5.5.2 pH & [H⁺]

• The acidity of an aqueous solution depends on the number of H⁺ (H₃O⁺) ions in solution
• The pH is defined as:

pH = -log[H⁺]

• • where [H⁺] is the concentration of hydrogen ions in mol dm^–3

• Similarly, the concentration of H⁺ of a solution can be calculated if the pH is known by rearranging the above equation to:

[H⁺] = 10^-pH

• The pH scale is a logarithmic scale with base 10
• This means that each value is 10 times the value below it. For example, pH 5 is 10 times more acidic than pH 6.
• pH values are usually given to 2 decimal places
• The relationship between concentration is easily seen on the following table

pH & [H+] Table

Answer

Answer 1:

The pH of the solution is:

pH  = -log[H⁺]

      = -log 1.6 x 10^-4

      = 3.80

Answer 2:

The hydrogen concentration can be calculated by rearranging the equation for pH

pH   = -log[H⁺]

[H⁺] = 10^-pH

       = 10^-3.10

       = 7.94 x 10^-4 mol dm^-3

Answer

The correct option is C.

• • The total volume after dilution is 1000.0 cm³ so the concentration of H⁺ has been reduced by a factor of 100 or 10^-2, which means an increase of 2 pH units
  • The final solution is therefore pH 3

Strong acids

• Strong acids are completely ionised in solution

HA (aq) → H⁺ (aq) + A^- (aq)

• Therefore, the concentration of hydrogen ions, H⁺, is equal to the concentration of acid, HA
• The number of hydrogen ions formed from the ionisation of water is very small relative to the [H⁺] due to ionisation of the strong acid and can therefore be neglected
• The total [H⁺] is therefore the same as the [HA]

 Answer

[HCl] = [H⁺] = 0.01 mol dm^-3

     pH = - log[H⁺]

     pH = - log[0.01] = 2.00

The pH of dibasic acids

• Dibasic or diprotic acids have two replaceable protons and will react in a 1:2 ratio with bases
• Sulfuric acid is an example

H₂SO₄ (aq)  + 2NaOH (aq) → Na₂SO₄ (aq) + 2H₂O (l)

• You might think that being a strong acid it is fully ionised so the concentration of the hydrogen is double the concentration of the acid
• This would mean that 0.1 mol dm^-3 would be 0.2 mol dm^-3 in [H⁺] and have a pH of 0.69
• However, measurements of the pH of  0.1 mol dm^-3 sulfuric acid show that it is actually about pH 0.98, which indicates it is not fully ionised
• The ionisation of sulfuric acid occurs in two steps

H₂SO₄ → HSO₄^- + H⁺

HSO₄^- ⇌ SO₄^2- + H⁺

• Although the first step is thought to be fully ionised, the second step is suppressed by the abundance of hydrogen ions from the first step creating an equilibrium
• The result is that the hydrogen ion concentration is less than double the acid concentration