(1) pH Measurement

Basic Principles of pH Measurement

Perhaps the most familiar and oldest zero-current measurement method used to characterize chemical reaction processes is pH measurement.

What is pH, and what should you know about pH measurement?

In general, pH measurement is used to determine the acidity or alkalinity of a solution.

When an acid is added to water, the acidity of the water increases and the pH value decreases. Conversely, when a base is added to water, the alkalinity of the water increases, and the pH is the unit used to express acidity or alkalinity. When we say that milk is “cool” or that an acid is “weak,” we are not providing a definitive description of the condition of the substance, because we have not specified the measurement unit or the measured value. By contrast, when we state that the temperature of the milk is 10°C, we are giving a precise and unambiguous description. Similarly, when we say that a weak acid has a pH of 5.2, this too is a precise statement.

There are many acids and bases in the world, each with varying degrees of acidity or alkalinity. For example, hydrochloric acid is a very strong acid, whereas boric acid is quite weak (and can be used to rinse eyes and wounds).

The strength of an acid is primarily determined by the extent to which hydrogen ions dissociate in solution. In strong acids, hydrogen ions dissociate extensively, whereas in weak acids, only a small fraction dissociates. Hydrochloric acid is classified as a strong acid because the chloride ion facilitates nearly complete dissociation of the hydrogen ion. Boric acid, on the other hand, is a weak acid because only a very limited number of hydrogen ions are released upon dissociation. Even chemically pure water contains trace amounts of dissociated species; strictly speaking, the hydrogen nucleus does not exist in a free state until it forms a hydration shell with water molecules.

H ₂ O+H ₂ O=H ₃ O ⁺ +OH ^-

Since the concentration of hydronium ions (H3O+) can be treated as equivalent to the concentration of hydrogen ions (H+), the above equation can be simplified into the following commonly used form:

H ₂ O=H ⁺ +OH ^-

The positively charged hydrogen ion is denoted in chemistry as “H⁺” or “hydrogen nucleus.” The hydrated hydrogen nucleus is referred to as the “hydronium ion.” The negatively charged hydroxide ion is called the “hydroxide ion.”

Using the law of mass action, the dissociation of pure water can be expressed in terms of an equilibrium constant:

Since only a very small fraction of water is ionized, the molar concentration of water is essentially constant, and the ionic product of water, Kw, can be determined from the equilibrium constant K.

KW = K × H ₂ O KW = H ₃ O ⁺ ·OH ^- =10 ^-7 ·10 ^-7 =10 mol/L (25°C)

In other words, for one liter of pure water at 25°C, there exists 10 ^-7 Moor H ₃ O ⁺ Ions and 10 ^-7 Moor OH ^- Ion.

To avoid the cumbersome calculations involved in using negative logarithms of molar concentrations, biologist Sørensen proposed in 1909 to replace this unwieldy quantity with a logarithmic scale and introduced the concept of “pH.” Mathematically, pH is defined as the negative common logarithm of the hydrogen ion concentration. That is:

pH = -log[H] ⁺

Strictly speaking, this formula ignores hydrogen ions (H ⁺ ) and hydroxide ions (OH ^- ) of the interaction, because the electrostatic forces between ions significantly reduce their mobility. In other words, the effective concentration (i.e., activity) of hydrogen ions is also dependent on all other ions present in the solution.

For example: when the hydrogen ion concentration is 10 ^-1 At 1 mol/L, the theoretical pH should be 1.0, yet we measured only a pH of 1.08. This indicates that the degree of dissociation factor f is not equal to 1, but rather 0.823. In other words, the precise definition of pH should be: pH

Measurement of the temperature coefficient of a solution:

Due to the strong temperature dependence of the ionic product, the neutral point of pure water exhibits the following distribution:

0℃ = pH

25℃ = pH

75℃ = pH

00℃ = pH

Acids and bases are diluted with water, and the pH values mentioned above will inevitably depend on temperature.

For strong acids, the effect of water’s autoionization is negligible, and the pH is determined solely by the acid’s degree of dissociation:

At 0℃ At 25℃ At 50℃

0.001 nH CL 3.00 pH 3.00 pH 3.00 pH

0.1 N HCl 1.08 pH 1.08 pH 1.08 pH

For alkaline solutions, the aforementioned effects are substantial. This is because the activity of hydrogen ions decreases, while the self-ionization of water becomes dominant.

At 0℃ At 25℃ At 50℃

0.001 N NaOH 11.94 pH 11.00 pH 10.26 pH

Saturated lime water ┄┄ 12.4 pH 11.68 pH

In practical terms, the following conclusions can be drawn:

For pH measurements in process control, the temperature characteristics of the solution must be known; pH values can only be compared when the measured medium is at the same temperature.

How to Measure pH

Almost everyone is familiar with the method of measurement that exploits the color-changing property of litmus paper in response to variations in pH. For example, litmus paper turns deep red or light red in acidic solutions and deep blue or light blue in alkaline solutions.

However, this method exhibits significant errors (≤2 pH units) in weak buffer solutions, solutions containing metal ions, or organic compound solutions.

To obtain accurate and reproducible pH values, potentiometric methods must be used for pH measurement.