# Kw Chemistry

## Introduction to the water ionization constant Kw

Pure water undergoes auto-ionization or self-ionization by donating or accepting a proton between two molecules of water to form H3O+ and OH ions. This is also known as autoprotolysis or amphoteric nature of water.

The hydronium ion is a very strong acid and hydroxide ion is a very strong base. Thus they can associate again to form water molecule. So water molecules and the ions always stay in equilibrium. And the equilibrium lies to the left. Thus a very small amount of hydronium ions and hydroxide ions are found in water.

The equilibrium constant for this autoionisation of water is known as Kw. Thus

Kw = [H3O+] [OH]

Or simply Kw = [H+] [OH]  ………………….(i)

Here we omit the concentration of water molecule which should stay as a denominator. The reason is, not much change in concentration is observed during this process.

## Value of Kw

The value of Kis constant at particular temperature. At room temperature, the value of equilibrium constant Kis 1.00 X 10-14 mol2 dm-6.

## Kw increases with increase of temperature

Autoionisation of water is an endothermic process. According to Le chatelier’s principle, if conditions are changed in a equilibrium process, the equilibrium will shift to such a direction where it can minimize the effect of the change of the condition. Thus if water is heated the equilibrium will shift to right to form more ions by absorbing extra heat as this is an endothermic process. According to the equation (i) of Kw, if the concentration of ions increases the Kw increases. So we can say that Kincreases with the increase of temperature.

## Calculation of [H]+ and [OH]–

To calculate the concentration of hydronium ion or hydroxide ion, we can rewrite the equation (i) as follows:

$$\left[ { H }^{ + } \right] =\frac { { K }_{ w } }{ \left[ { OH }^{ – } \right] }$$ $$\left[ { OH }^{ – } \right] =\frac { { K }_{ w } }{ \left[ { H }^{ + } \right] }$$

## pH of pure water

For pure water the concentration of [H+] and [OH] ions are same. That means,

[H+] = [OH]

So, from equation (i) we can write,

Kw = [H+]2

As     Kw = 1.00 X 10-14 mol2 dm-6

[H+]2 = 1.00 X 10-14 mol2 dm-6

Thus      [H+] = 1.00 X 10-7 mol dm-3

And   pH = – log10 [H+] = – log10 (1.00 X 10-7)

So     pH = 7

So, we can say that the pH of the pure water is 7. And the concentration of [H+] =[OH] = 10-7 mol dm-3.

## Acidic, basic and neutral solution

In pure water the concentration of hydronium ion and hydroxide ion are same and equal to 10-7 M at 25C. This types of solution is known as neutral solution. But depending on the difference between their concentration, the solution is named as acidic or basic. Such as

• If [H+] = [OH], it is a neutral solution.
• If [H+] > [OH], it is an acidic solution.
• If [H+] < [OH], it is a basic solution.

## Value of pKw

The relationship between Kand pKis

pK= – log10 K

If  Kw = 1.00 X 10-14 mol2 dm-6

pK= – log10 (1.00 X 10-14)

So pK= 14 …………………….(ii)

Remember that pKdoesn’t have any unit.

## Relation between pH and pOH from Kw

We can derive a relation between pH and pOH from the equation (i);

Kw = [H+] [OH]

Taking logarithm on both side, we get

log K= log [H+] + log [OH]

Or -log K= -log [H+] – log [OH]

So pK= pH + pOH

As pKw = 14   [from equation (ii)]

Thus pH + pOH = 14.

Using this relation we can solve many problems of pH and pOH.