• Henderson-Hasselbalch equation

pH and pK

For any acid/base,

HA <----> H⁺ + A^-

K = [H⁺][A^-]/[HA]

Thus,

pK = pH - log{[A^-]/[HA]}

--> pH = pK + log{[A^-]/[HA]}
* i.e. Henderson-Hasselbalch equation

NB:

• pH and pK are negative log of [H+] and K
• Most buffering occurs within pH of (pK +/- 1)

Henderson-Hasselbalch equation

--> pH = pK + log{[A^-]/[HA]}

(See above)

Carbon dioxide and pH

CO2 + H2O
<---> H₂CO₃
<---> H⁺ + HCO₃^-

Henderson-Hasselbalch equation for H2CO3

pH = pK + log {[HCO₃^-]/[H₂CO₃]}

When [H2CO3] is changed to [CO2]
--> pK becomes pK' to denote two related but different values

Also,

pKa varies with temperature
--> pKa = 6.1 at 37C

Thus,

pH = 6.1 + log {[HCO₃^-]/[CO2]}

Also,

CO2 solubility = 0.0301 mmol/L/mmHg of pCO2

Thus,

pH = 6.1 + log {[HCO₃^-]/(0.0301 x pCO2)}

NB:

• First part of the reaction
  (CO2 + H2O <---> H₂CO₃)
  --> Catalyzed by carbonic anhydrase
• The Henderson equation
  --> [H+] = 24 x ( pCO2 / [HCO3] )
• K applies only to infinitely dilute solution where interionic forces are negligible.
• In body fluids, K' is used to denote "apparently ionization constant"