pH calculations

Key Questions

  • Before answering this question, here is a short text about pH!

    pH or potential of hydrogen is a scale of acidity from 0 to 14. It tells how acidic or alkaline a substance is. More acidic solutions have lower pH (less than 7). More alkaline solutions have higher pH (greater than 7). Substances which are not acidic or alkaline (neutral) usually have a pH of 7 (this is the answer to your question).

    pH is a measure of the concentration of protons (H+) in a solution. Sørensen introduced this concept in 1909. The "p" stands for the German potenz, meaning power or concentration, and the "H" for the hydrogen ion (H+).

  • The "p"H of a solution is directly related to the "p"K_"a" of a solution via the Henderson-Hasselbach equation,

    "p"H = "p"K_"a" + log(([A^-])/([HA]))

    Let's do an example:

    What is the "p"H of a "1-L" solution of 0.12"M" of NH_4Cl to which "1 L" of 0.03"M" of NaOH was added ("p"K_"a" of NH_4^(+) is 9.25^([1]))?

    Consider the equilibrium,

    NH_4^(+) + OH^(-) rightleftharpoons H_2O + NH_3

    It is safe to assume that the hydroxide ion will consume one equivalent ammonium's protons, leaving 0.09"mol" NH_4^+ ions and 0.03"mol" NH_3.

    Since the total volume cancels out in the ratio of concentrations, we can translate these concentrations into mols and proceed.

    To be sure, the hydroxide is treated as a strong base, and the ammonium as a weak acid.

    Hence,

    "p"H = "p"K_"a" + log(([NH_3]_"eq")/([NH_4^+]_"eq"))

    = 9.25 + log("0.03 mols"/("0.12 mols" - "0.03 mols")) approx 8.77

    [1]: Nelson, D. L., Cox, M. M., & Lehninger, A. L. (2017). Lehninger Principles of Biochemistry. New York, NY: W.H. Freeman and Company.

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