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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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