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How to Calculate pH of Solutions for JEE

What is pH?

Last updated date: 14th Mar 2023
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The pH of an aqueous solution is a measure of how acidic or basic it is. The pH of an aqueous solution can be determined and calculated using the concentration of hydronium ions in the solution. pH is the negative logarithm of 10 (“log” in the calculator) of the hydrogen ion concentration of a solution. To calculate it, take the logarithm of the given hydrogen ion concentration and reverse the sign.


The pH of an aqueous solution is based on the pH scale and usually ranges from 0 to 14 in water (although this is not a formal rule, as explained below). pH 7 is considered neutral. A pH below 7 is considered acidic. In that case, pH values ​​above 7 are considered basic. Acidic solutions have a high hydronium concentration and a low hydroxide concentration. The basic solution has a high hydroxide concentration and a low hydronium concentration.


Self-Ionisation of Water

  • Self-ionisation of water allows the formation of hydronium (H3O+) and hydroxide ions (OH-) due to the amphibious ability of water to act as a donor and acceptor of protons.

  • In pure water, the concentration of hydronium ions is the same as the concentration of hydroxide ions. 

  • At 25oC, the concentration of both hydronium and hydroxide ions is $1.0\times {{10}^{-7}}$. 

  • The ionic product of water Kw is the equilibrium condition for self-ionisation of water and is expressed as follows.

${{K}_{W}}=\left[ {{H}_{3}}{{O}^{+}} \right]\left[ O{{H}^{-}} \right] =1.0\times {{10}^{-14}} $

  • pH:

The term pH refers to the "potential of hydrogen ions".

Danish biochemist Soren Sorensen proposed in 1909 to more conveniently explain the ionic concentrations of hydronium and hydroxides in aqueous solutions.

Both concentrations tend to be very low.

Sorensen defined pH as a negative logarithmic value of hydrogen ion concentration. 

The formula for the determination of pH of an aqueous solution with respect to the hydronium ion concentration is

$pOH=-\log \left[ {{H}_{3}}{{O}^{+}} \right]$

  • pOH: 

The pOH of the pH-related aqueous solution can be determined by the following formula. 

$pOH=-\log \left[ O{{H}^{-}} \right]$ 

This formula uses the hydroxide concentration of the aqueous solution instead of the hydronium concentration.


pH Value of Acid and Bases

  • There are several ways to define acids and bases, but pH is particularly relevant only to hydrogen ion concentration and applies to aqueous solutions (water-based). 

  • When water dissociates, hydrogen ions and hydroxides are produced. See this chemical formula below.

${{H}_{2}}O\leftrightarrow {{H}^{+}}+O{{H}^{-}}$

  • When calculating pH, keep in mind that [ ] refers to molarity, M. Molarity is expressed in moles of solute per litre of solution. 

  • If the concentration is specified in units other than molars (percentage by weight, molarity, etc.), convert it to molarity and use the pH formula.

  • The relationship between pH and molarity can be expressed as follows.

Kw is the dissociation constant of water

Acidic solution: $\left[ {{H}^{+}} \right]>1\times {{10}^{-7}}$

Basic solution: $\left[ {{H}^{+}} \right]<1\times {{10}^{-7}}$


How to Find pH Value?

  • The equilibrium equation gives the following equation for pH

$pH=-{{\log }_{10}}\left[ {{H}^{+}} \right] \left[ {{H}^{+}} \right]={{10}^{-pH}} $

  • In other words, pH is the negative logarithm of the molar ion concentration of hydrogen or the power of the negative pH of the ion concentration 10 equal to the mole of hydrogen. 

  • Most scientific calculators have a "log" button, so this calculation is easy to do with a scientific calculator. 

  • This is not the same as the ln button that references the natural logarithm.

  • If you remember, you can easily calculate pOH using pH.

pH + pOH = 14

  • This is especially useful when you need to find the pH of a base, as it is usually denoted by pOH, not pH.

Examples of pH

The normal pH range is 0 - 14, where 0 is concentrated hydrochloric acid (1M HCl), 7 is pure water (neutral pH), and 14 is concentrated caustic soda (1M NaOH). It is possible to reach -1 pH with 10M HCl, but that is the limit of practical acidity. In the other extreme example, a 10M NaOH solution would have a pH of 15.


Summary

pH is a measure of the acidity or basicity of a chemical solution. The pH scale runs from 0 to 14. A value of 7 is considered neutral, a value less than 7 is considered acidic, and a value greater than 7 is considered basic. In order to find the pH of any solution, we can find the negative logarithm of the concentration of hydrogen atoms in the solution.

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FAQs on How to Calculate pH of Solutions for JEE

1. What is pH metre temperature compensation? 

The electromotive force generated by the pH sensor varies with the temperature of the test solution. This is because the potential generated in the glass film of the pH sensor is proportional to the absolute temperature T expressed by the Nernst equation. Temperature compensation is performed to compensate for these temperature-related changes in the EMF using a pH analyser (or pH transmitter) regardless of temperature. 


Note that this temperature compensation is independent of temperature-related changes in the pH of the test solution. Some pH metres use an RTD integrated with a pH sensor to measure temperature and automatically compensate for the generated emf of the pH sensor.

2. What is acidic and alkaline error?

The acid error that occurs in the pH range of 3 or less depends on the composition of the glass film and the type of acid. If the glass electrode has an acid defect, it cannot be repaired immediately by immersing it in a neutral solution. Recovery will take a considerable amount of time. However, the acidity error is smaller than the alkalinity error, so it is not practically important. In the alkaline range from pH10, the EMF of the glass electrode deviates from the linear value on the alkaline side. This is called an "alkaline error". 


Since the magnitude of the alkali error depends on the composition of the glass film, it is necessary to use a highly alkaline glass electrode when using the pH sensor in the alkaline range. However, this does not guarantee that the alkali error will be resolved.