One of the basic chemical combinations P means power in chemistry and H means hydrogen ions thus, pH means power of hydrogen ions. The acidity and alkalinity of a substance are measured using a scale of numbers which ranges from 0 to 14 called the **pH** **scale. **It measures the concentration of hydrogen ions in a solution. Remember, the Arrhenius definition of an acid that says that an acid is a compound which when dissolved in water produces hydrogen ion as the only positive ion while according to Bronsted-lowry, an acid is a proton donor and a base is a proton acceptor. Recall that a proton is a hydrogen ion.

**HCl → H**^{+}** + Cl**^{–}

**H****2****SO****4**** → 2H**^{+}** + S** ^{−}

**HYDROGEN ION CONCENTRATION**

To understand this, we have to critically look at the dissociation of water. Pure water is a neutral solution. It ionizes very slightly to give equal concentrations of hydrogen ions and hydroxide ions. This is confirmed by conductivity measurements which shows that at 25^{o}C, the concentration of hydrogen ions [H^{+}] and the concentration of the hydroxide ions [OH^{–}] are both equal to 10^{-7} moldm^{-3} respectively.

H2O(l) H^{+}(aq) + OH^{—}(aq)

1mol 1mol 1mol

From the above equation, it shows that 1mol of water dissociates into 1mol of hydrogen ions and 1 mol of hydroxide ions.

[H^{+}] = [OH^{–}] =10^{-7}moldm^{-3}

**THE IONIC PRODUCT OF WATER K****W**

The ionic product of water is the product of the concentration of H^{+} and OH^{–}

KW = [H^{+}] [OH^{–}]

=10^{-7}moldm^{-3} x 10^{-7}moldm^{-3}

=10^{-14}mol^{2}dm^{-6}.

The ionic product of water, KW is kept constant under all circumstances at 25^{o}C. This means that in all neutral solutions, the concentration of both hydrogen ions and hydroxide ions would be 10^{-7}moldm^{-3} respectively. If an acid is added to an aqueous solution, the hydrogen ion concentration increases to above 10^{-7} moldm^{-3}. In order to maintain the ionic product of water, KW at 10^{-14} mol^{2}dm^{-6}, the hydroxide ions would decrease proportionally. For instance, if concentration of the [H^{+}] increases from 10^{-7} moldm^{-3} to 10^{-4}moldm^{-3}, the concentration of [OH^{–}] will decrease from 10^{-7}moldm^{-3} to 10^{-10}moldm^{-3}. The solution becomes more acidic since the concentration of H^{+} ions is more than the concentration of OH^{–} ions. A solution becomes more alkaline if the concentration of hydroxide ions is more than the concentration of hydrogen ions.

**pH SCALE**

pH scale ranges from 0 to 14 . As the value of pH decreases, the acidity of the solution increases and as the value of pH increases, the acidity decreases while the alkalinity increases. The pH of a neutral solution is 7.

This means that a value of less than 7 on the scale is acidic while a value greater than 7 on the scale is alkaline. **Note that the pH measures strengths of acids and alkalis and NOT their concentrations**. The lower the pH value on the scale, the stronger the acid hence, an acid with a pH value of 1 is stronger than an acid with a pH value of 4. Always remember that as acidity decreases, alkalinity increases and vice versa. When acidity increases, it means that H^{+} increases in the solution and when alkalinity increases, it means that OH^{–} increases in the solution.

**pH OF A SOLUTION**

There are three definitions:

- pH of a solution is a measure of the hydrogen ions concentration in the solution

- pH of a solution is a measure of the acidity or alkalinity of the solution

- According to Sorensen, pH of a solution is defined as the negative logarithm to base 10 of the hydrogen ion concentration. Mathematically,

pH = – log10 [H^{+}]

**Note that:**

- The negative sign is introduced to make the pH values positive in most cases.

- The logarithms used is to base 10 (not to the base of e),so make sure that when doing calculations, you press the log or lg button on your calculators
**NOT**the ln button.

- We can use this equation to convert [H
^{+}] to pH or pH to [H^{+}].

Calculations involving the pH or POH are done using various formulae. The particular one to be used depends on the question. The formulae are as illustrated below:

- pH = -log10 [H
^{+}]

_{[H}^{+}_{][OH}^{–}_{] = 10}^{-14}

- pOH = 14 – pH

- To calculate the [H
^{+}] from pH, the antilog of the pH will be used.

**CALCULATING pH FROM [H**^{+}**]**

1. Calculate the pH of a solution whose H^{+} ion concentration is 5.32 x 10^{-4} moldm^{-3}.

pH = -log10[H^{+}]

- – log10[5.32×10
^{-4}]- 3.3

- Calculate the pH of 0.005moldm
^{-3}H2SO4 The first thing to do is to dissociate the acid H2SO4 → 2H^{+}+ S_{4}^{2−}

1mol 2mols 1mol

0.005 2×0.005

=0.0100moldm^{-3}

pH ^{=} -log10[0.0100]

- – log10[1 x 10
^{-2}]

- 2log1010

pH = 2.

**CALCULATING [H**^{+}**] FROM pH**

To calculate H^{+} concentration from pH, antilog of the pH is determined.

1. Calculate the hydrogen ion concentration of a solution whose pH is 10.5.

pH = -log10 [H^{+}]

[H+] = 10^{-pH}

_{10}-10.5

- 3.16 x 10
^{-11}moldm^{-3}

- A glass of orange juice is found to have a pOH of 11.40. Calculate the concentration of the hydrogen ions in the juice

pH + pOH = 14

pH = 14 – pOH

=14 – 11.40

=2.60

pH = – log10[H^{+}]

2.60 = – log10[H^{+}]

-2.60 = log [H^{+}]

Antilog of – 2.60 = 2.51 x 10^{-3}moldm^{-3}

3. A solution has a pH of 4. What is the [H3O^{+}] concentration?

**Note that H**^{+}** and [H****3****O**^{+}**] can be used interchangeably.**

pH = -log10[H3O^{+}]

- = -log10[H3O
^{+}] -4 = log10[H3O^{+}]

Antilog of -4 = 1.00 x 10^{-4}moldm^{-3}

- What is the hydrogen ion concentration of 0.100moldm
^{-3}NaOH solution?**We first of all, dissociate NaOH**.

NaOH → Na^{+} + OH^{–}

6

1mol 1mol 1mol

0.100mol 0.100mol

[H^{+}][OH^{–}] = 10^{-14}

H^{+} = 1 x 10^{-14}

[OH^{–}]

- 1 x 10
^{-14}

1 x 10^{-1}

[H^{+}] = 1x 10^{-13}moldm^{-3}