Carbonate and hydrogen carbonate (bicarbonate) ions contribute to buffering in a variety of natural systems. You are investigating their role in groundwater percolating through limestone hills into a recently discovered cave system, and need to understand how the pH of the water is controlled. Calculate the ratio of the molar concentrations of CO₃^2– and HCO₃^– ions required to achieve buffering at pH = 9.50. The pK_a2 of H₂CO₃ is 10.25.

ANTICIPATE Because the desired pH is lower than the pK_a2 of H₂CO₃, you need the logarithm in the Henderson– Hasselbalch equation to be negative. That will be the case when the ratio [base]_initial/[acid]_initial is less than 1.

PLAN Rearrange the Henderson–Hasselbalch equation to solve for the ratio of the weak acid to its conjugate base.

What should you assume? As usual, assume that activities can be approximated by molar concentrations. You should also assume that the equilibrium concentrations of acid and its conjugate base can be approximated by their initial values.