Ionic Product of Water for IIT JEE

Ionic Product of Water - Examples with Solutions

Water is the very essential molecule for normal functioning of the body in all living organisms. Water in a pure form is made up of two molecules of hydrogen and one molecule of oxygen, which in the molecular formula is denoted as H2O. Pure water possess a very weak electrolyte property which can easily undergo to the Self ionization process and spit into two molecular ions parts 

  • 1. Hydrogen ion (H+)

  • 2. Hydroxide ion (OH-)


  • The process where water undergoes to self-ionization is also known as Auto protolysis. The equation of the auto protolysis (self-ionization) is shown as:

    H2O OH- + H+


    The hydrogen ion formed from the ionization of pure water is highly reactive in nature which further reacts with the other molecules of pure water and forms hydronium ion (H3O+)

    H2O + H+ H3O+


    The Law of mass action for the self-ionization reaction of pure water at chemical equilibrium, the value of dissociation constant K is relationship between the concentration of reactants and product, for this ionization of pure water reaction; equation of dissociation constant K written as:

    K = [H+] [OH-]/[H2O]
    Or  
    [H+][OH-] = K[H2O]


    Here the dissociation of the pure water occurs in a very small extent; hence the concentration of un-dissociated water molecules, [H20], is considered as constant. Thus, the product [H20] gives another constant which is denoted as Kw and equation of Kw shown as:

    [H+][OH-] = Kw


    Here, the constant (Kw), is termed as ionic product of water.

    During the self-ionization process, the pure water can dissociates the water molecule to form one hydroxyl OH- ion (which is alkaline in nature) and one hydroxide H+ ion (which is acidic in nature), hence the auto protolysis of pure water can act both as an acid as well as a base. 

    Water can be converted to the acidic state by such components/ substances which increase the concentration of Hydrogen (H+) ion or decrease the concentration of Hydroxide ion (OH-)ion. In the same way water can also be converted to the basis by such components/ substances which increase the concentration of Hydroxide ion (OH-) or decrease the concentration of Hydrogen (H+) ion.

    In pure water, the concentration of the hydrogen H+ ion (hydroxonium H3O+ ion) is always equivalent with the concentration of the hydroxide OH- ion. In simple terminology, it is also stated as generation of every single hydrogen H+ ion (hydroxonium H3O+ ion) equivalent ratio of hydroxide OH- ion is also generated as well. This statement also states reversely as the number of generated hydroxide OH-ion is equal with the number of generated hydrogen H+ion (hydroxonium H3O+ ion).

    Effect of Temperature on KW


    Concentrations H+ and OH- ions in pure water of product at a specific temperature is normally known as ionic product of water. The value of Kw (ionic product of water) rises with the rise of temperature, i.e., the concentration of H+ and OH- ions rises with temperature rises. Some constant values of KW at different temperature are shown in below table:

    Temperature (°C)Value of Kw
    00.11 x 10-14
    100.31 x 10-14
    251.00 x 10-14
    1007.50 x 10-14

    At 25°C temperature the value of KW of pure water is 1 x 10-14. Although the pure water is neutral in nature, hence the concentration of the H+ ion and OH- ion must be equal.

    So, [H+] = [OH˜] = X
    Put the value of [H+] and [OH˜]into the KW equation
    [H+][OH-]=KW= 1 x 10-14(at25°C temperature)
    [H+][OH-]=X2= 1 x 10-14

    Hence, X = 1 x 10-7 M
    So from the equation value of
    [OH-] = [H+] = X = 1 x 10-7 M
    which is also written as[H+] = [OH-] = 1 × 10-7 mol litre-1


    This interprets that at 25°C temperature; in 1 litre solution of pure water only 10-7 moles of water is present in the ionic form out of total moles of pure water (i.e. approximately 55.5 moles).

    When an addition of a acid or the base happens in the pure water, then the concentration of the ionic product concentration of the pure water can be calculated by using ionic product constant equation ([H+][OH-] = Kw), where the value of KW is constant at specific temperature but the concentration of the H+ and OH- ions are not remain the same. 

    The addition of the acid leads to the rise in the concentration of the hydrogen H+ ion or hydroxonium H3O+ ion or in other term we can say that it leads to decrease the concentration of the hydroxyl OH- ion.
    i.e. [H+] or [H3O+] > [OH-]; (Acidic solution)


    Similarly addition of the base leads to the rise in the concentration of the hydroxyl OH- ion or in other terminology it decreases the concentration of the hydrogen H+ion or hydroxonium H3O+ ion

    i.e. [OH-] > [H+]; (Alkaline or basic solution)

    Concentration of ions in Neutral acidic and basic condition


    In Neutral solution, the concentration of the H+ ion and OH- ion are equivalent to each other hence the value of the hydrogen ion and hydroxyl ion are the same.  

    [H+] = [OH-] = 1 x 10-7 M
    But in Acidic solution, the concentration of H+ ion is higher than the concentration of the OH- ion, hence the value of the H+ ion is always greater than the value of OH- ion. This shows that the concentration of H+ ion is always higher than the 1 x 10-7 M and similarly the concentration of OH- ion is always lesser than the 1 x 10-7 M as shown below:

    [H+] > [OH-]
    Where, [H+] > 1 x 10-7 M
    Or, [OH-] < 1 x 10-7 M

    In Alkaline (basic) solution, the concentration of OH- ion is higher than the concentration of the H+ ion, hence the value of the OH- ion is always greater than the value of H+ ion. That shows that the concentration of OH- ion is always higher than the 1 x 10-7 M and similarly the concentration of H+ ion is always lesser than the 1 x 10-7 M as shown below:     

    [OH-] > [H+]
    Where, [OH-] > 1 × 10-7 M
    Or, [H+] < 1 x 10-7 M

    Hence, the value shows that the solution of pure water must be acidic in nature if the concentration of the hydrogen H+ ion is higher than 1 x 10-7 M and alkaline or basic in nature if the concentration of the H+ ion is lesser than 1 x 10-7 M.
    The table shows the type of nature exhibited by water due to the amount of H+ ion concentration it consumes:

    Concentration of [H+] ionNature of Water
    10-0,10-1,10-2,10-3,10-4,10-5,10-6Acidic
    10-7Neutral
    10-14,10-13,10-12,10-11,10-10,10-9,10-8Alkaline

    Similarly, the value shows that the solution of pure water must be basic in nature if the concentration of the hydroxyl OH- ion is higher than 1 x 10-7 M and alkaline or basic in nature if the concentration of the OH- ion is lesser than 1 x 10-7 M.

    The table shows the type of nature exhibited by water due to the amount of OH- ion concentration it consumes:

    Concentration of [OH-] ionNature of Water
    10-14,10-13,10-12,10-11,10-10,10-9,10-8Acidic
    10-7Neutral
    10-0,10-1,10-2,10-3,10-4,10-5,10-6Alkaline

    It is concluded that each aqueous solution whether it is acidic, basic or neutral possesses both hydrogen H+ ion and hydroxyl OH- ion that is present in the same or different proportions. But the ionic product concentration KW of the water always remains constant 1 × 10-14 at a temperature of 25°C. Hence, when the concentration of one ion increases, accordingly the concentration of the other ion is decreased but the overall concentration of product remains constant.

    Example-1
    If the concentration of the [H+] ion is 10-2 M then what is the concentration of[OH-] ion and what is the nature of aqueous solution?

    Answer: Overall concentration of aqueous product (KW) = 10-14 M.
    Concentration of [H+] ion = 10-2 M
    Now, by applying the equation of ionic product of aqueous solution, KW = [H+][OH-]
    If the value of [H+] = 10-2 M and value of KW = 10-14 M, by putting the value into the equation
    KW= 10-14M= 10-2 M x [OH-]
    Hence, the obtained value of [OH-] ion from the equation is = 10-12 M;
    Here this aqueous product consumes 10-2 M concentration of hydrogen [H+] ion and 10-12 M hydroxyl [OH-] ion; that conclude the aqueous solution is acidic in nature.

    Example-2
    If the concentration of the [H+] ion is 10-10 M, then what is the concentration of [OH-] ion and what is the nature of aqueous solution?

    Answer: The concentration of [H+] ion = 10-10 M and concentration aqueous product = 10-14 M.
    By applying KW = [H+][OH-]; the obtained concentration of [OH-] ion = 10-4 M.
    Here this aqueous product consumes 10-10 M concentration of hydrogen [H+] ion and 10-4 M hydroxyl [OH-] ion, that concludes the aqueous solution is basic in nature.