Kw stands for the ionic product of water. This is derived by the equilibrium constant and an assumption that the concentration of water is constant. It can be used to calculate the pH of strong bases. Additionally, pKa can be used to calculate the pH of weak acids.
Kw stands for the ionic product of water. This is derived by the equilibrium constant and an assumption that the concentration of water is constant. This is because the equilibrium lies to the left, there's not a lot of water dissociating. The concentration of water is much more than the concentration of hydrogen ions and hydroxide ions.
Example
Derive the ionic product of water using the equilibrium for water.
H2O(l)⇌H+(aq)+OH−(aq)
Write the Kc equation.
Kc=[H+][OH−]=Kw
Pure water
Pure water is completely neutral. For pure water, the amount of hydrogen ions produced is equivalent to the amount of hydroxide ions produced. Therefore, their concentrations are equal. The ionic product of water for pure water can be written as:
Kw=[H+]2
Note: The value of Kw at 298K is 1.00×10−14mol2dm−6.
Kw and strong base
The ionic product of water can be used to calculate the pH value of a strong base. Strong bases such as, LiOH,NaOH and KOH dissociate fully in water. This can be used to find the concentration of hydroxide ions as the concentration of the base will be considered the same as the concentration of the hydroxide ions.
The known concentration of hydroxide ions and Kw can be used to calculate the concentration of hydrogen ions. Therefore, the pH can be calculated.
procedure
1.
Write the expression for Kw.
Kw=[H+][OH−]
2.
Rearrange for [H+].
[H+]=[OH−]Kw
3.
Calculate [H+].
4.
Write the equation for pH.
pH=−log10[H+]
5.
Calculate pH.
Example
Calculate the pH of 0.15moldm−3KOH at 298K. The value of Kw is 1.00×10−14mol2dm−6.
Insert calculated [H+] value into pH equation to calculate pH.
pH=−log10[6.666666667×10−14]=13.18
The pH is 13.18.
Note: Always round to two decimal places for pH.
pKw
The p stands for −log10. Kw can be used to calculate pKw.
Example
Calculate pKw under standard conditions.
Write the expression for pKw.
pKw=−log10Kw
The known value of Kw under standard conditions is used.
−log10Kw=−log101.00×10−14=14.00
The pKw is 14.00.
pKa and Ka
The acid dissociation constant, Ka, is important to find the pH of a weak acid. Sometimes the acid dissociation constant needs to be calculated from pKa. The procedure to calculate pH using pKa is written below.
procedure
1.
Write the equation for Ka from pKa.
Ka=10−pKa
2.
Insert known pKa to calculate Ka.
3.
Write the Ka equation for calculation.
Ka=[HA][H+]2
4.
Rearrange for [H+].
[H+]=Ka[HA]
5.
Insert known values to calculate [H+].
6.
Write the pH equation.
pH=−log10[H+]
7.
Insert calculated [H+] to calculate pH.
Example
Calculate the pH of 0.030moldm−3 ethanoic acid, CH3COOH. At this temperature, ethanoic acid has a pKa value is 3.20.
Write the equation linking Ka and pKa.
pKa=−log10(Ka)
Rearrange for Ka.
Ka=10−pKa
Insert known value to calculate Ka.
Ka=10−3.20=6.309573445×10−4moldm−3
Write the Ka equation for calculating ethanoic acid.