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Buffer Calculations (HL) (HL IB Chemistry)

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Buffer Calculations

  • The pH of a buffer solution can be calculated using:
    • The Ka of the weak acid
    • The equilibrium concentration of the weak acid and its conjugate base (salt)

  • To determine the pH, the concentration of hydrogen ions is needed which can be found using the equilibrium expression:
    • K subscript straight a space equals space fraction numerator open square brackets salt close square brackets open square brackets straight H to the power of plus close square brackets over denominator open square brackets acid close square brackets end fraction space which space can space be space rearranged space to space open square brackets straight H to the power of plus close square brackets space equals space K subscript straight a space fraction numerator open square brackets acid close square brackets over denominator open square brackets salt close square brackets end fraction

  • To simplify the calculations, logarithms are used such that the expression becomes:
    • negative log subscript 10 open square brackets straight H to the power of plus close square brackets space equals space minus log subscript 10 space K subscript straight a space cross times space minus log fraction numerator open square brackets acid close square brackets over denominator open square brackets salt close square brackets end fraction
  • Since -log10 [H+] = pH, the expression can also be rewritten as:
    • pH space equals space straight p K subscript straight a space plus space log subscript 10 fraction numerator open square brackets salt close square brackets over denominator open square brackets acid close square brackets end fraction
  • This is known as the Hendersen-Hasselbalch equation

Basic buffers

  • [OH–] = Kb begin mathsize 14px style fraction numerator open square brackets base close square brackets over denominator open square brackets salt close square brackets end fraction end style and pOH = pKb + log10 begin mathsize 14px style fraction numerator open square brackets salt close square brackets over denominator open square brackets base close square brackets end fraction end style

The pH of a buffer can be determined from:

  • The pKa or pKb values of its component acid or base
  • The ratio of initial concentrations of acid and salt used to prepare the buffer

Worked example

Calculate the pH of a buffer solution containing 0.305 mol dm-3 of ethanoic acid and 0.520 mol dm-3 sodium ethanoate.

The Ka of ethanoic acid  = 1.74 × 10-5 at 298 K

 

Answer:

  • Ethanoic acid is a weak acid that ionises as follows:

CH3COOH (aq) ⇌ H+ (aq) + CH3COO- (aq)

  • Step 1: Write down the equilibrium expression to find Ka
    • K subscript straight a space equals space fraction numerator open square brackets CH subscript 3 COO to the power of minus close square brackets open square brackets straight H to the power of plus close square brackets over denominator open square brackets CH subscript 3 COOH close square brackets end fraction
  • Step 2: Rearrange the equation to find [H+]
    • open square brackets straight H to the power of plus close square brackets space equals italic space K subscript straight a space cross times space fraction numerator open square brackets CH subscript 3 COOH close square brackets over denominator open square brackets CH subscript 3 COO to the power of minus close square brackets end fraction
  • Step 3: Substitute the values into the expression
    • open square brackets straight H to the power of plus close square brackets space equals space 1.74 space cross times 10 to the power of negative 5 end exponent cross times fraction numerator 0.305 over denominator 0.520 end fraction = 1.02 x 10-5 mol dm-3
  • Step 4: Calculate the pH
    • pH = - log [H+]   
    • pH = -log 1.02 x 10-5 = 4.99

Factors that can influence buffers

Dilution

  • Ka and Kb are equilibrium constants so are not changed by dilution
  • Dilution does not change the ratio of acid or base to the salt concentration as both components will be decreased by the same amount
  • The overall pH change of the buffer does not change

Temperature

  • A constant temperature must be maintained when using buffers as temperature will influence the pH of the solution
  • Temperature affects the values of Ka and Kb 
  • In medical procedures, temperature fluctuations should be avoided due to the effect on the buffers in the blood
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Philippa

Author: Philippa

Philippa has worked as a GCSE and A level chemistry teacher and tutor for over thirteen years. She studied chemistry and sport science at Loughborough University graduating in 2007 having also completed her PGCE in science. Throughout her time as a teacher she was incharge of a boarding house for five years and coached many teams in a variety of sports. When not producing resources with the chemistry team, Philippa enjoys being active outside with her young family and is a very keen gardener.