Iec tr 62434 2006

TECHNICAL REPORT IEC TR 62434 First edition 2006 03 pH measurements in difficult media – Definitions, standards and procedures Reference number IEC/TR 62434 2006(E) L IC E N SE D T O M E C O N L im it[.]

Terms and definitions

The necessary definitions will be provided in the sequence that the relevant physical quantities appear in the text, adhering to the applicable IUPAC documents and IEC 60746-2 standards.

Symbols

The meaning of each symbol used here is given immediately after its first appearance in the relevant equation and it is conform to the pertinent IUPAC documents [1,2] and

pH value

The pH of a solution, which measures the activity of hydrogen ions (H$^+$), is defined by the equation $ \text{pH} = -\log a_{H^+} = -\log(m_{H^+} \gamma_{H^+}) $, where $ \gamma_{H^+} $ represents the activity coefficient of the H$^+$ ion at a given molality $ m_{H^+} $ (moles of H$^+$ per kg of solvent) Since pH is a dimensionless quantity, it is essential to ensure that the logarithm is applied only to dimensionless numbers, emphasizing the importance of the full form of the equation.

1 Numbers in square brackets refer to the bibliography

The pH of a solution is defined by the equation \$pH = -\log a_{H^+} = -\log\left(\frac{m_{H^+} \gamma_{H^+}}{m^\circ}\right)\$, where \$m^\circ = 1 \text{ mol kg}^{-1}\$ represents the standard-state reference molality This definition, based on the molal scale recommended by IUPAC, is advantageous because molality is temperature-independent, reducing the need for repetitive cell construction and filling Alternatively, when considering pH in terms of amount-of-substance concentration \$c\$ (formerly known as molarity), the equation transforms to \$pH_c = -\log(a_{H^+})_c = -\log\left(\frac{c_{H^+} y_{H^+}}{c^\circ}\right)\$, where \$y_{H^+}\$ is the activity coefficient of \$H^+\$ at concentration \$c_{H^+}\$ (moles of \$H^+\$ per dm³ of solvent) It is important to note that pH and \$pH_c\$ are related by the equation \$pH_c = pH - \log\left[\frac{\rho}{\text{kg dm}^{-3}}\right]\$, where \$\rho\$ is the relative density of the solvent.

While equations (2) and (4) provide a way to interpret pH values under specific conditions, it is impossible to rigorously determine H+ concentrations through methods like potential difference measurements This limitation arises from the involvement of the non-thermodynamic single-H+ ion activity coefficient, y H+ Consequently, an operational definition of pH is utilized, based on values assigned to specific reference buffers.

pH measurement involves determining the potential difference (electromotive force) E X between two electrodes placed in a sample with an unknown pH X, using a non-aqueous or aqueous-organic solvent Z This process follows a specific cell scheme to ensure accurate readings.

Concentrated equitransferent salt bridge in solvent Z

Sample at unknown pH X in solvent Z H + − sensing electrode

(hydrogen gas electrode, or glass electrode)

To measure the potential difference $ E_S $, use the same electrode pair and salt bridge with identical composition and solvent $ Z $ at a consistent temperature This should be conducted in a reference buffer solution with a known standard pH, either $ pH_P $ or $ pH_S $.

Concentrated equitransferent salt bridge in solvent Z

Standard pH PS or pH SS in solvent Z H + −sensing electrode

(hydrogen gas electrode, or glass electrode)

The potentials E X and E S are defined as the difference between the right-hand (glass electrode) and left-hand (reference electrode) electrodes The pH of the sample, pH X, can be calculated using the formula: \[pH X = pH SS - \frac{(E X - E S)}{k} + \frac{(E JX - E JS)}{k}\]where $ k = 2.3026 \frac{RT}{F} $ The terms E JX and E JS represent the liquid junction potentials at the interfaces between the reference electrode and the unknown pH X, and the reference electrode and the known standard pH PS, respectively Utilizing a concentrated equitransferent salt bridge in solvent Z effectively reduces the liquid junction potentials, minimizing the difference $ (E JX - E JS) $.

(the so-called “residual liquid junction potential”) can be ignored, and the following operational equation is now internationally endorsed for the determination of pH X : pH X = pH SS − (E X − E S )/k (8)

At high levels of acidity, alkalinity, or salinity, the residual liquid junction potential can significantly impact the accuracy of pH measurements Therefore, it is essential to carefully consider this factor when evaluating the precision of the measured pH value.

LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU.

The cell diagrams (5) and (6), respectively, represent the well known “measure” and

“calibration” configurations of the “pH operational cell” Numerical values for k, the “Nernstian coefficient” or “theoretical slope factor”, at temperatures from (0 to 100) °C, are given in

As glass electrodes age, they exhibit an irreversible reduction in the slope factor, leading to a "practical slope factor" k' that is less than the original k This adjustment must be incorporated into the operational equation (8) The current method for addressing this issue is the "bracketing standards procedure," which involves using two standards: one (pH PS1) below and another (pH PS2) above the anticipated pH X, along with the corresponding measurements of E X.

E S1 , and E S2 , are then combined to give the following equations: k’ = −(E S2 − E S1 )/(pH S2 − pH S1 ) (9) pH X = pH S1 + (E X − E S1 )(pH S2 − pH S1 )/(E S2 − E S1 ) (10)

The electric potential difference that occurs at the junction of two electrolyte solutions with varying concentrations is typically reduced through the use of a salt bridge This practice, while not perfect, helps to minimize the potential difference Additionally, when the junction involves solutions that differ in both electrolyte composition and solvent, the implications for electric potential become more complex.

The heterosolvental junction features an intervening liquid junction potential that consists of an ionic liquid junction potential, which can be minimized by using an appropriate salt bridge, as discussed in section 3.6.5 In contrast, the solvental liquid junction potential cannot be minimized and may reach several tens of millivolts.

Standard reference buffer solutions (primary and secondary pH standards)

A reference buffer solution, or pH standard, is created using a specific formula and high-quality analytical-grade chemicals and solvents, which may be either non-aqueous or aqueous-organic, and should be redistilled if a pH accuracy of ±0.05 is required Due to variations in the purity of commercial chemicals, the pH value of these reference buffer solutions can differ by approximately ±0.01 from accepted standards For enhanced precision, such as achieving an accuracy of ±0.002, it is advisable to use chemicals that have been thoroughly characterized and validated.

Certified Reference Materials (CRM) are provided by national standards laboratories, while solvents, whether non-aqueous or aqueous-organic, undergo rigorous purification procedures and tests, including conductivity assessments when relevant.

Primary reference standards (pH PS) are defined as substances that can be prepared in a highly pure state and are available as certified reference materials These standards must exhibit solution stability over a reasonable duration and possess a low residual liquid junction potential They are specified in a solution of defined concentration within the appropriate solvent Z.

The pH PS values assigned to these primary standards are specifically derived from measurements on the following reversible cell (“Harned’s cell”):

Pt H 2 (gas, p = 101325 Pa) pH PS + KCl, in Z AgCl Ag Pt (11)

The structure of MECON Limited, located in Ranchi and Bangalore, is illustrated schematically in Figure 1, along with the parallel cell (13) This information is provided for internal use only and is supplied by the Book Supply Bureau.

The optimal pH values for various standard buffer solutions in 45 nonaqueous or aqueous-organic solvents at different temperatures are detailed in Annexes B, C, and D, which also include instructions for the correct preparation of the chemicals.

The potential difference E of cell (11), omitting to write the term m°= 1 mol kg − 1 for convenience, is given by:

E = E° − k log[m H+ m Cl – γ H+ γ Cl –] (12) where the standard potential difference E° is derived separately from measurements on the cell (13):

The relationship between the pH of a solution and its ionic activity coefficients can be derived from the equation $ pH = \frac{(E - E°)}{k} + \log(m_{Cl^-}) + \log(\gamma_{Cl^-}) $ Here, $ \gamma_{Cl^-} $ is calculated using the Bates-Guggenheim equation, which accounts for the ionic strength of the solution and the properties of the solvent Specifically, the equation for $ \log(\gamma_{Cl^-}) $ incorporates the Debye-Hückel constant and the permittivities and densities of both the solvent and water In cases where the solvent is water, the equation simplifies, highlighting the importance of ionic strength in determining the activity coefficients in aqueous solutions.

The Bates-Guggenheim equation is utilized for standardizing pH in a pure water medium The pH values derived from this equation exhibit slight variations with m Cl due to ionic interactions between the pH PS buffer and KCl in the mixed electrolyte Consequently, these pH values are plotted against m Cl, with the intercept at m Cl = 0 identified as the primary standard pH PS.

Values of the required ancillary quantities A Z , γ ± , and E° are available (see [1] and literature cited therein)

Figure 1 – Schematic structure of the hydrogen gas electrode and of the AgCl electrode forming the cell (13)

Secondary standards (pH SS) are defined as substances that can be prepared in a highly pure state consistently and maintain solution stability over a reasonable duration These standards are utilized in solutions of specified concentration within general solvents, which may include non-aqueous or aqueous-organic mixtures.

The values of pH SS can be assigned by comparison with the pH PS values in cells with liquid junction of the type

In the context of cell (16), the pH of the solution (pH SS) can either match the nominal composition of the reference solution (pH PS) or differ significantly To ensure precise and reproducible potential values, it is essential to form the junctions within capillary tubes, which provide a well-defined geometry for the liquid junction If we denote the potential difference of cell (16) as E 16, and assume that the liquid junction potentials are negligible, the relationship between pH SS and pH PS can be expressed as follows: pH SS = pH PS − E 16 / k.

An IUPAC-approved method for measuring pH involves using a modified version of cell (11), where the glass electrode, a non-thermodynamic H$^+$-sensing membrane electrode, substitutes the H$^+$-reversible hydrogen-gas electrode.

The Pt glass electrode pH SS + KCl, in Z AgCl Ag Pt (18), creates a non-reversible cell with a potential difference of E 18 The data processing for E 18 follows the same methodology outlined in equations (12) to (15) It is essential to specify the procedure used, whether it is based on cell (16) or cell (18).

Certified chemicals from a national metrological institution are essential for establishing a primary buffer solution To qualify as a primary buffer, it must meet the highest standards of metrological quality, aligning with the definition of a primary standard.

To be classified as Certified Reference Materials (CRMs), primary and secondary standard materials must be accompanied by certificates from national metrological institutes.

3.4.1.5 Storage of standard pH buffers in certain solvents

To ensure the long-term stability of pH PS or pH SS buffer solutions in alcohols, glycols, and glycerols (including their mixtures with water), it is advisable to store them at freezer temperatures of approximately -15 °C This practice helps prevent unwanted esterification.

3.4.2 Measurement of pH X - Choice of the standard reference solutions

In contrast to purely aqueous solutions, which have a wide range of primary and secondary standards, non-aqueous or aqueous-organic solvent Z lacks sufficient standards The notable exceptions are methanol-water and ethanol-water mixtures, where electrochemists have primarily focused their research efforts.

Widths of normal pH scales or normal pH ranges in the general solvents Z

The temperature-dependent autoprotolysis constant $ K_Z $ is a crucial parameter for each solvent $ Z $, indicating its ability to self-ionize and release $ H^+ $ ions This is represented by the negative logarithm of $ K_Z $, denoted as $ pK_Z = -\log K_Z $.

The conventional normal pH scale is defined at 25 °C for each solvent Z The pK Z values for various nonaqueous and aqueous-organic solvents are detailed in the IUPAC document The neutral pH point serves as the midscale reference.

In aqueous solutions, the pK Z value is 14, resulting in a pH scale that spans 14 units with a neutral point at pH 7 Conversely, in acetonitrile, the pK Z value rises to 28, establishing a neutral point at pH 14 This discrepancy highlights the challenge of comparing pH values across different solvents, which is closely related to the primary medium effect on the H$^+$ ion.

–20 –10 0 10 20 30 40 50 60 pH (water-referred intersolvental scale)

WATER Methanol Ethanol n-Propanol Acetonitrile Formamide n-Butanol i-Butanol

Figure 2 – Intercomparing widths and relative positions of normal pH scales

(with neutral points indicated by halving dots) in different solvents

3.5.2 Conditions for comparability of pH scales in different solvents Z with the aqueous pH scale: definition of an intersolvental scale of pH

pH values measured in solvent Z are only valid within that specific solvent and cannot be directly compared to pH standards or values measured in water To establish a physical comparison between pH in solvent Z and pH in water, a conversion to a unified intersolvental pH scale is necessary This conversion is represented by the equation: \$$\text{pH}_{Z/W} = \text{pH}_Z - \log(\gamma_T) = \text{pH}_Z + \frac{(E^\circ_H)_W - (E^\circ_H)_Z}{k}\$$ where $\gamma_T$ is the transfer activity coefficient of H$^+$, reflecting the primary medium effect.

The term log(γ T) represents the change in standard Gibbs free energy associated with the transfer of the H$^+$ ion from water (W) to solvent Z, quantified by the difference in energy levels.

The standard absolute potential difference of the H$^+$ sensing electrode in W and Z, represented as $(E°_H)_W - (E°_H)_Z$, cannot be determined through any thermodynamically correct method, necessitating the use of extrathermodynamic methods or assumptions This leads to significant discrepancies in the log($\gamma_T$) values reported by various authors Consequently, the conversion expressed by equation (20) remains theoretical, making the pH$_Z$ scale incompatible with the aqueous pH$_W$ scale Figure 2 provides the best available overview, though it holds only qualitative value.

3.5.3 Incorrect use of two-solvent cells for pH measurements

An improductive, but all too frequently tried, approach to obtaining a comparability of pH Z with pH W is that [see 11] which is based on measuring the potential difference (E X ) Z of the cell

Sample at unknown pH X in solvent Z

H + − sensing electrode (hydrogen gas electrode, or glass electrode)

LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU. the Nernstian expression of which is expressed by:

(E X ) Z = U Z − k (pH X ) Z + (E JX ) Z (22) after a deceptive “calibration” based on measuring the special potential difference *E S of the two-solvent (“heterosolvental”) cell (23):

Standard at known pH PS in water

(hydrogen gas electrode, or glass electrode) which is expressed by

From equations (22) and (23), a new supposed “operational” equation is derived:

The equation $(pH X ) Z = (pH S ) W - \frac{(E X ) Z - *E S}{k}$ suggests that pH Z can be directly measured and compared to the aqueous standard pH S W However, deriving this equation by subtracting (23) from (22) is invalid, as U Z and *U are fundamentally different and cannot be disregarded This discrepancy arises from the fact that $(E° H ) W$ is not equal to $(E° H ) Z$, and the activities of hydrogen ions $(a H+ ) W$ and $(a H+ ) Z$ are not comparable Additionally, the liquid junction potential *E JS includes a solvental contribution that is not accounted for in $(E JX ) Z$, further complicating the difference.

However, a heterosolvental cell configuration of the type:

Various samples at unknown (pH X ) Z ’s in same solvent Z

H + − sensing electrode in same solvent Z (25) whose potential difference can be expressed as:

The equation \$E_X = U - k (pH_X)_Z + E_{JX}\$ can effectively measure variations in \$ (pH_X)_Z \$ across different samples in the same solvent \$ Z \$ As indicated by this equation, the change in \$ (pH_X)_Z \$, denoted as \$ \Delta (pH_X)_Z \$, is equal to \$ \Delta E_X / k \$, since the constant terms \$ U \$ and the liquid junction potential \$ E_{JX} \$ cancel out in the difference However, if the cell is switched from solvent \$ Z \$ to a different solvent, the measurement may be affected.

The observed values of ∆(pHX)Z’ in the aqueous reference electrode Z’ do not physically correlate with the ∆(pH X)Z values in Z, due to changes in the solvental component of the liquid junction potential *E JX.

Electrodes and operating conditions

3.6.1 pH sensor (pH glass electrode)

The most commonly used pH sensor is the glass electrode [9], other potentiometric sensors, for example, the antimony electrode are only adopted when its use is precluded The pH isfet

(ion selective field effect transistor) sensor is an alternative to potentiometric sensors, necessitating manufacturer-specific instrumentation

The precision H$^+$-sensing electrode is a thin foil of platinum coated electrolytically with finely divided platinum or palladium, which catalyzes the electrode reaction $ \text{H}^+ + e^- \rightarrow \text{H}_2 $ in hydrogen-saturated solutions This electrode is essential for thermodynamic studies and the determination of pH standards, although it is not suitable for routine measurements.

However, in certain non-aqueous solvents (for example acetonitrile, dimethylsulfoxide) the hydrogen electrode does not work properly and should be replaced by another appropriate

H +- sensing electrode, for example the quinhydrone electrode described in 3.6.3

This is a wire of noble metal (platinum or gold) placed in a solution to which a small amount

Quinhydrone, approximately 0.1 g, is used to saturate a solution with equimolar amounts of quinone and hydroquinone This quinhydrone electrode serves as a reliable alternative to the hydrogen electrode in specific nonaqueous solvents, such as acetonitrile and dimethylsulfoxide, where the hydrogen gas electrode may exhibit inconsistent behavior for pH standard determination Additionally, under neutral or acidic pH conditions, and in the absence of strong oxidizing and reducing agents as well as high concentrations of salts, the quinhydrone electrode can effectively replace the glass electrode for routine pH measurements.

A stable half-cell potential is essential for accurately measuring the pH sensor's potential at a constant temperature Electrical contact with the sample occurs through a liquid junction, utilizing either a reference electrolyte or a salt-bridge solution.

This is a concentrated solution of a binary electrolyte MX having cation M + and anion X − of equal mobility (“equitransferent concentrated bridge” in common terminology, with M + = K + ,

To minimize the residual liquid junction potential error, it is essential to insert ions such as NH₄⁺, Rb⁺, Cs⁺, and X⁻ (where X⁻ can be Cl⁻, Br⁻, I⁻, or NO₃⁻) between the internal filling solution of the reference electrode and the sample solution at pH X (or the reference standard at pH PS) in the same solvent Z This practice, first introduced by Guggenheim, is widely recognized in the field.

Common examples of salt bridges include saturated KCl, RbCl, CVsCl, and NH₄Cl in water or various water-rich aqueous-organic solvents In many cases, such as with the alkali halides mentioned, the salt bridge serves as the internal filling solution for halide-reversible second-kind reference electrodes, simplifying their design and function However, when transitioning from pure water to aqueous-organic mixtures or nonaqueous solvents, the equitransference properties of some MX salts may be compromised For example, in a study, it was found that NH₄Cl is the only suitable equitransferent salt bridge when switching from pure water to pure formamide, while other salts fail The effectiveness of the NH₄Cl bridge also extends to other amides and N-alkylamides with high permittivities, as well as mixed solvents like water-alcohol, water-glycol, and water-acetonitrile Additionally, when halide-based salt bridges are chemically incompatible with certain ions, such as Ag⁺, Tl⁺, or Hg₂⁺, the Li₂SO₄ salt bridge can be utilized.

A reference electrode, such as one based on Hg$_2$SO$_4$ or Pb$_2$SO$_4$, can be effectively utilized in specific solvents In commercial applications, these reference electrodes are designed to include an appropriate salt bridge within their structure.

3.6.5.2 Second bridge, or bridge solution (of a double-junction reference electrode)

A concentrated solution of an inert binary electrolyte, featuring cations and anions with equal mobility, can be placed between a standard salt bridge and both the sample pH (X) and standard pH (PS) solutions to address any chemical incompatibility.

The second bridge must be compatible with the solvent used in the salt bridge 3.6.5.1 Suitable options for second bridges include KNO₃, NH₄NO₃, RbNO₃, CsNO₃, Li₂SO₄, and Lithium Acetate in water However, further research is necessary to determine the suitability of these compounds, particularly Li₂SO₄, in nonaqueous or aqueous-organic solvents.

The standardization of pH in non-aqueous solvents and aqueous-organic solvent mixtures shares several characteristics with pH standardization in aqueous solutions Water, with a relative permittivity of approximately 78 at 25 °C, is a typical ionizing solvent, while organic solvents vary widely, from non-ionizing solvents like benzene and 1,4-dioxane to strongly ionizing solvents like N-methylacetamide, which has a relative permittivity of about 182 Numerous non-aqueous solvents, including alcohols, glycols, and ethers, are widely used in industrial chemistry, analytical chemistry, engineering, and corrosion Additionally, there are hundreds of binary aqueous-organic solvent mixtures that are equally significant, indicating a vast range of possibilities in this field It is also essential to establish the boundaries of the "normal pH scale" or "normal pH range."

3.4) in each (non-aqueous or mixed) solvent for obvious comparison purposes For example, if the above normal range in water is 14 pH units wide, with the neutrality point

At pH 7 in acetonitrile, the normal pH range spans 28 units, with neutrality at pH 14, which is not directly comparable to pH 14 in water To establish a coherent "intersolvental" pH scale, it is essential to define the relative positions of pH scales in various non-aqueous or mixed solvents with reference to water, given its critical role among solvents Additionally, it is crucial to develop sufficient primary pH standards (pH PS) to encompass the normal pH scale across different solvents and temperatures, although currently, these standards are limited in availability The International Union of Pure and Applied Chemistry (IUPAC) has recently set forth criteria for determining primary and secondary pH standards in non-aqueous solvents and aqueous-organic mixtures with relative permittivities above 25 to 30, under conditions of negligible ionic association This range includes many common ionizing solvents, and the available primary standards are detailed in the IUPAC annexes.

6 Recommended standard values and ranges of influence quantities

All the relevant data are to be found in Annexes B, C, D, E, and F

8 Other difficult media for pH determinations

pH measurement presents significant methodological challenges not only in non-aqueous or aqueous-organic media but also in specialized aquatic environments These include physiological solutions, low-ionic-strength freshwaters, estuarine waters, seawater, and highly saline waters.

The challenges posed by these media include the interpretation of acid-base equilibria in conjunction with other dissociative equilibria, the selection and adaptation of pH-metric standards, the design and choice of salt bridges at liquid junctions, the selection of reference electrodes, the type and design of operational pH-metric cells, and the control of influencing quantities.

All these problems, and the related methodological recommendations, are dealt with exhaustively in specific IUPAC documents [13 to 16], and need not be redescribed here

Values of the Nernstian slope factor k = 2,3026 RT/F

Table A.1 – Values of the Nernstian slope factor k = 2,3026 RT/F t / °C k /V t / °C k /V

The values of primary pH-metric standards (pH PS) for a 0.05 m Potassium Hydrogen Phthalate buffer in aqueous-organic solvent mixtures are presented, along with the overall estimated standard errors (δ) These values are analyzed at various mass percent concentrations of the nonaqueous component, corresponding mole fractions (x), and different temperatures ranging from 3 to 7 °C.

Mass percent of nonaqueous solvent in admixture with water

SULFOXIDE δ ± 0,002 ± 0,002 a) ethylene glycol b) methyl cellosolve

The values of primary pH-metric standards (pH PS) for a 0.05 m Potassium Hydrogen Phthalate buffer in aqueous-organic solvent mixtures are presented, along with the overall estimated standard errors (δ) These values are analyzed at various mass percent concentrations of the nonaqueous component, corresponding mole fractions (x), and different temperatures ranging from 3 to 7 °C.

Mass percent of nonaqueous solvent in water mixture

N-METHYL-ACETAMIDE ±0,009 ±0,020 a) 1,3-Dioxolan-2-one b) 4-Methyl-1,3-dioxolan-2-one

Values of primary pD-metric standards (pD PS ), with overall estimated uncertainty δ, for the

0,05 m Potassium Deuterium Phthalate buffer in Deuterium Oxide (D 2 O) at different temperatures t/°C t /°C 5 10 15 20 25 30 35 40 45 50 pD PS 4,546 4,534 4,529 4,522 4,521 4,523 4,528 4,532 4,542 4,552 δ ± 0,007

The primary standards (pH PS) of various buffers are essential for accurate pH measurements in different solvents and aqueous-organic solvent mixtures at varying temperatures The concentrations of the organic components in these solvent mixtures are represented as mass percent.

BUFFERS ACETATE a SUCCINATE b PHOSPHATE c TRIS+

SOLVENT DIMETHYLSULFOXIDE SOLVENT DEUTERIUM OXIDE *

Tiêu đề	pH measurements in difficult media – Definitions, standards and procedures
Trường học	International Electrotechnical Commission
Chuyên ngành	Electrotechnology Standards
Thể loại	Technical report
Năm xuất bản	2006
Thành phố	Geneva

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