The ionization constant of water is .

(a)

Find  .

Express in terms of  and .

Apply logarithm on each side.

Apply product property of logarithm : .

.

The equation of is .

(b)

Find equation with constant value of  .

The value of constant is .

.

Apply logarithm on each side.

Apply power property of logarithm : .

.

The property of logarithm is : .

.

Substitute in .

.

(c)

Find the concentration of hydroxide ions in water.

The concentration of hydrogen ions is moles per liter.

Substitute in .

Apply power property of logarithm : .

The property of logarithm is : .

The concentration of hydroxide ions in water  moles per litre.

a.  The equation of is .

b.  The equation with constant value of  is .

c.  The concentration of hydroxide ions in water moles per litre.