 25 mL. Step 2. Insert the clean and dry electrode of the pH meter to selected solution (e.g. 0.0001M). Step 3. Record the values of pH in Table 1. Step 4. Clean the electrode of the pH meter with distilled water and dry it with tissue. Step 5. Repeat measurement procedure (steps 2-4) to remaining acid solution(e.g.0.001, 0.01, 0.1 and 1.0M) Step 6. In the next step: compare values of pH from measurement and calculated, make the graph pHexp. vs. pHcal. Table 1. Determined and calculated data for H2SO4. Concentration of H2SO4 [mol/L] pH calculated from equation: pH = - log [H+] pH measured experimentally 1.0 0.1 0.01 0.001 0.0001 Lab.13.pH measurement Step 7. Prepare 5 solutions of HCl (concentration from 0.0001 to 1.0 M, according to data in Table 2) in the beakers of capacity 25 mL. Step 8 Repeat steps 2-6. Report data in Table 2. Table 2.Determined and calculated data for HCl. Concentration of HCl [mol/L] 1.0 0.1 0.01 0.001 0.0001 pH calculated from equation: pH = - log [H+] pH measured experimentally 2.Measurement pH of weak acid. Step 9. Prepare 5 solutions of acetic acid in the beakers of capacity 25 mL(concentration from 0.0001 to 1.0 M according to data in Table 3). Step 10. Repeat steps from 2-6. Record the values of pH in Table 3. Table 3. Determined and calculated data for acetic acid. Concentration of acetic acid[mol/L] 1.0 0.1 0.01 0.001 0.0001 pH calculated from equation: pH = - log [H+] pH measured experimentally For calculation pH of weak acid apply the formula: [H ] K a Cacid where Ka = 1.7 ∙10-5 3.Measurement pH of weak base. Step 11. Prepare 5 solutions of ammonia in the beakers of capacity 25 mL( concentration from 0.0001 to 1 M, according to data in Table 4) Lab.13.pH measurement Step. 12. Repeat steps 2-6. Record the values of pH in Table 4. Table 4. Determined and calculated data for ammonia. Concentration of ammonia [mol/L] 1.0 0.1 0.01 0.001 0.0001 pH calculated from equation: pH = - log [H+] pH measured experimentally For calculation pH of weak base apply the formula: [OH ] K b Cbase where Kb = 1.75 ∙10-5 4.Measurement of pH of different salts 4.Measurement of pH of different salts Step 13. Prepare 0.1M solutions of salts from Table 5 in the beakers of capacity 25 mL. Step 14. Repeat steps 2-6. Record the values of pH in Table 5. Table 5. Determined and calculated data for salts Salt Concentration pHexp pHcalc NH4Cl CH3COONa Calculate pH of the salts solutions. For salts with one strong and one weak component the best way of pH calculation it to treat conjugate acid (or base) as the only source of H+ (or OH-) ions. For example if we have solution of salt of weak acid (with dissociation constant Ka) and strong base, reaction of hydrolysis is and the equilibrium is described by conjugate base dissociation constant Lab.13.pH measurement where Starting from these equations we can calculate pOH and pH of the solution using method and assumptions shown for weak acid and base. Exactly the same approach can be used for salt of strong acid and weak base - just using the Ka constant for acid conjugate with weak base. In the case of salt of weak acid and weak base situation is more complicated, but sometimes we can get pretty good results assuming similar degree of both hydrolysis processes (as seen above). Let's say we have a solution of AB salt of weak acid and weak base of concentration C and dissociation constants Ka and Kb. Our first assumption is that the hydrolysis is not too strong, so that in the equilibrium [A-]=[B+]=C. If so, equations for Ka and Kb take forms We will solve them for [H+] and [OH-]: Multiplying: Lab.13.pH measurement and rearranging: Please note that these Ka and Kb values are not related by KaKb=Kw, as they describe different substances. Now it is time for the second assumption - that degree of both hydrolysis reactions is similar, so [HA]=[BOH]: It gives concentration of HA which can be used for [H+] calculation. If equation above is insert into It is obtain: or ph of salt of weak acid and strong base: ph of salt of weak base and strong acid: Lab.13.pH measurement 5.Determination of Buffer Capacity A. Determination of Buffer Capacity with HCl Step 15. Transfer 5 mL of the test solution [ BUFFER PH 4 AND BUFFER PH 10] to another beaker (use a graduated cylinder) and set aside. Step 16. Using the automatic dispenser add 0.25 mL of 0.5 M HCl to the test solution. (One pump of the dispenser). Step 17. Mix well with the glass stirring rod and then measure the pH of the solution. Record data in Table 6. Step 18. Discard the solution from the beaker into the waste bottle. Thoroughly rinse the beaker with DI water and then dry the beaker. B. Determination of the Buffer Capacity with NaOH Step 19. Transfer 5 mL of the test solution [ BUFFER PH 4 AND BUFFER PH 10] to another beaker (use a graduated cylinder) and set aside. Step 20. To the remaining 5 mL portion of the test solution add 0.25 mL of 0.5 M NaOH (one pump of the automatic dispenser). Step 21 Mix well with the glass stirring rod and then measure the pH. Record data in Table 6 Step 22. Discard the solution in the waste bottle. Thoroughly rinse the beaker with water and then dry the beaker. Lab.13.pH measurement Table 6. Buffer capacity data Solution Initial pH pH after H+ pH after OH- Buffer Buffer Addition Addition Capacity Capacity (mmol (mmol H+/∆pH) OH+/∆pH) Buffer pH=4 Buffer pH=4 Buffer pH=10 Buffer pH=10 Calculations to be shown in your lab notebook: Calculate the buffer capacity (mmoles of acid or base added/change in pH) Buffer solutions as mmoles H+/∆pH and as mmoles OH-/∆pH.
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