Decimal Logarithm of the reciprocal of the hydrogen ion activity, aH+, in a solution is used to calculate pH.

pH = -log[aH+]

For example, the argument of the logarithm for a solution with a hydrogen ion activity of 5×10-6 (at that level, this is effectively the number of moles of hydrogen ions per litre of solution) is 1/(5×10-6) = 2×105; consequently, the pH of such a solution is log10(2×105) = 5.3. Consider the following illustration: Nearly 18 g of dissociated hydrogen ions are present in 107 moles of pure (pH 7) water, or 180 metric tonnes (18×107 g).

It’s important to remember that pH is affected by temperature. Pure water, for example, has a pH of 7.47 at 0 degrees Celsius. It is 7.00 degrees Celsius at 25 degrees Celsius and 6.14 degrees Celsius at 100 degrees Celsius.

p[H]

This was Srensen’s original definition in 1909,which was superseded in 1924 by pH. In modern chemistry, [H] denotes the concentration of hydrogen ions, which appears to have units of concentration. The thermodynamic activity of H+ in dilute solution should be substituted by [H+]/c0, with c0 = 1 mol/L as the reference state concentration. This ratio is a pure number with a defined logarithm.

However, if the electrode is calibrated in terms of hydrogen ion concentrations, it is feasible to measure the concentration of hydrogen ions directly. Titrate a solution of known concentration of a strong acid with a solution of known concentration of a strong alkaline in the presence of a reasonably high concentration of background electrolyte is one method that has been utilised widely. Because the quantities of acid and alkali are known, calculating the concentration of hydrogen ions to link the measured potential with concentrations is simple. Typically, a Gran plot is used to calibrate the system. Using this approach has the effect of making activity equal to the numerical value of concentration.

In a medium similar to the one being researched, the glass electrode (and other ion selective electrodes) should be calibrated. If one wants to test the pH of a seawater sample, for example, the electrode should be calibrated in a solution with a chemical composition similar to seawater, as described below.

The difference between p[H] and pH isn’t significant. pH = p[H] + 0.04 is what has been stated[15]. The word “pH” is commonly used to refer to both sorts of measurements.

pH indicators

By utilising the fact that indicators’ colour varies with pH, they can be utilised to monitor pH. The colour of a test solution can be visually compared to a standard colour chart to obtain a pH reading that is accurate to the nearest whole integer. Color can be measured spectrophotometrically with a colorimeter or spectrophotometer for more exact results. A universal indication is made up of a group of indicators that exhibit a continuous colour shift from pH 2 to pH 10 over time. The universal indicator paper is comprised of absorbent paper that has been impregnated with the universal indicator. Another approach for measuring pH is to use an electronic pH metre.

pOH

The concentration of hydroxide ions, OH, is sometimes expressed as pOH. pH measurements are used to calculate pOH values. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by

[OH-]= Kw/[H+]

here KW is the self-ionization constant of water.By taking logarithm

pOH= pKw – pH

At ambient temperature, pOH equals 14 pH. However, in some cases, such as soil alkalinity measurements.

Calculations of pH

A chemical speciation calculation is a mathematical technique for calculating the quantities of all chemical species present in a solution containing acids and/or bases. The type of solution determines the procedure’s complexity. Strong acids and bases do not require calculations, except in extreme instances. To determine the pH of a weak acid solution, a quadratic equation must be solved. A cubic equation may be required to determine the pH of a weak base solution. In the general case, a set of non-linear simultaneous equations must be solved.

The fact that water is both a weak acid and a weak base adds to the complexity (see amphoterism). According to the equilibrium, it dissociates as:

2 H2O ⇌ H3O+ (aq) + OH− (aq)

& its dissociation constant is defined as:

Kw = [H+][OH-]/M2

where [H+] = conc. of the aq. Hydronium ion 

[OH−] = conc. of the Hydroxide ion.

 This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.

Strong acids and bases

Strong acids and bases are substances that are entirely dissociated in water for practical purposes. This indicates that the concentration of hydrogen ions in an acidic solution can be assumed to be equal to the concentration of the acid in typical circumstances. 

 pH = -logarithm10 conc.

Example of strong acid is HCl. A 0.01M HCl solution has a pH of log10(0.01), which equals pH = 2. A strong base, such as sodium hydroxide (NaOH), is an example. A 0.01M NaOH solution has a p[OH] value of log10(0.01), which means p[OH] = 2. According to the definition of p[OH] in the pOH section above, the pH is approximately 12. The self-ionization equilibrium must be considered for sodium hydroxide solutions at greater concentrations.

When concentrations are exceedingly low, self-ionization must also be considered. Consider a hydrochloric acid solution with a concentration of 5×10-8M. According to the basic process outlined above, it has a pH of 7.3. An acid solution should have a pH of less than 7, therefore this is clearly incorrect. A pH of 6.89 is obtained by treating the system as a mixture of hydrochloric acid and the amphoteric material water.

Weak acids and bases

Using the same formalism, a weak acid or the conjugate acid of a weak base can be treated

• Acid HA: HA ⇌ H+ + A−

• Base A: HA+ ⇌ H+ + A

The following is how an acid dissociation constant is defined. For the purpose of simplicity, electrical charges are excluded from the following equations.

             Ka= [H] [A] / [HA]

and its worth is thought to have been found through experimentation. Because of this, there are three unknown concentrations to calculate: [HA], [H+], and [A]. Two more equations are required. Applying the rule of mass conservation to the two “reagents” H and A is one technique to provide them.

CA = [A] + [HA]

CH = [H] + [HA]

Analytical concentration is denoted by the letter C. In some literature, a charge balance equation is used instead of a mass balance equation. This is sufficient in basic circumstances such as this one, but it is more difficult to use in more complex cases such as those listed below. There are now three equations in three unknowns, in addition to the equation determining Ka. When an acid is dissolved in water, the concentration of the acid is CA = CH = Ca, therefore [A] = [H]. After some further algebraic manipulation, a hydrogen ion concentration equation can be produced.

[H]2 + Ka [H] – KaCa =0

The hydrogen ion concentration is obtained by solving this quadratic equation, and hence p[H] or pH. 

An additional factor is added to the mass-balance equation for hydrogen in alkaline liquids. The hydrogen ion concentration is reduced by adding hydroxide, and the hydroxide ion concentration is restricted by the self-ionization equilibrium to be equal to Kw/[H].

CH = ( [H] + [HA] – Kw ) / [H]

Resulting equation will be cubic in [H].

Extremes of pH

Because the Nernst law breaks down when measuring pH below approximately 2.5 (ca. 0.003 mol/dm3 acid) and above about 10.5 (ca. 0.0003 mol/dm3 alkaline), specific methods are required when using the glass electrode. This is due to a number of causes. Liquid junction potentials cannot be considered to be pH-independent.Also, because a high pH indicates that the solution is concentrated, ionic strength changes alter electrode potentials. Because the electrode becomes sensitive to the concentration of cations such as Na+ and K+ in the solution at high pH, the glass electrode may be impacted by “alkaline mistake.”Specially designed electrodes are available to help mitigate some of these issues.

Runoff from mines or mine tailings can produce some very low pH values.

Applications

Pure water is a neutral substance. When an acid is dissolved in water, the pH falls below 7 (at 25 degrees Celsius). The pH of water will be more than 7 when a base, or alkali, is dissolved in it. A pH of 0 is found in a solution of a strong acid, such as hydrochloric acid, with a concentration of 1 mol dm3. A pH of 14 is found in a solution of a strong alkali, such as sodium hydroxide, with a concentration of 1 mol dm3. As a result, observed pH values will generally fall between 0 and 14, while negative pH readings and values higher than 14 are also possible. Because pH is a logarithmic scale, a change of one pH unit corresponds to a tenfold change in hydrogen ion concentration.

However, if the electrode is calibrated in terms of hydrogen ion concentrations, it is feasible to measure the concentration of hydrogen ions directly. Titrate a solution of known concentration of a strong acid with a solution of known concentration of a strong alkaline in the presence of a reasonably high concentration of background electrolyte is one method that has been utilised widely. Because the quantities of acid and alkali are known, calculating the concentration of hydrogen ions to link the measured potential with concentrations is simple. Typically, a Gran plot is used to calibrate the system. Using this approach has the effect of making activity equal to the numerical value of concentration. Because the activity of hydrogen and hydroxide ions is dependent on ionic strength, the pH of the neutral NaCl solution will change somewhat from that of neutral pure water. As a result, Kw varies with ionic strength.

When pure water comes into contact with air, it turns slightly acidic. This is due to the fact that water absorbs carbon dioxide from the air, which is subsequently transformed into bicarbonate and hydrogen ions over time (essentially creating carbonic acid).

Conclusion 

Finally, the pH value reflects how much hydrogen ions (H+) have been separated from molecules in a solution. The larger the concentration of H+ ions in a solution and the stronger the acid, the lower the pH value. Similarly, as the pH rises, the concentration of H+ ions in the solution decreases, and the acid becomes weaker.