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Buffer Calculations (HL) (HL IB Chemistry)

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Philippa

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16 December 2023

Buffer Calculations

The pH of a buffer solution can be calculated using:
- The K_a 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:
- $K_{a} = \frac{[salt] [H^{+}]}{[acid]} which can be rearranged to [H^{+}] = K_{a} \frac{[acid]}{[salt]}$

To simplify the calculations, logarithms are used such that the expression becomes:
- $- \log_{10} [H^{+}] = - \log_{10} K_{a} \times - \log \frac{[acid]}{[salt]}$

Since -log₁₀ [H⁺] = pH, the expression can also be rewritten as:
- $pH = p K_{a} + \log_{10} \frac{[salt]}{[acid]}$

This is known as the Hendersen-Hasselbalch equation

Basic buffers

[OH^–] = K_b $\frac{[base]}{[salt]}$ and pOH = pK_b + log₁₀ $\frac{[salt]}{[base]}$

The pH of a buffer can be determined from:

The pK_a or pK_b 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 K_aof 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 K_a
- _{$K_{a} = \frac{[{CH}_{3} {COO}^{-}] [H^{+}]}{[{CH}_{3} COOH]}$}

Step 2: Rearrange the equation to find [H⁺]
- $[H^{+}] = K_{a} \times \frac{[{CH}_{3} COOH]}{[{CH}_{3} {COO}^{-}]}$
Step 3: Substitute the values into the expression
- $[H^{+}] = 1.74 \times 10^{- 5} \times \frac{0.305}{0.520}$ = 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

K_a and K_b 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 K_a and K_b
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

Expertise: Chemistry

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.