Chemical and Ionic Equilibrium 2 Question 65

65. The pH of blood stream is maintained by a proper balance of $\mathrm{H}{2} \mathrm{CO}{3}and\mathrm{NaHCO}{3}concentrations.Whatvolumeof5 \mathrm{M}\mathrm{NaHCO}{3}solutionshouldbemixedwitha10 \mathrm{~mL}sampleofbloodwhichis2 \mathrm{M}in\mathrm{H}{2} \mathrm{CO}{3},inordertomaintaina\mathrm{pH}of7.4?\left(K_{a}\right.for\mathrm{H}{2} \mathrm{CO}{3}inbloodis7.8 \times 10^{-7}$ )

(1993, 2M)

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Solution:

  1. Mixing $\mathrm{H}{2} \mathrm{CO}{3}with\mathrm{NaHCO}_{3}$ results in buffer solution.

$\mathrm{pH}=\mathrm{p} K_{a}+\log \frac{\left[\mathrm{NaHCO}{3}\right]}{\left[\mathrm{H}{2} \mathrm{CO}{3}\right]}=\mathrm{p} K{a}+\log \frac{n\left(\mathrm{NaHCO}{3}\right)}{n\left(\mathrm{H}{2} \mathrm{CO}_{3}\right)}$

7.4=log(7.8×107)+logx20

x=400mmol

NaHCO3=5×VV=80 mL