22.1 pH, fta, pfta and ftw

The ionic product of  water, ftw

• Water is able to act as an acid as well as a base. Therefore whenever liquid water is present, the following equilibrium occurs
  2H2O ⇌ H3O⁺ + OH⁻
  Or the more simplified version(Note that H⁺ ≡  H3O⁺):
  H2O ⇌ H⁺ + OH⁻

• Therefore the ionic product of water is defined as:

 

• It means that the product of hydrogen and hydroxide concentrations at a certain temperature is constant, this is true no matter the water is pure or impure.

 

• At 25 °C, the value of ftw is 00 x 10⁻¹⁴ mol² dm⁻⁶.

 

• Since the above reaction is an endothermic reaction, the value of ftw increases with increasing temperature. At 100 °C, the value is 13 x 10⁻¹³ mol² dm⁻⁶.

 

pH of a substance

• pH of a substance is defined as:

• To calculate the pH of pure water at 25 °C:
  1. Since the water is pure, the hydrogen ion concentration must be equal to the hydroxide ion concentration. For every hydrogen ion formed, there is a hydroxide ion formed as well.
  2. So, the expression for Kw can be simplified to:
     [H⁺]² = 1.00 x 10⁻¹⁴      ; since [H⁺] = [OH⁻]
     ‹  [H⁺] = 1.00 x 10⁻⁷
  3. Therefore the pH of water is given by
     pH = -log(1.00 x 10⁻⁷)
     pH = 7.00
  4. This implies that at 24 °C, pH 7.00 is the neutral point of water, equal amounts of hydrogen and hydroxide ions are present

• • At 100 °C, the pH of pure water is 14. This does not mean the water is more acidic at higher temperature.
  • pH of 6.14 is the neutral point of water at 100 °C, there are still equal amounts of hydrogen and hydroxide ions present.

 

Strong and weak acids

• • A strong acid ionises completely in the presence of
    HA + H2O → H3O⁺ + A⁻
  • Therefore the pH of strong monoprotic acid can be calculated using:
    pH = -log[H3O⁺]
    Since the acid ionises completely, [H3O⁺] = [HA]
    pH = -log[HA]
  • A weak acid ionises partially in the presence of water.
    HA + H2O ⇌ H3O⁺ + A⁻
  • The pH of a weak acid is calculated using the acid dissociation constant, fta.

 

Acid dissociation constant, fta

• • For the dissociation of a weak acid, ftc can be written as:
  • However, the concentration of water is fairly constant. This is because at any one time, only about 1 % of the HA has reacted
  • Therefore a new equilibrium constant, fta is defined as:
  • fta can be used to measure the strength of weak acids.
  • A stronger acid has the position of equilibrium further to the right, therefore a higher Ka value.
  • A weaker acid has the position of equilibrium further to the right, therefore a lower Ka value.

• To make the comparison easier to see, the strength of acids is measured on the pfta Just like pH, pfta is defined as:

 

• The numbers now become:

• Conclusion:
  i) The stronger the acid, the higher the Ka and the lower the pKa.
  ii) The weaker the acid, the lower the Ka and the higher the pKa.

 

Calculations on pH

• 1. A strong acid ionises completely in the presence ofTo calculate the pH of a strong acid:
     HA + H2O → H3O⁺ + A⁻
  2. Therefore the pH of a strong monoprotic acid can be calculated using:
     pH = -log[H3O⁺]
     Since the acid ionises completely, [H3O⁺] = [HA]
     pH = -log[HA]         ; if [HA] is given
  3. For a diprotic acid, [H2A] = 2[H3O⁺]
  4. For a triprotic acid, [H₃A] = 3[H3O⁺]
  1. Then use the formula for fta to obtain the concentration of hydrogen ions, given the value of fta.
  2. Then use the pH formula to calculate the
     1. A weak acid ionises partially in the presence of waterTo calculate pH of a weak acid:
        HA + H2O ⇌ H3O⁺ + A⁻
     2. For example, if you have c mol dm⁻³ of  weak acid, HA. Do a calculation to find the concentration of  H3O⁺ and A⁻ at equilibrium.

      

  3. Important approximations when calculating pH of a weak acid:
     – So little acid has ionised that the concentration of HA at equilibrium is the same as the initial concentration. That is, c – x ≈ c.- If the acid is pure, then the concentration of hydrogen ions and the negative ions are the same. That is, [H3O⁺] = [A⁻] = x.
  4. Then use the formula for fta to obtain the concentration of hydrogen ions, given the value of fta.
  5. Then use the pH formula to calculate the pH
• To calculate the pH of a strong base:
  1. A strong base ionises completely in the presence of water
     B + H2O → BH⁺ + OH⁻
  2. Since the base ionises completely, [OH⁻] = [B] ; if  [B] is given
  3. Obtain the concentration of hydrogen ions from the expression of ftw. This is valid because the product of [H⁺] and [OH⁻] is constant at constant temperature
  4. Then use the pH formula to calculate its pH
  5. Alternatively, a quantity known as pOH can be calculated where
     pOH = -log[OH⁻]

  Then use the fact that pH + pOH = 14 to calculate its pH. [ Note: Calculation involving weak bases is not required. ]