Kw Chemistry

Introduction to the water ionization constant K_w

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 K_w. Thus

K_w = [H₃O⁺] [OH^–]

Or simply K_w = [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 K_w

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

K_w 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 K_w, if the concentration of ions increases the K_w increases. So we can say that K_w increases 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,

K_w = [H⁺]²

As     K_w = 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 25⁰ C. 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 pK_w

The relationship between K_w and pK_w is

pK_w = – log₁₀ K_w 

If  K_w = 1.00 X 10^-14 mol² dm^-6

pK_w = – log₁₀ (1.00 X 10^-14)

So pK_w = 14 …………………….(ii)

Remember that pK_w doesn’t have any unit.

Relation between pH and pOH from K_w

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

K_w = [H⁺] [OH^–] 

Taking logarithm on both side, we get

log K_w = log [H⁺] + log [OH^–] 

Or -log K_w = -log [H⁺] – log [OH^–] 

So pK_w = pH + pOH

As pK_w = 14   [from equation (ii)]

Thus pH + pOH = 14.

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

 

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