Buffers and Biological pH

Introduction

Human blood is held between pH 7.35 and 7.45. Outside roughly 6.8 to 7.8, enzymes and membranes cannot function and life is not sustained. Remarkably, the main buffer in blood, CO₂/HCO₃⁻, has an apparent pKa of 6.1 at body temperature, more than a unit below blood pH. By the rules for closed buffers it should be poor. It works so well because the body runs it as an open system, continuously adjusting both components.

Core explanation

The Henderson–Hasselbalch equation for blood. At 37 °C, with dissolved CO₂ proportional to its partial pressure:

pH = 6.1 + log([HCO₃⁻] / (0.0301 × pCO₂))

with [HCO₃⁻] in mmol dm⁻³ and pCO₂ in mmHg (0.0301 is the solubility factor). Normal values are [HCO₃⁻] = 24 mmol dm⁻³ and pCO₂ = 40 mmHg (5.3 kPa), giving dissolved CO₂ = 1.2 mmol dm⁻³. The ratio is 20 : 1 and pH = 6.1 + log 20 = 6.1 + 1.30 = 7.40.

Why a 20 : 1 ratio would normally be weak. In a closed container such a lopsided ratio means very little acid component. Added base would be poorly resisted, and even added acid would shift the small CO₂ reservoir significantly.

The open-system advantage. In the body, CO₂ is not trapped. When metabolic acid enters the blood, H⁺ + HCO₃⁻ → CO₂ + H₂O, but the extra CO₂ is breathed out by the lungs, so dissolved CO₂ stays near 1.2 mmol dm⁻³. Only the HCO₃⁻ term changes. Over hours to days, the kidneys also regenerate HCO₃⁻ and excrete acid. The two components are therefore controlled independently by two organs, and the effective buffering is far greater than a closed calculation predicts.

Respiratory adjustment. Breathing faster lowers pCO₂ and raises pH; breathing more slowly raises pCO₂ and lowers pH. The respiratory centre in the brainstem responds to pH changes within minutes, providing rapid compensation.

Phosphate inside cells. The phosphate pair H₂PO₄⁻/HPO₄²⁻ has an apparent pKa of about 6.8 under physiological ionic strength, close to intracellular pH (about 7.0–7.2). Its concentration in blood plasma is low, but inside cells and in urine it is an important buffer. In the kidney, filtered HPO₄²⁻ accepts protons and carries acid out of the body.

Proteins. The imidazole side chains of histidine (pKa near 6–7) in proteins, especially haemoglobin, provide substantial buffering in blood and cells. Haemoglobin also carries H⁺ released when CO₂ is converted to HCO₃⁻ in red blood cells.

Formulae

Blood pH = 6.1 + log([HCO₃⁻]/(0.0301 × pCO₂)), with pCO₂ in mmHg; equivalently dissolved CO₂ ≈ 0.23 mmol dm⁻³ per kPa of pCO₂.

Step-by-step reasoning

1. Convert pCO₂ into dissolved CO₂ concentration. 2. Form the ratio [HCO₃⁻]/[CO₂]. 3. Apply pH = 6.1 + log(ratio). 4. For an acid load, reduce HCO₃⁻ by the amount of acid. 5. In a closed model, add the same amount to CO₂; in an open model, hold CO₂ constant. 6. Compare the two pH values.

Visual explanation

Sketch blood as a tank with two taps: the lungs, adjusting CO₂ in minutes, and the kidneys, adjusting HCO₃⁻ over hours. Metabolic acid drips in, converting HCO₃⁻ into CO₂, which drains away through the lung tap instead of accumulating.

Real-world analogy

A closed buffer is like a sealed bucket catching drips; it fills and overflows. An open buffer is a bucket with a drain whose size can be adjusted, so the level stays nearly steady however much drips in.

Real-world example

During intense exercise, muscles release lactic acid into the blood. Breathing rate rises sharply, not only to supply oxygen but to expel the extra CO₂ generated as hydrogencarbonate neutralises the acid, limiting the fall in blood pH.

Why?

Why does holding CO₂ constant help so much? In the ratio [HCO₃⁻]/[CO₂], the small denominator would otherwise grow proportionally faster than the large numerator falls. Removing that growth leaves only a modest drop in the numerator.

Common misconception

"Blood uses the bicarbonate buffer because its pKa equals blood pH." It does not; the apparent pKa of 6.1 is well below 7.40. The system is effective because lungs and kidneys regulate its components, not because the ratio is near 1.

Worked example

Question: Blood with [HCO₃⁻] = 24 mmol dm⁻³ and dissolved CO₂ = 1.2 mmol dm⁻³ receives 10 mmol dm⁻³ of strong acid. Compare the pH for (a) a closed system and (b) an open system with CO₂ held constant.

Reasoning: The acid converts HCO₃⁻ into CO₂: HCO₃⁻ becomes 14 mmol dm⁻³. (a) Closed: CO₂ = 1.2 + 10 = 11.2 mmol dm⁻³; pH = 6.1 + log(14/11.2) = 6.1 + 0.10 = 6.20. (b) Open: CO₂ stays 1.2 mmol dm⁻³; pH = 6.1 + log(14/1.2) = 6.1 + 1.07 = 7.17.

Answer: Closed 6.20, open 7.17. Venting CO₂ keeps the pH far closer to normal, and faster breathing would raise it further.

Quick check

1. What is the normal ratio of [HCO₃⁻] to dissolved CO₂ in arterial blood, and what pH does it give? Answer: About 20 to 1, giving pH = 6.1 + log 20 = 7.40.

Exam focus

Explain the open-system idea explicitly: the lungs control CO₂ and the kidneys control HCO₃⁻. Examiners often ask why the buffer works despite its pKa; quoting the 20 : 1 ratio and the role of breathing earns the key marks.

Advanced insight

The conversion CO₂ + H₂O ⇌ H₂CO₃ is slow uncatalysed. Carbonic anhydrase in red blood cells accelerates it by a factor of about a million, allowing CO₂ to be loaded in tissues and released in the lungs within the second or so that blood spends in the capillaries.

Summary

Blood pH, about 7.40, is maintained mainly by the CO₂/HCO₃⁻ buffer, with an apparent pKa of 6.1 and a 20 : 1 ratio. It is effective because it is an open system: the lungs hold CO₂ nearly constant and the kidneys regulate HCO₃⁻. Phosphate, with pKa′ near 6.8, buffers inside cells and in urine, while protein histidine groups add further capacity.

Practice questions

1. Calculate blood pH when [HCO₃⁻] = 24 mmol dm⁻³ and pCO₂ = 60 mmHg. Answer: Dissolved CO₂ = 0.0301 × 60 = 1.81 mmol dm⁻³; pH = 6.1 + log(24/1.81) = 6.1 + 1.12 = 7.22. 2. Explain why rapid breathing raises blood pH. Answer: It lowers pCO₂, reducing dissolved CO₂, which increases the [HCO₃⁻]/[CO₂] ratio and hence the pH. 3. Why is phosphate a more important buffer inside cells than in plasma? Answer: Its concentration is much higher inside cells, and its apparent pKa of about 6.8 is close to intracellular pH. 4. State the roles of the lungs and the kidneys in maintaining blood pH. Answer: The lungs rapidly adjust CO₂ by changing breathing rate; the kidneys slowly regenerate HCO₃⁻ and excrete excess acid.